lambeq.backend

lambeq.backend.grammar

Grammar category

Lambeq’s internal representation of the grammar category. This work is based on DisCoPy (https://discopy.org/) which is released under the BSD 3-Clause “New” or “Revised” License.

class lambeq.backend.grammar.Box(name: str, dom: Ty, cod: Ty, z: int = 0)

Bases: Entity

A box in the grammar category.

Parameters:

namestr

The name of the box.

domTy

The domain of the box.

codTy

The codomain of the box.

zint, optional

The winding number of the box, by default 0.

__init__(name: str, dom: Ty, cod: Ty, z: int = 0) → None

apply_functor(functor: Functor) → Diagrammable

category: ClassVar[Category] = Category(name='grammar', Ty=<class 'lambeq.backend.grammar.Ty'>, Box=<class 'lambeq.backend.grammar.Box'>, Layer=<class 'lambeq.backend.grammar.Layer'>, Diagram=<class 'lambeq.backend.grammar.Diagram'>)

cod: Ty

dagger() → Daggered | Box

dom: Ty

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property l: Self

name: str

property r: Self

rotate(z: int) → Self

Rotate the box, changing the winding number.

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.grammar.Cap(left: Ty, right: Ty, is_reversed: bool = False)

Bases: Box

The unit of the adjunction for an atomic type.

Parameters:

leftTy

The type of the left output.

rightTy

The type of the right output.

is_reversedbool, default: False

Whether the cap is reversed or not. Normally, caps only allow outputs where right is the left adjoint of left. However, to facilitate operations like dagger, we pass in a flag that indicates that the inputs are the opposite way round, which initialises a reversed cap. Then, when a cap is adjointed, it turns into a reversed cap, which can be adjointed again to turn it back into a normal cap.

__init__(left: Ty, right: Ty, is_reversed: dataclasses.InitVar[bool] = False) → None

apply_functor(functor: Functor) → Diagrammable

category: ClassVar[Category] = Category(name='grammar', Ty=<class 'lambeq.backend.grammar.Ty'>, Box=<class 'lambeq.backend.grammar.Box'>, Layer=<class 'lambeq.backend.grammar.Layer'>, Diagram=<class 'lambeq.backend.grammar.Diagram'>)

cod: Ty

dagger() → Cup

dom: Ty

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

is_reversed: dataclasses.InitVar[bool] = False

property l: Self

left: Ty

name: str

property r: Self

right: Ty

rotate(z: int) → Self

Rotate the cap.

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

classmethod to_left(right: Ty, is_reversed: bool = False) → Self | Diagram

classmethod to_right(left: Ty, is_reversed: bool = False) → Self | Diagram

unwind() → Self

z: int = 0

class lambeq.backend.grammar.Category(name: str)

Bases: object

The base class for all categories.

Box: type[lambeq.backend.grammar.Box]

Diagram: type[lambeq.backend.grammar.Diagram]

Layer: type[lambeq.backend.grammar.Layer]

Ty: type[lambeq.backend.grammar.Ty]

__call__(name_or_entity: str) → Callable[[_EntityType], _EntityType]

__call__(name_or_entity: _EntityType) → _EntityType

Call self as a function.

__init__(name: str) → None

from_json(data: Dict[str, Any] | str) → Entity

Decode a JSON object or string into an entity from this category.

Returns:

Entity

The entity generated from the JSON data. This could be a Ty, a Box subclass, or a Diagram instance.

name: str

set(name: str, entity: _EntityType) → _EntityType

class lambeq.backend.grammar.Cup(left: Ty, right: Ty, is_reversed: bool = False)

Bases: Box

The counit of the adjunction for an atomic type.

Parameters:

leftTy

The type of the left output.

rightTy

The type of the right output.

is_reversedbool, default: False

Whether the cup is reversed or not. Normally, cups only allow inputs where right is the right adjoint of left. However, to facilitate operations like dagger, we pass in a flag that indicates that the inputs are the opposite way round, which initialises a reversed cup. Then, when a cup is adjointed, it turns into a reversed cup, which can be adjointed again to turn it back into a normal cup.

__init__(left: Ty, right: Ty, is_reversed: dataclasses.InitVar[bool] = False) → None

apply_functor(functor: Functor) → Diagrammable

category: ClassVar[Category] = Category(name='grammar', Ty=<class 'lambeq.backend.grammar.Ty'>, Box=<class 'lambeq.backend.grammar.Box'>, Layer=<class 'lambeq.backend.grammar.Layer'>, Diagram=<class 'lambeq.backend.grammar.Diagram'>)

cod: Ty

dagger() → Cap

dom: Ty

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

is_reversed: dataclasses.InitVar[bool] = False

property l: Self

left: Ty

name: str

property r: Self

right: Ty

rotate(z: int) → Self

Rotate the cup.

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

classmethod to_left(right: Ty, is_reversed: bool = False) → Self | Diagram

classmethod to_right(left: Ty, is_reversed: bool = False) → Self | Diagram

unwind() → Self

z: int = 0

class lambeq.backend.grammar.Daggered(box: Box)

Bases: Box

A daggered box.

Parameters:

boxBox

The box to be daggered.

__init__(box: Box) → None

apply_functor(functor: Functor) → Diagrammable

box: Box

category: ClassVar[Category] = Category(name='grammar', Ty=<class 'lambeq.backend.grammar.Ty'>, Box=<class 'lambeq.backend.grammar.Box'>, Layer=<class 'lambeq.backend.grammar.Layer'>, Diagram=<class 'lambeq.backend.grammar.Diagram'>)

cod: Ty

dagger() → Box

dom: Ty

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property l: Self

name: str

property r: Self

rotate(z: int) → Self

Rotate the daggered box.

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.grammar.Diagram(dom: Ty, cod: Ty, layers: list[lambeq.backend.grammar.Layer])

Bases: Entity

A diagram in the grammar category.

Parameters:

domTy

The type of the input wires.

codTy

The type of the output wires.

layerslist[Layer]

The layers of the diagram.

__init__(dom: Ty, cod: Ty, layers: list[lambeq.backend.grammar.Layer]) → None

apply_functor(functor: Functor) → Diagram

classmethod ba(left, right) → Self

classmethod bc(left, middle, right) → Self

property boxes: list[lambeq.backend.grammar.Box]

classmethod bx(left, middle, right) → Self

classmethod caps(left: Ty, right: Ty, is_reversed=False) → Diagrammable

category: ClassVar[Category] = Category(name='grammar', Ty=<class 'lambeq.backend.grammar.Ty'>, Box=<class 'lambeq.backend.grammar.Box'>, Layer=<class 'lambeq.backend.grammar.Layer'>, Diagram=<class 'lambeq.backend.grammar.Diagram'>)

cod: Ty

classmethod create_pregroup_diagram(words: list[lambeq.backend.grammar.Word], morphisms: list[tuple[type, int, int]]) → Self

Create a Diagram from cups and swaps.

>>> n, s = Ty('n'), Ty('s')
>>> words = [Word('she', n), Word('goes', n.r @ s @ n.l),
...          Word('home', n)]
>>> morphs = [(Cup, 0, 1), (Cup, 3, 4)]
>>> diagram = Diagram.create_pregroup_diagram(words, morphs)

Parameters:

wordslist of Word

A list of Word s corresponding to the words of the sentence.

morphisms: list of tuple[type, int, int]

A list of tuples of the form:

(morphism, start_wire_idx, end_wire_idx).

Morphisms can be Cup s or Swap s, while the two numbers define the indices of the wires on which the morphism is applied.

Returns:

Diagram

The generated pregroup diagram.

Raises:

ValueError

If the provided morphism list does not type-check properly.

classmethod cups(left: Ty, right: Ty, is_reversed=False) → Diagrammable

curry(n: int = 1, left: bool = True) → Self

dagger() → Self

dom: Ty

draw(draw_as_pregroup=True, **kwargs: Any) → None

Draw the diagram.

Parameters:

draw_as_pregroupbool, optional

Whether to try drawing the diagram as a pregroup diagram, default is True.

draw_as_nodesbool, optional

Whether to draw boxes as nodes, default is False.

colorstring, optional

Color of the box or node, default is white (‘#ffffff’) for boxes and red (‘#ff0000’) for nodes.

textpadpair of floats, optional

Padding between text and wires, default is (0.1, 0.1).

draw_type_labelsbool, optional

Whether to draw type labels, default is False.

draw_box_labelsbool, optional

Whether to draw box labels, default is True.

aspectstring, optional

Aspect ratio, one of [‘auto’, ‘equal’].

marginstuple, optional

Margins, default is (0.05, 0.05).

nodesizefloat, optional

BoxNode size for spiders and controlled gates.

fontsizeint, optional

Font size for the boxes, default is 12.

fontsize_typesint, optional

Font size for the types, default is 12.

figsizetuple, optional

Figure size.

pathstr, optional

Where to save the image, if None we call plt.show().

to_tikzbool, optional

Whether to output tikz code instead of matplotlib.

asymmetryfloat, optional

Make a box and its dagger mirror images, default is .25 * any(box.is_dagger for box in diagram.boxes).

classmethod fa(left, right) → Self

classmethod fc(left, middle, right) → Self

classmethod from_discopy(diagram: discopy.monoidal.Diagram) → Diagram

Import discopy diagram to lambeq diagram.

Parameters:

diagramdiscopy.monoidal.Diagram

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Diagram.

Returns:

Diagram

The diagram generated from the JSON data.

classmethod fx(left, middle, right) → Self

classmethod id(dom: Ty | None = None) → Self

property is_id: bool

property is_pregroup: bool

Check if a diagram is a pregroup diagram.

Adapted from discopy.grammar.pregroup.draw.

Returns:

bool

Whether the diagram is a pregroup diagram.

property l: Self

layers: list[lambeq.backend.grammar.Layer]

classmethod lift(diagrams: Iterable[Diagrammable | Ty]) → list[Self]

Lift diagrams to the current category.

Given a list of boxes or diagrams, call to_diagram on each, then check all of the diagrams are in the same category as the calling class.

Parameters:

diagramsiterable

The diagrams to lift and check.

Returns:

list of Diagram

The diagrams after calling to_diagram on each.

Raises:

ValueError

If any of the diagrams are not in the same category of the calling class.

normal_form(left: bool = False) → Diagram

Returns the normal form of a connected diagram, see arXiv:1804.07832.

Parameters:

leftbool, optional

Whether to apply left interchangers.

Raises:

NotImplementedError

Whenever normalizer yields the same rewrite steps twice.

property offsets: list[int]

The offset of a box is the length of the type on its left.

classmethod permutation(dom: Ty, permutation: Iterable[int]) → Self

Create a layer of Swaps that permutes the wires.

permuted(permutation: Iterable[int]) → Self

pregroup_normal_form()

Applies normal form to a pregroup diagram of the form word @ ... @ word >> wires by normalising words and wires seperately before combining them, so it can be drawn with draw().

property r: Self

classmethod register_special_box(name: str, diagram_factory: None = None) → Callable[[_DiagrammableFactoryT], _DiagrammableFactoryT]

classmethod register_special_box(name: str, diagram_factory: _DiagrammableFactory) → None

render_as_str(**kwargs: Any) → str

Render the diagram as text.

Presently only implemented for pregroup diagrams.

Parameters:

word_spacingint, default: 2

The number of spaces between the words of the diagrams.

use_at_separatorbool, default: False

Whether to represent types using @ as the monoidal product. Otherwise, use the unicode dot character.

compress_layersbool, default: True

Whether to draw boxes in the same layer when they can occur simultaneously, otherwise, draw one box per layer.

use_ascii: bool, default: False

Whether to draw using ASCII characters only, for compatibility reasons.

Returns:

str

Drawing of diagram in string format.

rotate(z: int) → Self

Rotate the diagram.

special_boxes: ClassVar[dict[str, collections.abc.Callable[..., lambeq.backend.grammar.Diagrammable]]] = {'cap': <class 'lambeq.backend.grammar.Cap'>, 'cup': <class 'lambeq.backend.grammar.Cup'>, 'spider': <class 'lambeq.backend.grammar.Spider'>, 'swap': <class 'lambeq.backend.grammar.Swap'>}

classmethod swap(left: Ty, right: Ty) → Diagrammable

tensor(*diagrams: Diagrammable | Ty) → Self

then(*diagrams: Diagrammable) → Self

then_at(diagram: Diagrammable, index: int) → Self

to_diagram() → Self

to_discopy() → discopy.monoidal.Diagram

Export lambeq diagram to discopy diagram.

Returns:

discopy.monoidal.Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this diagram to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

transpose(left: bool = False) → Self

Construct the diagrammatic transpose.

The transpose of any diagram in a category with cups and caps can be constructed as follows:

                        (default)
Left transpose       Right transpose
    │╭╮                  ╭╮│
    │█│                  │█│
    ╰╯│                  │╰╯

The input and output types of the transposed diagram are the adjoints of the respective types of the original diagram. This means that for diagrams with composite types, the order of the objects are reversed.

Parameters:

leftbool, default: False

Whether to transpose to the diagram to the left.

Returns:

Diagram

The transposed diagram, constructed as shown above.

class lambeq.backend.grammar.Diagrammable(*args, **kwargs)

Bases: Protocol

An abstract base class describing the behavior of a diagram.

This is used by static type checkers that recognize structural sub-typing (duck-typing) and does not need to be explicitly subclassed.

__init__(*args, **kwargs)

apply_functor(functor: Functor) → Diagrammable

Apply a functor to the current object.

property cod: Ty

The co-domain of the diagram.

property dom: Ty

The domain of the diagram.

property is_id: bool

Whether the current diagram is an identity diagram.

rotate(z: int) → Diagrammable

Apply the adjoint operation z times.

If z is positive, apply the right adjoint z times. If z is negative, apply the left adjoint -z times.

to_diagram() → Diagram

Transform the current object into an actual Diagram object.

class lambeq.backend.grammar.Entity

Bases: object

__init__() → None

category: ClassVar[Category]

class lambeq.backend.grammar.Functor(target_category: Category, ob: Callable[[Functor, Ty], Ty], ar: Callable[[Functor, Box], Diagrammable] | None = None)

Bases: object

A functor that maps between categories.

Parameters:

target_categoryCategory

The category to which the functor maps.

obcallable, optional

A function that maps types to types, by default None

arcallable, optional

A function that maps boxes to Diagrammables, by default None

Examples

>>> n = Ty('n')
>>> diag = Cap(n, n.l) @ Id(n) >> Id(n) @ Cup(n.l, n)
>>> diag.draw(
...     figsize=(2, 2), path='./snake.png')

>>> F = Functor(grammar, lambda _, ty : ty @ ty)
>>> F(diag).draw(
...     figsize=(2, 2), path='./snake-2.png')

__call__(entity: Ty) → Ty

__call__(entity: Box) → Diagrammable

__call__(entity: Diagram) → Diagram

__call__(entity: Diagrammable) → Diagrammable

Apply the functor to a type or a diagrammable.

Parameters:

entityTy or Diagrammable

The type or diagrammable to which the functor is applied.

__init__(target_category: Category, ob: Callable[[Functor, Ty], Ty], ar: Callable[[Functor, Box], Diagrammable] | None = None) → None

ar(ar: Box) → Diagrammable

Apply the functor to a box.

ar_with_cache(ar: Diagrammable) → Diagrammable

Apply the functor to a diagrammable, caching the result.

ob(ob: Ty) → Ty

Apply the functor to a type.

ob_with_cache(ob: Ty) → Ty

Apply the functor to a type, caching the result.

target_category: Category

lambeq.backend.grammar.Id(dom: Ty | None = None) → Self

class lambeq.backend.grammar.Layer(left: Ty, box: Box, right: Ty)

Bases: Entity

A layer in a diagram.

Parameters:

boxBox

The box in the layer.

leftTy

The wire type to the left of the box.

rightTy

The wire type to the right of the box.

__init__(left: Ty, box: Box, right: Ty) → None

box: Box

category: ClassVar[Category] = Category(name='grammar', Ty=<class 'lambeq.backend.grammar.Ty'>, Box=<class 'lambeq.backend.grammar.Box'>, Layer=<class 'lambeq.backend.grammar.Layer'>, Diagram=<class 'lambeq.backend.grammar.Diagram'>)

property cod: Ty

dagger() → Self

property dom: Ty

extend(left: Ty | None = None, right: Ty | None = None) → Self

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Layer.

Returns:

Layer

The layer generated from the JSON data.

left: Ty

right: Ty

rotate(z: int) → Self

Rotate the layer.

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this layer to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unpack() → tuple[lambeq.backend.grammar.Ty, lambeq.backend.grammar.Box, lambeq.backend.grammar.Ty]

class lambeq.backend.grammar.Spider(type: Ty, n_legs_in: int, n_legs_out: int)

Bases: Box

A spider in the grammar category.

Parameters:

typeTy

The atomic type of the spider.

n_legs_inint

The number of input legs.

n_legs_outint

The number of output legs.

__init__(type: Ty, n_legs_in: int, n_legs_out: int) → None

apply_functor(functor: Functor) → Diagrammable

category: ClassVar[Category] = Category(name='grammar', Ty=<class 'lambeq.backend.grammar.Ty'>, Box=<class 'lambeq.backend.grammar.Box'>, Layer=<class 'lambeq.backend.grammar.Layer'>, Diagram=<class 'lambeq.backend.grammar.Diagram'>)

cod: Ty

dagger() → Self

dom: Ty

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property l: Self

n_legs_in: int

n_legs_out: int

name: str

property r: Self

rotate(z: int) → Self

Rotate the spider.

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

type: Ty

unwind() → Self

z: int = 0

class lambeq.backend.grammar.Swap(left: Ty, right: Ty)

Bases: Box

A swap in the grammar category.

Swaps two wires.

Parameters:

leftTy

The atomic type of the left input wire.

rightTy

The atomic type of the right input wire.

__init__(left: Ty, right: Ty) → None

apply_functor(functor: Functor) → Diagrammable

category: ClassVar[Category] = Category(name='grammar', Ty=<class 'lambeq.backend.grammar.Ty'>, Box=<class 'lambeq.backend.grammar.Box'>, Layer=<class 'lambeq.backend.grammar.Layer'>, Diagram=<class 'lambeq.backend.grammar.Diagram'>)

cod: Ty

dagger() → Self

dom: Ty

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property l: Self

left: Ty

name: str

property r: Self

right: Ty

rotate(z: int) → Self

Rotate the swap.

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.grammar.Ty(name: str | None = None, objects: list[typing.Self] = <factory>, z: int = 0)

Bases: Entity

A type in the grammar category.

Every type is either atomic, complex, or empty. Complex types are tensor products of atomic types, and empty types are the identity type.

Parameters:

namestr, optional

The name of the type, by default None.

objectslist[Ty], optional

The objects defining a complex type, by default [].

zint, optional

The winding number of the type, by default 0.

__init__(name: str | None = None, objects: list[typing.Self] = <factory>, z: int = 0) → None

apply_functor(functor: Functor) → Ty

category: ClassVar[Category] = Category(name='grammar', Ty=<class 'lambeq.backend.grammar.Ty'>, Box=<class 'lambeq.backend.grammar.Box'>, Layer=<class 'lambeq.backend.grammar.Layer'>, Diagram=<class 'lambeq.backend.grammar.Diagram'>)

count(other: Self) → int

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Ty.

Returns:

Ty

The type generated from the JSON data.

property is_atomic: bool

property is_complex: bool

property is_empty: bool

property l: Self

name: str | None = None

objects: list[Self]

property r: Self

repeat(times: int) → Self

rotate(z: int) → Self

Rotate the type, changing the winding number.

tensor(other: Iterable[Self]) → Self

tensor(other: Self, *rest: Self) → Self

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this type to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.grammar.Word(name: str, cod: Ty, z: int = 0)

Bases: Box

A word in the grammar category.

A word is a Box with an empty domain.

Parameters:

namestr

The name of the word.

codTy

The codomain of the word.

zint, optional

The winding number of the word, by default 0

__init__(name: str, cod: Ty, z: int = 0) → None

apply_functor(functor: Functor) → Diagrammable

category: ClassVar[Category] = Category(name='grammar', Ty=<class 'lambeq.backend.grammar.Ty'>, Box=<class 'lambeq.backend.grammar.Box'>, Layer=<class 'lambeq.backend.grammar.Layer'>, Diagram=<class 'lambeq.backend.grammar.Diagram'>)

cod: Ty

dagger() → Daggered

dom: Ty

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property l: Self

name: str

property r: Self

rotate(z: int) → Self

Rotate the Word box, changing the winding number.

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

lambeq.backend.tensor

Tensor category

Lambeq’s internal representation of the tensor category. This work is based on DisCoPy (https://discopy.org/) which is released under the BSD 3-Clause ‘New’ or ‘Revised’ License.

class lambeq.backend.tensor.Box(name: str, dom: Dim, cod: Dim, data: float | ndarray | None = None, z: int = 0)

Bases: Box

Box (tensor) in the the tensor category.

Attributes:

datanp.array or float or None

Data used to represent the array attribute. Typically either the array itself, or a symbolic array.

arraynp.array or float

Tensor which the box represents.

free_symbolsset of sympy.Symbol

In case of a symbolic tensor, set of symbols in the box’s data.

__init__(name: str, dom: Dim, cod: Dim, data: float | ndarray | None = None, z: int = 0)

Initialise a tensor.Box type.

Parameters:

namestr

Name for the box.

domDim

Dimension of the box’s domain.

codDim

Dimension of the box’s codomain.

datafloat or np.ndarray, optional

The concrete tensor the box represents.

zint, optional

Winding number of the box, indicating conjugation. Starts at 0 if not provided.

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='tensor', Ty=<class 'lambeq.backend.tensor.Dim'>, Box=<class 'lambeq.backend.tensor.Box'>, Layer=<class 'lambeq.backend.tensor.Layer'>, Diagram=<class 'lambeq.backend.tensor.Diagram'>)

cod: Dim

dagger()

Get the dagger (adjoint) of the box.

Returns:

Box

Dagger of the box.

data: float | np.ndarray | None

dom: Dim

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

name: str

property r: Self

rotate(z: int)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.tensor.Cap(left: Ty, right: Ty, is_reversed: bool = False)

Bases: Cap, Box

A Cap in the tensor category.

__init__(left: Dim, right: Dim, is_reversed: bool = False)

Initialise a tensor Cap.

Parameters:

leftDim

Dimension (type) of the left leg of the cap. Must be the conjugate of right.

rightDim

Dimension (type) of the right leg of the cap. Must be the conjugate of left.

is_reversedbool, default False

Ignored parameter, since left and right conjugates are equivalent in the tensor category. Necessary to inherit from grammar.Cap appropriately.

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='tensor', Ty=<class 'lambeq.backend.tensor.Dim'>, Box=<class 'lambeq.backend.tensor.Box'>, Layer=<class 'lambeq.backend.tensor.Layer'>, Diagram=<class 'lambeq.backend.tensor.Diagram'>)

cod: Dim

dagger() → Cup

Get the dagger (adjoint) of the box.

Returns:

Box

Dagger of the box.

data: float | np.ndarray | None

dom: Dim

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

is_reversed: bool = False

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

left: Dim

name: str

property r: Self

right: Dim

rotate(z: int) → Self

Rotate the cap.

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

classmethod to_left(right: Ty, is_reversed: bool = False) → Self | Diagram

classmethod to_right(left: Ty, is_reversed: bool = False) → Self | Diagram

unwind() → Self

z: int = 0

class lambeq.backend.tensor.Cup(left: Ty, right: Ty, is_reversed: bool = False)

Bases: Cup, Box

A Cup in the tensor category.

__init__(left: Dim, right: Dim, is_reversed: bool = False)

Initialise a tensor Cup.

Parameters:

leftDim

Dimension (type) of the left leg of the cup. Must be the conjugate of right.

rightDim

Dimension (type) of the right leg of the cup. Must be the conjugate of left.

is_reversedbool, default False

Ignored parameter, since left and right conjugates are equivalent in the tensor category. Necessary to inherit from grammar.Cup appropriately.

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='tensor', Ty=<class 'lambeq.backend.tensor.Dim'>, Box=<class 'lambeq.backend.tensor.Box'>, Layer=<class 'lambeq.backend.tensor.Layer'>, Diagram=<class 'lambeq.backend.tensor.Diagram'>)

cod: Dim

dagger() → Cap

Get the dagger (adjoint) of the box.

Returns:

Box

Dagger of the box.

data: float | np.ndarray | None

dom: Dim

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

is_reversed: bool = False

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

left: Dim

name: str

property r: Self

right: Dim

rotate(z: int) → Self

Rotate the cup.

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

classmethod to_left(right: Ty, is_reversed: bool = False) → Self | Diagram

classmethod to_right(left: Ty, is_reversed: bool = False) → Self | Diagram

unwind() → Self

z: int = 0

class lambeq.backend.tensor.Daggered(box: Box)

Bases: Daggered, Box

A daggered box.

Attributes:

boxBox

The box to be daggered.

__init__(box: Box) → None

Initialise a tensor.Box type.

Parameters:

namestr

Name for the box.

domDim

Dimension of the box’s domain.

codDim

Dimension of the box’s codomain.

datafloat or np.ndarray, optional

The concrete tensor the box represents.

zint, optional

Winding number of the box, indicating conjugation. Starts at 0 if not provided.

apply_functor(functor: Functor) → Diagrammable

property array

box: Box

category: ClassVar[Category] = Category(name='tensor', Ty=<class 'lambeq.backend.tensor.Dim'>, Box=<class 'lambeq.backend.tensor.Box'>, Layer=<class 'lambeq.backend.tensor.Layer'>, Diagram=<class 'lambeq.backend.tensor.Diagram'>)

cod: Dim

dagger() → Box

Get the dagger (adjoint) of the box.

Returns:

Box

Dagger of the box.

data: float | np.ndarray | None = None

dom: Dim

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

name: str

property r: Self

rotate(z: int) → Self

Rotate the daggered box.

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.tensor.Diagram(dom: Dim, cod: Dim, layers: list[lambeq.backend.tensor.Layer])

Bases: Diagram

Diagram in the tensor category.

__init__(dom: Dim, cod: Dim, layers: list[lambeq.backend.tensor.Layer]) → None

apply_functor(functor: Functor) → Diagram

classmethod ba(left, right) → Self

classmethod bc(left, middle, right) → Self

property boxes: list[lambeq.backend.grammar.Box]

classmethod bx(left, middle, right) → Self

classmethod caps(left: Ty, right: Ty, is_reversed=False) → Diagrammable

category: ClassVar[Category] = Category(name='tensor', Ty=<class 'lambeq.backend.tensor.Dim'>, Box=<class 'lambeq.backend.tensor.Box'>, Layer=<class 'lambeq.backend.tensor.Layer'>, Diagram=<class 'lambeq.backend.tensor.Diagram'>)

cod: Dim

classmethod create_pregroup_diagram(words: list[lambeq.backend.grammar.Word], morphisms: list[tuple[type, int, int]]) → Self

Create a Diagram from cups and swaps.

>>> n, s = Ty('n'), Ty('s')
>>> words = [Word('she', n), Word('goes', n.r @ s @ n.l),
...          Word('home', n)]
>>> morphs = [(Cup, 0, 1), (Cup, 3, 4)]
>>> diagram = Diagram.create_pregroup_diagram(words, morphs)

Parameters:

wordslist of Word

A list of Word s corresponding to the words of the sentence.

morphisms: list of tuple[type, int, int]

A list of tuples of the form:

(morphism, start_wire_idx, end_wire_idx).

Morphisms can be Cup s or Swap s, while the two numbers define the indices of the wires on which the morphism is applied.

Returns:

Diagram

The generated pregroup diagram.

Raises:

ValueError

If the provided morphism list does not type-check properly.

classmethod cups(left: Ty, right: Ty, is_reversed=False) → Diagrammable

curry(n: int = 1, left: bool = True) → Self

dagger() → Self

dom: Dim

draw(draw_as_pregroup=True, **kwargs: Any) → None

Draw the diagram.

Parameters:

draw_as_pregroupbool, optional

Whether to try drawing the diagram as a pregroup diagram, default is True.

draw_as_nodesbool, optional

Whether to draw boxes as nodes, default is False.

colorstring, optional

Color of the box or node, default is white (‘#ffffff’) for boxes and red (‘#ff0000’) for nodes.

textpadpair of floats, optional

Padding between text and wires, default is (0.1, 0.1).

draw_type_labelsbool, optional

Whether to draw type labels, default is False.

draw_box_labelsbool, optional

Whether to draw box labels, default is True.

aspectstring, optional

Aspect ratio, one of [‘auto’, ‘equal’].

marginstuple, optional

Margins, default is (0.05, 0.05).

nodesizefloat, optional

BoxNode size for spiders and controlled gates.

fontsizeint, optional

Font size for the boxes, default is 12.

fontsize_typesint, optional

Font size for the types, default is 12.

figsizetuple, optional

Figure size.

pathstr, optional

Where to save the image, if None we call plt.show().

to_tikzbool, optional

Whether to output tikz code instead of matplotlib.

asymmetryfloat, optional

Make a box and its dagger mirror images, default is .25 * any(box.is_dagger for box in diagram.boxes).

eval(contractor=<function auto>, dtype: type | None = None)

Evaluate the tensor diagram.

Parameters:

contractortn contractor

tensornetwork contractor for chosen contraction algorithm.

dtypetype, optional

Data type of the resulting array. Defaults to np.float32.

Returns:

numpy.ndarray

n-dimension array representing the contracted tensor.

classmethod fa(left, right) → Self

classmethod fc(left, middle, right) → Self

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_discopy(diagram: discopy.monoidal.Diagram) → Diagram

Import discopy diagram to lambeq diagram.

Parameters:

diagramdiscopy.monoidal.Diagram

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Diagram.

Returns:

Diagram

The diagram generated from the JSON data.

classmethod fx(left, middle, right) → Self

classmethod id(dom: Ty | None = None) → Self

property is_id: bool

property is_pregroup: bool

Check if a diagram is a pregroup diagram.

Adapted from discopy.grammar.pregroup.draw.

Returns:

bool

Whether the diagram is a pregroup diagram.

property l: Self

lambdify(*symbols, **kwargs)

layers: list[Layer]

classmethod lift(diagrams: Iterable[Diagrammable | Ty]) → list[Self]

Lift diagrams to the current category.

Given a list of boxes or diagrams, call to_diagram on each, then check all of the diagrams are in the same category as the calling class.

Parameters:

diagramsiterable

The diagrams to lift and check.

Returns:

list of Diagram

The diagrams after calling to_diagram on each.

Raises:

ValueError

If any of the diagrams are not in the same category of the calling class.

normal_form(left: bool = False) → Diagram

Returns the normal form of a connected diagram, see arXiv:1804.07832.

Parameters:

leftbool, optional

Whether to apply left interchangers.

Raises:

NotImplementedError

Whenever normalizer yields the same rewrite steps twice.

property offsets: list[int]

The offset of a box is the length of the type on its left.

classmethod permutation(dom: Ty, permutation: Iterable[int]) → Self

Create a layer of Swaps that permutes the wires.

permuted(permutation: Iterable[int]) → Self

pregroup_normal_form()

Applies normal form to a pregroup diagram of the form word @ ... @ word >> wires by normalising words and wires seperately before combining them, so it can be drawn with draw().

property r: Self

classmethod register_special_box(name: str, diagram_factory: Callable[[...], Diagrammable] | None = None) → None | Callable[[_DiagrammableFactoryT], _DiagrammableFactoryT]

render_as_str(**kwargs: Any) → str

Render the diagram as text.

Presently only implemented for pregroup diagrams.

Parameters:

word_spacingint, default: 2

The number of spaces between the words of the diagrams.

use_at_separatorbool, default: False

Whether to represent types using @ as the monoidal product. Otherwise, use the unicode dot character.

compress_layersbool, default: True

Whether to draw boxes in the same layer when they can occur simultaneously, otherwise, draw one box per layer.

use_ascii: bool, default: False

Whether to draw using ASCII characters only, for compatibility reasons.

Returns:

str

Drawing of diagram in string format.

rotate(z: int) → Self

Rotate the diagram.

special_boxes: ClassVar[dict[str, _DiagrammableFactory]] = {'cap': <class 'lambeq.backend.tensor.Cap'>, 'cup': <class 'lambeq.backend.tensor.Cup'>, 'spider': <class 'lambeq.backend.tensor.Spider'>, 'swap': <class 'lambeq.backend.tensor.Swap'>}

classmethod swap(left: Ty, right: Ty) → Diagrammable

tensor(*diagrams: Diagrammable | Ty) → Self

then(*diagrams: Diagrammable) → Self

then_at(diagram: Diagrammable, index: int) → Self

to_diagram() → Self

to_discopy() → discopy.monoidal.Diagram

Export lambeq diagram to discopy diagram.

Returns:

discopy.monoidal.Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this diagram to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

to_tn(dtype: type | None = None)

Convert the diagram to a tensornetwork TN.

Parameters:

dtypetype, optional

Data type of the resulting array. Defaults to np.float32.

Returns:

tuple[list[tn.Node], list[tn.Edge]]

tensornetwork representation of the diagram. An edge object is returned for each dangling edge in the network.

transpose(left: bool = False) → Self

Construct the diagrammatic transpose.

The transpose of any diagram in a category with cups and caps can be constructed as follows:

                        (default)
Left transpose       Right transpose
    │╭╮                  ╭╮│
    │█│                  │█│
    ╰╯│                  │╰╯

The input and output types of the transposed diagram are the adjoints of the respective types of the original diagram. This means that for diagrams with composite types, the order of the objects are reversed.

Parameters:

leftbool, default: False

Whether to transpose to the diagram to the left.

Returns:

Diagram

The transposed diagram, constructed as shown above.

class lambeq.backend.tensor.Dim(*dim: int, objects: list[Self] | None = None)

Bases: Ty

Dimension in the tensor category.

Attributes:

dimtuple of int

Tuple of dimensions represented by the object.

product: int

Product of contained dimensions.

__init__(*dim: int, objects: list[Self] | None = None) → None

Initialise a Dim type.

Parameters:

dimlist[int]

List of dimensions to initialise.

objects: list[Self] or None, default None

List of Dim`s, to prepare a non-atomic `Dim object.

apply_functor(functor: Functor) → Ty

category: ClassVar[Category] = Category(name='tensor', Ty=<class 'lambeq.backend.tensor.Dim'>, Box=<class 'lambeq.backend.tensor.Box'>, Layer=<class 'lambeq.backend.tensor.Layer'>, Diagram=<class 'lambeq.backend.tensor.Diagram'>)

count(other: Self) → int

property dim: tuple[int, ...]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Ty.

Returns:

Ty

The type generated from the JSON data.

property is_atomic: bool

property is_complex: bool

property is_empty: bool

property l: Self

name: str | None = None

objects: list[Self]

property product: int

property r: Self

repeat(times: int) → Self

rotate(z: int) → Self

Rotate the type, changing the winding number.

tensor(other: Self | Iterable[Self], *rest: Self) → Self

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this type to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.tensor.Layer(left: Dim, box: Box, right: Dim)

Bases: Layer

Layer in the tensor category.

__init__(left: Dim, box: Box, right: Dim) → None

box: Box

category: ClassVar[Category] = Category(name='tensor', Ty=<class 'lambeq.backend.tensor.Dim'>, Box=<class 'lambeq.backend.tensor.Box'>, Layer=<class 'lambeq.backend.tensor.Layer'>, Diagram=<class 'lambeq.backend.tensor.Diagram'>)

property cod: Ty

dagger() → Self

property dom: Ty

extend(left: Ty | None = None, right: Ty | None = None) → Self

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Layer.

Returns:

Layer

The layer generated from the JSON data.

left: Dim

right: Dim

rotate(z: int) → Self

Rotate the layer.

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this layer to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unpack() → tuple[lambeq.backend.grammar.Ty, lambeq.backend.grammar.Box, lambeq.backend.grammar.Ty]

class lambeq.backend.tensor.Spider(type: Ty, n_legs_in: int, n_legs_out: int)

Bases: Spider, Box

A Spider in the tensor category.

Concretely represented by a copy node.

__init__(type: Dim, n_legs_in: int, n_legs_out: int)

Initialise a tensor Spider.

Parameters:

typeDim

Dimension (type) of each leg of the spider.

n_legs_inint

Number of input legs of the spider.

n_legs_outint

Number of input legs of the spider.

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='tensor', Ty=<class 'lambeq.backend.tensor.Dim'>, Box=<class 'lambeq.backend.tensor.Box'>, Layer=<class 'lambeq.backend.tensor.Layer'>, Diagram=<class 'lambeq.backend.tensor.Diagram'>)

cod: Dim

dagger() → Self

Get the dagger (adjoint) of the box.

Returns:

Box

Dagger of the box.

data: float | np.ndarray | None

dom: Dim

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

n_legs_in: int

n_legs_out: int

name: str

property r: Self

rotate(z: int) → Self

Rotate the spider.

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

type: Dim

unwind() → Self

z: int = 0

class lambeq.backend.tensor.Swap(left: Ty, right: Ty)

Bases: Swap, Box

A Swap in the tensor category.

__init__(left: Dim, right: Dim)

Initialise a tensor Swap.

Parameters:

leftDim

Dimension (type) of the left input of the swap.

rightDim

Dimension (type) of the right input of the swap.

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='tensor', Ty=<class 'lambeq.backend.tensor.Dim'>, Box=<class 'lambeq.backend.tensor.Box'>, Layer=<class 'lambeq.backend.tensor.Layer'>, Diagram=<class 'lambeq.backend.tensor.Diagram'>)

cod: Dim

dagger()

Get the dagger (adjoint) of the box.

Returns:

Box

Dagger of the box.

data: float | np.ndarray | None

dom: Dim

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

left: Dim

name: str

property r: Self

right: Dim

rotate(z: int) → Self

Rotate the swap.

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

lambeq.backend.quantum

Quantum category

Lambeq’s internal representation of the quantum category. This work is based on DisCoPy (https://discopy.org/) which is released under the BSD 3-Clause ‘New’ or ‘Revised’ License.

Notes

In lambeq, gates are represented as the transpose of their matrix according to the standard convention in quantum computing. This makes composition of gates using the tensornetwork library easier.

class lambeq.backend.quantum.AntiConjugate(name: str, dom: Ty, cod: Ty, data: float | ndarray | None = None, z: int = 0, is_mixed: bool = False, self_adjoint: bool = False)

Bases: Box

An anti-conjugate box is equal to the conjugate of its conjugate.

__init__(name: str, dom: Ty, cod: Ty, data: float | ndarray | None = None, z: int = 0, is_mixed: bool = False, self_adjoint: bool = False)

Initialise a box in the quantum category.

Parameters:

namestr

Name of the box.

domTy

Domain of the box.

codTy

Codomain of the box.

datafloat | np.ndarray, optional

Array defining the tensor of the box, by default None

zint, optional

The winding number, by default 0

is_mixedbool, optional

Whether the box is mixed, by default False

self_adjointbool, optional

Whether the box is self-adjoint, by default False

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger() → Daggered | Box

Return the dagger of the box.

data: float | np.ndarray | None

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

name: str

property r: Self

rotate(z)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.Bit(*bitstring: int)

Bases: Box

Classical state for a given bit.

__init__(bit_value: int) → None

Initialise a ket box.

Parameters:

bit_valueint

The state of the qubit (either 0 or 1).

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger() → Daggered | Box

Return the dagger of the box.

data: float | np.ndarray | None

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

name: str

property r: Self

rotate(z: int)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.Box(name: str, dom: Ty, cod: Ty, data: float | ndarray | None = None, z: int = 0, is_mixed: bool = False, self_adjoint: bool = False)

Bases: Box

A box in the quantum category.

__init__(name: str, dom: Ty, cod: Ty, data: float | ndarray | None = None, z: int = 0, is_mixed: bool = False, self_adjoint: bool = False)

Initialise a box in the quantum category.

Parameters:

namestr

Name of the box.

domTy

Domain of the box.

codTy

Codomain of the box.

datafloat | np.ndarray, optional

Array defining the tensor of the box, by default None

zint, optional

The winding number, by default 0

is_mixedbool, optional

Whether the box is mixed, by default False

self_adjointbool, optional

Whether the box is self-adjoint, by default False

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger() → Daggered | Box

Return the dagger of the box.

data: float | np.ndarray | None

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

name: str

property r: Self

rotate(z: int)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.Bra(*bitstring: int)

Bases: SelfConjugate, Box

A bra in the quantum category.

A bra is a box that measures a qubit in the computational basis and post-selects on a given state.

__init__(bit: int)

Initialise a bra box.

Parameters:

bitint

The state of the qubit to post-select on (either 0 or 1).

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger() → Self

Return the dagger of the box.

data: float | np.ndarray | None

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

name: str

property r: Self

rotate(z)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

lambeq.backend.quantum.CRx(phi, distance=1)

lambeq.backend.quantum.CRy(phi, distance=1)

lambeq.backend.quantum.CRz(phi, distance=1)

class lambeq.backend.quantum.Controlled(controlled: Box, distance=1)

Bases: Parametrized

A gate that applies a unitary controlled by a qubit’s state.

__init__(controlled: Box, distance=1)

Initialise a controlled box.

Parameters:

controlledBox

The box to be controlled.

distanceint, optional

The distance between the control and the target, by default 1

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger()

Return the dagger of the box.

data: float

decompose() → Diagram | Box

Split a box (distance >1) into distance 1 box + swaps.

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool = False

property l: Self

lambdify(*symbols, **kwargs)

Return a lambda function that evaluates the box.

property modules

name: str

property phase: float

property r: Self

rotate(z)

Conjugate the box.

self_adjoint: bool = False

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.Daggered(box: ~lambeq.backend.quantum.Box, __hash__: ~collections.abc.Callable[[~lambeq.backend.quantum.Box], int] = <function Box.__hash__>, __repr__: ~collections.abc.Callable[[~lambeq.backend.quantum.Box], str] = <function Box.__repr__>)

Bases: Daggered, Box

A daggered gate reverses the box’s effect on a quantum state.

Parameters:

boxBox

The box to be daggered.

__init__(box: ~lambeq.backend.quantum.Box, __hash__: ~collections.abc.Callable[[~lambeq.backend.quantum.Box], int] = <function Box.__hash__>, __repr__: ~collections.abc.Callable[[~lambeq.backend.quantum.Box], str] = <function Box.__repr__>) → None

Initialise a box in the quantum category.

Parameters:

namestr

Name of the box.

domTy

Domain of the box.

codTy

Codomain of the box.

datafloat | np.ndarray, optional

Array defining the tensor of the box, by default None

zint, optional

The winding number, by default 0

is_mixedbool, optional

Whether the box is mixed, by default False

self_adjointbool, optional

Whether the box is self-adjoint, by default False

apply_functor(functor: Functor) → Diagrammable

property array

box: Box

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger() → Box

Return the dagger of the box.

data: float | np.ndarray | None = None

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool = False

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

name: str

property r: Self

rotate(z: int) → Self

Rotate the daggered box.

self_adjoint: bool = False

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.Diagram(dom: ~lambeq.backend.quantum.Ty, cod: ~lambeq.backend.quantum.Ty, layers: list[lambeq.backend.quantum.Layer], __hash__: ~collections.abc.Callable[[], int] = <function Diagram.__hash__>)

Bases: Diagram

A diagram in the quantum category.

Parameters:

domTy

The type of the input wires.

codTy

The type of the output wires.

layerslist[Layer]

The layers of the diagram.

__init__(dom: ~lambeq.backend.quantum.Ty, cod: ~lambeq.backend.quantum.Ty, layers: list[lambeq.backend.quantum.Layer], __hash__: ~collections.abc.Callable[[], int] = <function Diagram.__hash__>) → None

apply_functor(functor: Functor) → Diagram

apply_gate(gate: Box, *qubits: int) → Self

apply_parametrized_gate(gate: Callable[[float], Parametrized], param: float, *qubits: int) → Self

classmethod ba(left, right) → Self

classmethod bc(left, middle, right) → Self

property boxes: list[lambeq.backend.grammar.Box]

classmethod bx(left, middle, right) → Self

classmethod caps(left: Ty, right: Ty, is_reversed=False) → Diagrammable

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

classmethod create_pregroup_diagram(words: list[lambeq.backend.grammar.Word], morphisms: list[tuple[type, int, int]]) → Self

Create a Diagram from cups and swaps.

>>> n, s = Ty('n'), Ty('s')
>>> words = [Word('she', n), Word('goes', n.r @ s @ n.l),
...          Word('home', n)]
>>> morphs = [(Cup, 0, 1), (Cup, 3, 4)]
>>> diagram = Diagram.create_pregroup_diagram(words, morphs)

Parameters:

wordslist of Word

A list of Word s corresponding to the words of the sentence.

morphisms: list of tuple[type, int, int]

A list of tuples of the form:

(morphism, start_wire_idx, end_wire_idx).

Morphisms can be Cup s or Swap s, while the two numbers define the indices of the wires on which the morphism is applied.

Returns:

Diagram

The generated pregroup diagram.

Raises:

ValueError

If the provided morphism list does not type-check properly.

classmethod cups(left: Ty, right: Ty, is_reversed=False) → Diagrammable

curry(n: int = 1, left: bool = True) → Self

dagger() → Self

dom: Ty

draw(draw_as_pregroup=True, **kwargs: Any) → None

Draw the diagram.

Parameters:

draw_as_pregroupbool, optional

Whether to try drawing the diagram as a pregroup diagram, default is True.

draw_as_nodesbool, optional

Whether to draw boxes as nodes, default is False.

colorstring, optional

Color of the box or node, default is white (‘#ffffff’) for boxes and red (‘#ff0000’) for nodes.

textpadpair of floats, optional

Padding between text and wires, default is (0.1, 0.1).

draw_type_labelsbool, optional

Whether to draw type labels, default is False.

draw_box_labelsbool, optional

Whether to draw box labels, default is True.

aspectstring, optional

Aspect ratio, one of [‘auto’, ‘equal’].

marginstuple, optional

Margins, default is (0.05, 0.05).

nodesizefloat, optional

BoxNode size for spiders and controlled gates.

fontsizeint, optional

Font size for the boxes, default is 12.

fontsize_typesint, optional

Font size for the types, default is 12.

figsizetuple, optional

Figure size.

pathstr, optional

Where to save the image, if None we call plt.show().

to_tikzbool, optional

Whether to output tikz code instead of matplotlib.

asymmetryfloat, optional

Make a box and its dagger mirror images, default is .25 * any(box.is_dagger for box in diagram.boxes).

eval(*others, backend=None, mixed=False, contractor=<function auto>, **params)

Evaluate the circuit represented by the diagram.

Be aware that this method is only suitable for small circuits with a small number of qubits (depending on hardware resources).

Parameters:

otherslambeq.backend.quantum.Diagram

Other circuits to process in batch if backend is set to tket.

backendpytket.Backend, optional

Backend on which to run the circuit, if none then we apply tensor contraction.

mixedbool, optional

Whether the circuit is mixed, by default False

contractorCallable, optional

The contractor to use, by default tn.contractors.auto

Returns:

np.ndarray or list of np.ndarray

The result of the circuit simulation.

classmethod fa(left, right) → Self

classmethod fc(left, middle, right) → Self

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_discopy(diagram: discopy.monoidal.Diagram) → Diagram

Import discopy diagram to lambeq diagram.

Parameters:

diagramdiscopy.monoidal.Diagram

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Diagram.

Returns:

Diagram

The diagram generated from the JSON data.

classmethod fx(left, middle, right) → Self

classmethod id(dom: Ty | None = None) → Self

init_and_discard()

Return circuit with empty domain and only bits as codomain.

property is_id: bool

property is_mixed: bool

Whether the diagram is mixed.

A diagram is mixed if it contains a mixed box or if it has both classical and quantum wires.

property is_pregroup: bool

Check if a diagram is a pregroup diagram.

Adapted from discopy.grammar.pregroup.draw.

Returns:

bool

Whether the diagram is a pregroup diagram.

property l: Self

lambdify(*symbols, **kwargs)

layers: list[Layer]

classmethod lift(diagrams: Iterable[Diagrammable | Ty]) → list[Self]

Lift diagrams to the current category.

Given a list of boxes or diagrams, call to_diagram on each, then check all of the diagrams are in the same category as the calling class.

Parameters:

diagramsiterable

The diagrams to lift and check.

Returns:

list of Diagram

The diagrams after calling to_diagram on each.

Raises:

ValueError

If any of the diagrams are not in the same category of the calling class.

normal_form(left: bool = False) → Diagram

Returns the normal form of a connected diagram, see arXiv:1804.07832.

Parameters:

leftbool, optional

Whether to apply left interchangers.

Raises:

NotImplementedError

Whenever normalizer yields the same rewrite steps twice.

property offsets: list[int]

The offset of a box is the length of the type on its left.

classmethod permutation(dom: Ty, permutation: Iterable[int]) → Self

Create a layer of Swaps that permutes the wires.

permuted(permutation: Iterable[int]) → Self

pregroup_normal_form()

Applies normal form to a pregroup diagram of the form word @ ... @ word >> wires by normalising words and wires seperately before combining them, so it can be drawn with draw().

property r: Self

classmethod register_special_box(name: str, diagram_factory: Callable[[...], Diagrammable] | None = None) → None | Callable[[_DiagrammableFactoryT], _DiagrammableFactoryT]

render_as_str(**kwargs: Any) → str

Render the diagram as text.

Presently only implemented for pregroup diagrams.

Parameters:

word_spacingint, default: 2

The number of spaces between the words of the diagrams.

use_at_separatorbool, default: False

Whether to represent types using @ as the monoidal product. Otherwise, use the unicode dot character.

compress_layersbool, default: True

Whether to draw boxes in the same layer when they can occur simultaneously, otherwise, draw one box per layer.

use_ascii: bool, default: False

Whether to draw using ASCII characters only, for compatibility reasons.

Returns:

str

Drawing of diagram in string format.

rotate(z: int) → Self

Rotate the diagram.

special_boxes: ClassVar[dict[str, _DiagrammableFactory]] = {'cap': <function generate_cap>, 'cup': <function generate_cup>, 'spider': <function generate_spider>, 'swap': <class 'lambeq.backend.quantum.Swap'>}

classmethod swap(left: Ty, right: Ty) → Diagrammable

tensor(*diagrams: Diagrammable | Ty) → Self

then(*diagrams: Diagrammable) → Self

then_at(diagram: Diagrammable, index: int) → Self

to_diagram() → Self

to_discopy() → discopy.monoidal.Diagram

Export lambeq diagram to discopy diagram.

Returns:

discopy.monoidal.Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this diagram to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

to_pennylane(probabilities=False, backend_config=None, diff_method='best')

Export lambeq circuit to PennylaneCircuit.

Parameters:

probabiltiesbool, default: False

If True, the PennylaneCircuit will return the normalized probabilties of measuring the computational basis states when run. If False, it returns the unnormalized quantum states in the computational basis.

backend_configdict, default: None

A dictionary of PennyLane backend configration options, including the provider (e.g. IBM or Honeywell), the device, the number of shots, etc. See the PennyLane plugin documentation for more details.

diff_methodstr, default: “best”

The differentiation method to use to obtain gradients for the PennyLane circuit. Some gradient methods are only compatible with simulated circuits. See the PennyLane documentation for more details.

Returns:

lambeq.backend.pennylane.PennylaneCircuit

to_tk()

Export to t|ket>.

Returns:

tk_circuitlambeq.backend.converters.tk.Circuit

A lambeq.backend.converters.tk.Circuit.

Examples

>>> from lambeq.backend.quantum import *

>>> bell_test = H @ Id(qubit) >> CX >> Measure() @ Measure()
>>> bell_test.to_tk()
tk.Circuit(2, 2).H(0).CX(0, 1).Measure(0, 0).Measure(1, 1)

>>> circuit0 = (Sqrt(2) @ H @ Rx(0.5) >> CX >>
...             Measure() @ Discard())
>>> circuit0.to_tk()
tk.Circuit(2, 1).H(0).Rx(1.0, 1).CX(0, 1).Measure(0, 0).scale(2)

>>> circuit1 = Ket(1, 0) >> CX >> Id(qubit) @ Ket(0) @ Id(qubit)
>>> circuit1.to_tk()
tk.Circuit(3).X(0).CX(0, 2)

>>> circuit2 = X @ Id(qubit ** 2) \
...     >> Id(qubit) @ SWAP >> CX @ Id(qubit) >> Id(qubit) @ SWAP
>>> circuit2.to_tk()
tk.Circuit(3).X(0).CX(0, 2)

>>> circuit3 = Ket(0, 0)\
...     >> H @ Id(qubit)\
...     >> CX\
...     >> Id(qubit) @ Bra(0)
>>> print(repr(circuit3.to_tk()))
tk.Circuit(2, 1).H(0).CX(0, 1).Measure(1, 0).post_select({0: 0})

to_tn(mixed=False)

Send a diagram to a mixed tensornetwork.

Parameters:

mixedbool, default: False

Whether to perform mixed (also known as density matrix) evaluation of the circuit.

Returns:

nodestensornetwork.Node

Nodes of the network.

output_edge_orderlist of tensornetwork.Edge

Output edges of the network.

transpose(left: bool = False) → Self

Construct the diagrammatic transpose.

The transpose of any diagram in a category with cups and caps can be constructed as follows:

                        (default)
Left transpose       Right transpose
    │╭╮                  ╭╮│
    │█│                  │█│
    ╰╯│                  │╰╯

The input and output types of the transposed diagram are the adjoints of the respective types of the original diagram. This means that for diagrams with composite types, the order of the objects are reversed.

Parameters:

leftbool, default: False

Whether to transpose to the diagram to the left.

Returns:

Diagram

The transposed diagram, constructed as shown above.

class lambeq.backend.quantum.Discard

Bases: SelfConjugate

Discard a qubit. This is a measurement without post-selection.

__init__()

Initialise a box in the quantum category.

Parameters:

namestr

Name of the box.

domTy

Domain of the box.

codTy

Codomain of the box.

datafloat | np.ndarray, optional

Array defining the tensor of the box, by default None

zint, optional

The winding number, by default 0

is_mixedbool, optional

Whether the box is mixed, by default False

self_adjointbool, optional

Whether the box is self-adjoint, by default False

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger()

Return the dagger of the box.

data: float | np.ndarray | None

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

name: str

property r: Self

rotate(z)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.Encode

Bases: SelfConjugate

Encode a classical information bit into a qubit.

__init__()

Initialise a box in the quantum category.

Parameters:

namestr

Name of the box.

domTy

Domain of the box.

codTy

Codomain of the box.

datafloat | np.ndarray, optional

Array defining the tensor of the box, by default None

zint, optional

The winding number, by default 0

is_mixedbool, optional

Whether the box is mixed, by default False

self_adjointbool, optional

Whether the box is self-adjoint, by default False

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger()

Return the dagger of the box.

data: float | np.ndarray | None

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

name: str

property r: Self

rotate(z)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

lambeq.backend.quantum.Id(ty: Ty | int | None = None) → Diagram

class lambeq.backend.quantum.Ket(*bitstring: int)

Bases: SelfConjugate, Box

A ket in the quantum category.

A ket is a box that initializes a qubit to a given state.

__init__(bit: int) → None

Initialise a ket box.

Parameters:

bitint

The state of the qubit (either 0 or 1).

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger() → Self

Return the dagger of the box.

data: float | np.ndarray | None

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

name: str

property r: Self

rotate(z)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.Layer(left: Ty, box: Box, right: Ty)

Bases: Layer

A Layer in a quantum Diagram.

Parameters:

boxBox

The box of the layer.

leftTy

The wire type to the left of the box.

rightTy

The wire type to the right of the box.

__init__(left: Ty, box: Box, right: Ty) → None

box: Box

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

property cod: Ty

dagger() → Self

property dom: Ty

extend(left: Ty | None = None, right: Ty | None = None) → Self

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Layer.

Returns:

Layer

The layer generated from the JSON data.

left: Ty

right: Ty

rotate(z: int) → Self

Rotate the layer.

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this layer to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unpack() → tuple[lambeq.backend.grammar.Ty, lambeq.backend.grammar.Box, lambeq.backend.grammar.Ty]

class lambeq.backend.quantum.Measure

Bases: SelfConjugate

Measure a qubit and return a classical information bit.

__init__()

Initialise a box in the quantum category.

Parameters:

namestr

Name of the box.

domTy

Domain of the box.

codTy

Codomain of the box.

datafloat | np.ndarray, optional

Array defining the tensor of the box, by default None

zint, optional

The winding number, by default 0

is_mixedbool, optional

Whether the box is mixed, by default False

self_adjointbool, optional

Whether the box is self-adjoint, by default False

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger()

Return the dagger of the box.

data: float | np.ndarray | None

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

name: str

property r: Self

rotate(z)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.MixedState

Bases: SelfConjugate

A mixed state is a state with a density matrix proportional to the identity matrix.

__init__()

Initialise a box in the quantum category.

Parameters:

namestr

Name of the box.

domTy

Domain of the box.

codTy

Codomain of the box.

datafloat | np.ndarray, optional

Array defining the tensor of the box, by default None

zint, optional

The winding number, by default 0

is_mixedbool, optional

Whether the box is mixed, by default False

self_adjointbool, optional

Whether the box is self-adjoint, by default False

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger()

Return the dagger of the box.

data: float | np.ndarray | None

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

name: str

property r: Self

rotate(z)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.Parametrized(name: str, dom: Ty, cod: Ty, data: float | ndarray | None = None, z: int = 0, is_mixed: bool = False, self_adjoint: bool = False)

Bases: Box

A parametrized box in the quantum category.

A parametrized box is a unitary gate that can be parametrized by a real number.

Parameters:

namestr

The name of the box.

domTy

The domain of the box.

codTy

The codomain of the box.

datafloat

The parameterised unitary of the box.

is_mixedbool, default: False

Whether the box is mixed

self_adjointbool, default: False

Whether the box is self-adjoint

__init__(name: str, dom: Ty, cod: Ty, data: float | ndarray | None = None, z: int = 0, is_mixed: bool = False, self_adjoint: bool = False)

Initialise a box in the quantum category.

Parameters:

namestr

Name of the box.

domTy

Domain of the box.

codTy

Codomain of the box.

datafloat | np.ndarray, optional

Array defining the tensor of the box, by default None

zint, optional

The winding number, by default 0

is_mixedbool, optional

Whether the box is mixed, by default False

self_adjointbool, optional

Whether the box is self-adjoint, by default False

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger() → Daggered | Box

Return the dagger of the box.

data: float

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool = False

property l: Self

lambdify(*symbols, **kwargs)

Return a lambda function that evaluates the box.

property modules

name: str

property r: Self

rotate(z: int)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool = False

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.Rotation(phase)

Bases: Parametrized

Single qubit gate defining a rotation around the bloch sphere.

__init__(phase)

Initialise a box in the quantum category.

Parameters:

namestr

Name of the box.

domTy

Domain of the box.

codTy

Codomain of the box.

datafloat | np.ndarray, optional

Array defining the tensor of the box, by default None

zint, optional

The winding number, by default 0

is_mixedbool, optional

Whether the box is mixed, by default False

self_adjointbool, optional

Whether the box is self-adjoint, by default False

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger() → Self

Return the dagger of the box.

data: float

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool = False

property l: Self

lambdify(*symbols, **kwargs)

Return a lambda function that evaluates the box.

property modules

name: str

property phase: float

property r: Self

rotate(z: int)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool = False

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.Rx(phase)

Bases: AntiConjugate, Rotation

Single qubit gate defining a rotation aound the x-axis.

__init__(phase)

Initialise a box in the quantum category.

Parameters:

namestr

Name of the box.

domTy

Domain of the box.

codTy

Codomain of the box.

datafloat | np.ndarray, optional

Array defining the tensor of the box, by default None

zint, optional

The winding number, by default 0

is_mixedbool, optional

Whether the box is mixed, by default False

self_adjointbool, optional

Whether the box is self-adjoint, by default False

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger() → Self

Return the dagger of the box.

data: float

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool = False

property l: Self

lambdify(*symbols, **kwargs)

Return a lambda function that evaluates the box.

property modules

name: str

property phase: float

property r: Self

rotate(z)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool = False

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.Ry(phase)

Bases: SelfConjugate, Rotation

Single qubit gate defining a rotation aound the y-axis.

__init__(phase)

Initialise a box in the quantum category.

Parameters:

namestr

Name of the box.

domTy

Domain of the box.

codTy

Codomain of the box.

datafloat | np.ndarray, optional

Array defining the tensor of the box, by default None

zint, optional

The winding number, by default 0

is_mixedbool, optional

Whether the box is mixed, by default False

self_adjointbool, optional

Whether the box is self-adjoint, by default False

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger() → Self

Return the dagger of the box.

data: float

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool = False

property l: Self

lambdify(*symbols, **kwargs)

Return a lambda function that evaluates the box.

property modules

name: str

property phase: float

property r: Self

rotate(z)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool = False

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.Rz(phase)

Bases: AntiConjugate, Rotation

Single qubit gate defining a rotation aound the z-axis.

__init__(phase)

Initialise a box in the quantum category.

Parameters:

namestr

Name of the box.

domTy

Domain of the box.

codTy

Codomain of the box.

datafloat | np.ndarray, optional

Array defining the tensor of the box, by default None

zint, optional

The winding number, by default 0

is_mixedbool, optional

Whether the box is mixed, by default False

self_adjointbool, optional

Whether the box is self-adjoint, by default False

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger() → Self

Return the dagger of the box.

data: float

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool = False

property l: Self

lambdify(*symbols, **kwargs)

Return a lambda function that evaluates the box.

property modules

name: str

property phase: float

property r: Self

rotate(z)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool = False

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.Scalar(data: float | ~numpy.ndarray, __hash__: ~collections.abc.Callable[[~lambeq.backend.quantum.Box], int] = <function Box.__hash__>)

Bases: Box

A scalar amplifies a quantum state by a given factor.

__init__(data: float | ~numpy.ndarray, __hash__: ~collections.abc.Callable[[~lambeq.backend.quantum.Box], int] = <function Box.__hash__>) → None

Initialise a box in the quantum category.

Parameters:

namestr

Name of the box.

domTy

Domain of the box.

codTy

Codomain of the box.

datafloat | np.ndarray, optional

Array defining the tensor of the box, by default None

zint, optional

The winding number, by default 0

is_mixedbool, optional

Whether the box is mixed, by default False

self_adjointbool, optional

Whether the box is self-adjoint, by default False

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty = Ty()

dagger()

Return the dagger of the box.

data: float | np.ndarray

dom: Ty = Ty()

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool = False

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

name: str

property r: Self

rotate(z: int)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool = False

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.SelfConjugate(name: str, dom: Ty, cod: Ty, data: float | ndarray | None = None, z: int = 0, is_mixed: bool = False, self_adjoint: bool = False)

Bases: Box

A self-conjugate box is equal to its own conjugate.

__init__(name: str, dom: Ty, cod: Ty, data: float | ndarray | None = None, z: int = 0, is_mixed: bool = False, self_adjoint: bool = False)

Initialise a box in the quantum category.

Parameters:

namestr

Name of the box.

domTy

Domain of the box.

codTy

Codomain of the box.

datafloat | np.ndarray, optional

Array defining the tensor of the box, by default None

zint, optional

The winding number, by default 0

is_mixedbool, optional

Whether the box is mixed, by default False

self_adjointbool, optional

Whether the box is self-adjoint, by default False

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger() → Daggered | Box

Return the dagger of the box.

data: float | np.ndarray | None

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

name: str

property r: Self

rotate(z)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.Sqrt(data: float | ~numpy.ndarray, __hash__: ~collections.abc.Callable[[], int] = <function Box.__hash__>)

Bases: Scalar

A Square root.

__init__(data: float | ~numpy.ndarray, __hash__: ~collections.abc.Callable[[], int] = <function Box.__hash__>) → None

Initialise a box in the quantum category.

Parameters:

namestr

Name of the box.

domTy

Domain of the box.

codTy

Codomain of the box.

datafloat | np.ndarray, optional

Array defining the tensor of the box, by default None

zint, optional

The winding number, by default 0

is_mixedbool, optional

Whether the box is mixed, by default False

self_adjointbool, optional

Whether the box is self-adjoint, by default False

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty = Ty()

dagger()

Return the dagger of the box.

data: float | np.ndarray

dom: Ty = Ty()

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool = False

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

name: str

property r: Self

rotate(z: int)

Get the result of conjugating the box z times.

Parameters:

zint

Winding count. The number of conjugations to apply to the box.

Returns:

Box

The box conjugated z times.

self_adjoint: bool = False

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

class lambeq.backend.quantum.Swap(left: Ty, right: Ty)

Bases: Swap, SelfConjugate, Box

A swap box in the quantum category.

__init__(left: Ty, right: Ty)

Initialise a swap box.

Parameters:

leftTy

The left type of the swap.

rightTy

The right type of the swap.

apply_functor(functor: Functor) → Diagrammable

property array

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

cod: Ty

dagger()

Return the dagger of the box.

data: float | np.ndarray | None

dom: Ty

property free_symbols: set[sympy.core.symbol.Symbol]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Box.

Returns:

Box

The box generated from the JSON data.

property is_classical: bool

is_mixed: bool

property l: Self

lambdify(*symbols: Symbol, **kwargs) → Callable

Get a lambdified version of a symbolic box.

Returns a function which when provided appropriate parameters, initialises a concrete box.

Parameters:

symbolslist of sympy.Symbols

List of symbols in the box in the order in which their assigned values will appear in the concretisation call.

kwargs:

Additional parameters to pass to sympy.lambdify.

Returns:

Callable[…, Box]:

A lambda function which when invoked with appropriate parameters, returns a concrete version of the box.

left: Dim

n_legs_in: int

n_legs_out: int

name: str

property r: Self

right: Dim

rotate(z: int) → Self

Rotate the swap.

self_adjoint: bool

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this box to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

type: Ty

unwind() → Self

z: int = 0

class lambeq.backend.quantum.Ty(name: str | None = None, objects: list[Self] | None = None)

Bases: Dim

A type in the quantum category.

__init__(name: str | None = None, objects: list[Self] | None = None)

Initialise a type in the quantum category.

Parameters:

namestr, optional

The name of the type, by default None

objectslist[Ty], optional

The objects defining a complex type, by default None

apply_functor(functor: Functor) → Ty

category: ClassVar[Category] = Category(name='quantum', Ty=<class 'lambeq.backend.quantum.Ty'>, Box=<class 'lambeq.backend.quantum.Box'>, Layer=<class 'lambeq.backend.quantum.Layer'>, Diagram=<class 'lambeq.backend.quantum.Diagram'>)

count(other: Self) → int

property dim: tuple[int, ...]

classmethod from_json(data: Dict[str, Any] | str) → Self

Decode a JSON object or string into a Ty.

Returns:

Ty

The type generated from the JSON data.

property is_atomic: bool

property is_complex: bool

property is_empty: bool

property l: Self

name: str | None = None

objects: list[Self]

property product: int

property r: Self

repeat(times: int) → Self

rotate(z: int) → Self

Rotate the type, changing the winding number.

tensor(other: Self | Iterable[Self], *rest: Self) → Self

to_diagram() → Diagram

to_json(is_top_level: bool = True) → Dict[str, Any]

Encode this type to a JSON object.

Parameters:

is_top_levelbool, optional

This flag indicates that this object is the top-most object and should have the global metadata (e.g. category). This should be set to False when calling to_json on attribute instances to avoid duplication of said global metadata.

unwind() → Self

z: int = 0

lambeq.backend.quantum.generate_cap(left: Ty, right: Ty, is_reversed=False) → Diagram

Generate a cap diagram.

Parameters:

leftTy

The left type of the cap.

rightTy

The right type of the cap.

is_reversedbool, optional

Unused, by default False

Returns:

Diagram

The cap diagram.

lambeq.backend.quantum.generate_cup(left: Ty, right: Ty, is_reversed=False) → Diagram

Generate a cup diagram.

Parameters:

leftTy

The left type of the cup.

rightTy

The right type of the cup.

is_reversedbool, optional

Unused, by default False

Returns:

Diagram

The cup diagram.

lambeq.backend.quantum.generate_spider(type: Ty, n_legs_in: int, n_legs_out: int) → Diagram

lambeq.backend.numerical_backend

Numerical Backend

Module unifying the use of numerical backends for lambeq. This module is used to provide a common interface to different numerical backends, such as NumPy, JAX, PyTorch, and TensorFlow.

class lambeq.backend.numerical_backend.Backend(module: module, array: Callable | None = None)

Bases: object

A matrix backend.

Parameters:

module : The main module of the backend. array : The array class of the backend.

__init__(module: module, array: Callable | None = None)

property name

class lambeq.backend.numerical_backend.JAX

Bases: Backend

JAX backend.

__init__()

property name

class lambeq.backend.numerical_backend.NumPy

Bases: Backend

NumPy backend.

__init__()

property name

class lambeq.backend.numerical_backend.PyTorch

Bases: Backend

PyTorch backend.

__init__()

property name

class lambeq.backend.numerical_backend.TensorFlow

Bases: Backend

TensorFlow backend.

__init__()

property name

lambeq.backend.numerical_backend.backend(name: str | None = None, _stack=['numpy'], _cache={}) → Generator[Backend, None, None]

Context manager for matrix backend.

Parameters:

name : The name of the backend, default is "numpy".

lambeq.backend.numerical_backend.get_backend() → Backend

Get the current backend.

lambeq.backend.numerical_backend.set_backend(name: str) → None

Override the default backend.

Parameters:

name : The name of the backend.

lambeq.backend.converters.discopy

Interface with discopy

Module containing the functions to convert from and to discopy. This work is based on DisCoPy (https://discopy.org/) which is released under the BSD 3-Clause “New” or “Revised” License.

lambeq.backend.converters.discopy.box_d2l(box: Box, target: type[_LAMBEQ_BOX_VAR]) → _LAMBEQ_BOX_VAR

lambeq.backend.converters.discopy.box_l2d(box: Box, target: type[_DISCOPY_BOX_VAR]) → _DISCOPY_BOX_VAR

lambeq.backend.converters.discopy.convert_grammar_d2l(box: Box) → Box

lambeq.backend.converters.discopy.convert_grammar_l2d(box: Box) → Box

lambeq.backend.converters.discopy.convert_quantum_d2l(box: Box) → Box | Diagram

lambeq.backend.converters.discopy.convert_quantum_l2d(box: Box) → Box

lambeq.backend.converters.discopy.convert_tensor_d2l(box: Box) → Box

lambeq.backend.converters.discopy.convert_tensor_l2d(box: Box) → Box

lambeq.backend.converters.discopy.from_discopy(diagram: Diagram | Circuit | Diagram) → Diagram | Diagram | Diagram

Takes a discopy.grammar.pregroup.Diagram, discopy.quantum.Diagram, or discopy.tensor.Diagram, and converts it to a lambeq.backend.grammar.Diagram, lambeq.backend.quantum.Diagram, or lambeq.backend.tensor.Diagram, respectively.

Parameters:

diagramdiscopy.grammar.pregroup.Diagram |

discopy.quantum.Diagram | discopy.tensor.Diagram The diagram to convert.

Returns:

lambeq.backend.grammar.Diagram |

lambeq.backend.quantum.Diagram | lambeq.backend.tensor.Diagram The converted diagram.

lambeq.backend.converters.discopy.to_discopy(diagram: Diagram | Diagram | Diagram) → Diagram | Circuit | Diagram

Takes a lambeq.backend.grammar.Diagram, lambeq.backend.quantum.Diagram, or lambeq.backend.tensor.Diagram, and converts it to a discopy.grammar.pregroup.Diagram, discopy.quantum.Diagram, or discopy.tensor.Diagram, respectively.

Parameters:

diagramlambeq.backend.grammar.Diagram |

lambeq.backend.quantum.Diagram | lambeq.backend.tensor.Diagram The diagram to convert.

Returns:

:class:discopy.grammar.pregroup.Diagram |

discopy.quantum.Diagram | discopy.tensor.Diagram The converted diagram.

lambeq.backend.converters.discopy.ty_d2l(ty: Ty | Ty | Dim, target_type: Type[_LAMBEQ_TY_VAR]) → _LAMBEQ_TY_VAR

lambeq.backend.converters.discopy.ty_l2d(ty: Ty | Ty | Dim, target_type: Type[_DISCOPY_TY_VAR]) → _DISCOPY_TY_VAR

lambeq.backend.converters.tk

Interface with tket

Module containing the functions to convert from and to tket. This work is based on DisCoPy (https://discopy.org/) which is released under the BSD 3-Clause “New” or “Revised” License.

class lambeq.backend.converters.tk.Circuit(n_qubits: int = 0, n_bits: int = 0, post_selection: dict[int, int] | None = None, scalar: float | None = None, post_processing: Diagram | None = None)

Bases: Circuit

Extend pytket.Circuit with counts post-processing.

AAMS(*args, **kwargs)

Overloaded function.

1. AAMS(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], angle2: typing.Union[sympy.Expr, float], qubit0: int, qubit1: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends an AAMS gate with possibly symbolic angles (specified in half-turns).

Returns:

the new Circuit

2. AAMS(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], angle2: typing.Union[sympy.Expr, float], qubit0: pytket._tket.unit_id.Qubit, qubit1: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends an AAMS gate with possibly symbolic angles (specified in half-turns).

Returns:

the new Circuit

CCX(*args, **kwargs)

Overloaded function.

1. CCX(self: pytket._tket.circuit.Circuit, control_0: int, control_1: int, target: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CCX gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CCX(self: pytket._tket.circuit.Circuit, control_0: pytket._tket.unit_id.Qubit, control_1: pytket._tket.unit_id.Qubit, target: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CCX gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

CH(*args, **kwargs)

Overloaded function.

1. CH(self: pytket._tket.circuit.Circuit, control_qubit: int, target_qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CH gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CH(self: pytket._tket.circuit.Circuit, control_qubit: pytket._tket.unit_id.Qubit, target_qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CH gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

CRx(*args, **kwargs)

Overloaded function.

1. CRx(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], control_qubit: int, target_qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CRx gate with a possibly symbolic angle (specified in half-turns) on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CRx(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], control_qubit: pytket._tket.unit_id.Qubit, target_qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CRx gate with a symbolic angle (specified in half-turns) on the wires for the specified control and target qubits.

Returns:

the new Circuit

CRy(*args, **kwargs)

Overloaded function.

1. CRy(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], control_qubit: int, target_qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CRy gate with a possibly symbolic angle (specified in half-turns) on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CRy(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], control_qubit: pytket._tket.unit_id.Qubit, target_qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CRy gate with a symbolic angle (specified in half-turns) on the wires for the specified control and target qubits.

Returns:

the new Circuit

CRz(*args, **kwargs)

Overloaded function.

1. CRz(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], control_qubit: int, target_qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CRz gate with a possibly symbolic angle (specified in half-turns) on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CRz(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], control_qubit: pytket._tket.unit_id.Qubit, target_qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CRz gate with a symbolic angle (specified in half-turns) on the wires for the specified control and target qubits.

Returns:

the new Circuit

CS(*args, **kwargs)

Overloaded function.

1. CS(self: pytket._tket.circuit.Circuit, control_qubit: int, target_qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CS gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CS(self: pytket._tket.circuit.Circuit, control_qubit: pytket._tket.unit_id.Qubit, target_qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CS gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

CSWAP(*args, **kwargs)

Overloaded function.

1. CSWAP(self: pytket._tket.circuit.Circuit, control: int, target_0: int, target_1: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CSWAP gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CSWAP(self: pytket._tket.circuit.Circuit, control: pytket._tket.unit_id.Qubit, target_0: pytket._tket.unit_id.Qubit, target_1: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CSWAP gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

CSX(*args, **kwargs)

Overloaded function.

1. CSX(self: pytket._tket.circuit.Circuit, control_qubit: int, target_qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CSX gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CSX(self: pytket._tket.circuit.Circuit, control_qubit: pytket._tket.unit_id.Qubit, target_qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CSX gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

CSXdg(*args, **kwargs)

Overloaded function.

1. CSXdg(self: pytket._tket.circuit.Circuit, control_qubit: int, target_qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CSXdg gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CSXdg(self: pytket._tket.circuit.Circuit, control_qubit: pytket._tket.unit_id.Qubit, target_qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CSXdg gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

CSdg(*args, **kwargs)

Overloaded function.

1. CSdg(self: pytket._tket.circuit.Circuit, control_qubit: int, target_qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CSdg gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CSdg(self: pytket._tket.circuit.Circuit, control_qubit: pytket._tket.unit_id.Qubit, target_qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CSdg gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

CU1(*args, **kwargs)

Overloaded function.

1. CU1(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], control_qubit: int, target_qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CU1 gate with a possibly symbolic angle (specified in half-turns) on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CU1(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], control_qubit: pytket._tket.unit_id.Qubit, target_qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CU1 gate with a possibly symbolic angle (specified in half-turns) on the wires for the specified control and target qubits.

Returns:

the new Circuit

CU3(*args, **kwargs)

Overloaded function.

1. CU3(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], angle2: typing.Union[sympy.Expr, float], control_qubit: int, target_qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CU3 gate with possibly symbolic angles (specified in half-turns) on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CU3(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], angle2: typing.Union[sympy.Expr, float], control_qubit: pytket._tket.unit_id.Qubit, target_qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CU3 gate with possibly symbolic angles (specified in half-turns) on the wires for the specified control and target qubits.

Returns:

the new Circuit

CV(*args, **kwargs)

Overloaded function.

1. CV(self: pytket._tket.circuit.Circuit, control_qubit: int, target_qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CV gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CV(self: pytket._tket.circuit.Circuit, control_qubit: pytket._tket.unit_id.Qubit, target_qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CV gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

CVdg(*args, **kwargs)

Overloaded function.

1. CVdg(self: pytket._tket.circuit.Circuit, control_qubit: int, target_qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CVdg gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CVdg(self: pytket._tket.circuit.Circuit, control_qubit: pytket._tket.unit_id.Qubit, target_qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CVdg gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

CX(*args, **kwargs)

Overloaded function.

1. CX(self: pytket._tket.circuit.Circuit, control_qubit: int, target_qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CX gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CX(self: pytket._tket.circuit.Circuit, control_qubit: pytket._tket.unit_id.Qubit, target_qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CX gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

CY(*args, **kwargs)

Overloaded function.

1. CY(self: pytket._tket.circuit.Circuit, control_qubit: int, target_qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CY gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CY(self: pytket._tket.circuit.Circuit, control_qubit: pytket._tket.unit_id.Qubit, target_qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CY gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

CZ(*args, **kwargs)

Overloaded function.

1. CZ(self: pytket._tket.circuit.Circuit, control_qubit: int, target_qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CZ gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

2. CZ(self: pytket._tket.circuit.Circuit, control_qubit: pytket._tket.unit_id.Qubit, target_qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a CZ gate on the wires for the specified control and target qubits.

Returns:

the new Circuit

ECR(*args, **kwargs)

Overloaded function.

1. ECR(self: pytket._tket.circuit.Circuit, qubit_0: int, qubit_1: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends an ECR gate on the wires for the specified qubits.

Returns:

the new Circuit

2. ECR(self: pytket._tket.circuit.Circuit, qubit_0: pytket._tket.unit_id.Qubit, qubit_1: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends an ECR gate on the wires for the specified qubits.

Returns:

the new Circuit

ESWAP(*args, **kwargs)

Overloaded function.

1. ESWAP(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit0: int, qubit1: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends an ESWAP gate with a possibly symbolic angle (specified in half-turns) on the wires for the specified two qubits.

Returns:

the new Circuit

2. ESWAP(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit0: pytket._tket.unit_id.Qubit, qubit1: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends an ESWAP gate with a possibly symbolic angle (specified in half-turns) on the wires for the specified two qubits.

Returns:

the new Circuit

FSim(*args, **kwargs)

Overloaded function.

1. FSim(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], qubit0: int, qubit1: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends an FSim gate with possibly symbolic angles (specified in half-turns) on the wires for the specified qubits.

Returns:

the new Circuit

2. FSim(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], qubit0: pytket._tket.unit_id.Qubit, qubit1: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends an FSim gate with possibly symbolic angles (specified in half-turns) on the wires for the specified qubits.

Returns:

the new Circuit

GPI(*args, **kwargs)

Overloaded function.

1. GPI(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a GPI gate with a possibly symbolic angle (specified in half-turns).

Returns:

the new Circuit

2. GPI(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a GPI gate with a possibly symbolic angle (specified in half-turns).

Returns:

the new Circuit

GPI2(*args, **kwargs)

Overloaded function.

1. GPI2(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a GPI2 gate with a possibly symbolic angle (specified in half-turns).

Returns:

the new Circuit

2. GPI2(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a GPI2 gate with a possibly symbolic angle (specified in half-turns).

Returns:

the new Circuit

H(*args, **kwargs)

Overloaded function.

1. H(self: pytket._tket.circuit.Circuit, qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a Hadamard gate.

Returns:

the new Circuit

2. H(self: pytket._tket.circuit.Circuit, qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a Hadamard gate.

Returns:

the new Circuit

ISWAP(*args, **kwargs)

Overloaded function.

1. ISWAP(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit0: int, qubit1: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends an ISWAP gate with a possibly symbolic angle (specified in half-turns) on the wires for the specified qubits.

Returns:

the new Circuit

2. ISWAP(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit0: pytket._tket.unit_id.Qubit, qubit1: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends an ISWAP gate with a possibly symbolic angle (specified in half-turns) on the wires for the specified qubits.

Returns:

the new Circuit

ISWAPMax(*args, **kwargs)

Overloaded function.

1. ISWAPMax(self: pytket._tket.circuit.Circuit, qubit0: int, qubit1: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends an ISWAPMax gate on the wires for the specified qubits.

Returns:

the new Circuit

2. ISWAPMax(self: pytket._tket.circuit.Circuit, qubit0: pytket._tket.unit_id.Qubit, qubit1: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends an ISWAPMax gate on the wires for the specified qubits.

Returns:

the new Circuit

Measure(*args, **kwargs)

Overloaded function.

1. Measure(self: pytket._tket.circuit.Circuit, qubit: int, bit_index: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a single-qubit measurement in the computational (Z) basis.

Returns:

the new Circuit

2. Measure(self: pytket._tket.circuit.Circuit, qubit: pytket._tket.unit_id.Qubit, bit: pytket._tket.unit_id.Bit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a single-qubit measurement in the computational (Z) basis.

Returns:

the new Circuit

Phase(self: pytket._tket.circuit.Circuit, arg0: Union[sympy.Expr, float], **kwargs) → pytket._tket.circuit.Circuit

PhasedISWAP(*args, **kwargs)

Overloaded function.

1. PhasedISWAP(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], qubit0: int, qubit1: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a PhasedISWAP gate with possibly symbolic angles (specified in half-turns) on the wires for the specified qubits.

Returns:

the new Circuit

2. PhasedISWAP(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], qubit0: pytket._tket.unit_id.Qubit, qubit1: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a PhasedISWAP gate with posisbly symbolic angles (specified in half-turns) on the wires for the specified qubits.

Returns:

the new Circuit

PhasedX(*args, **kwargs)

Overloaded function.

1. PhasedX(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a PhasedX gate with possibly symbolic angles (specified in half-turns) on the wires for the specified qubits.

Returns:

the new Circuit

2. PhasedX(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a PhasedX gate with possibly symbolic angles (specified in half-turns) on the wires for the specified qubits.

Returns:

the new Circuit

Reset(*args, **kwargs)

Overloaded function.

1. Reset(self: pytket._tket.circuit.Circuit, qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a Reset operation. Sets a qubit to the Z-basis 0 state. Non-unitary operation.

Returns:

the new Circuit

2. Reset(self: pytket._tket.circuit.Circuit, qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a Reset operation. Sets a qubit to the Z-basis 0 state. Non-unitary operation.

Returns:

the new Circuit

Rx(*args, **kwargs)

Overloaded function.

1. Rx(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends an Rx gate with a possibly symbolic angle (specified in half-turns).

Returns:

the new Circuit

2. Rx(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends an Rx gate with a possibly symbolic angle (specified in half-turns).

Returns:

the new Circuit

Ry(*args, **kwargs)

Overloaded function.

1. Ry(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends an Ry gate with a possibly symbolic angle (specified in half-turns).

Returns:

the new Circuit

2. Ry(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends an Ry gate with a possibly symbolic angle (specified in half-turns).

Returns:

the new Circuit

Rz(*args, **kwargs)

Overloaded function.

1. Rz(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends an Rz gate with a possibly symbolic angle (specified in half-turns).

Returns:

the new Circuit

2. Rz(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends an Rz gate with a possibly symbolic angle (specified in half-turns).

Returns:

the new Circuit

S(*args, **kwargs)

Overloaded function.

1. S(self: pytket._tket.circuit.Circuit, qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends an S gate (equivalent to U1(0.5,-)).

Returns:

the new Circuit

2. S(self: pytket._tket.circuit.Circuit, qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends an S gate (equivalent to Rz(0.5,-)).

Returns:

the new Circuit

SWAP(*args, **kwargs)

Overloaded function.

1. SWAP(self: pytket._tket.circuit.Circuit, qubit_0: int, qubit_1: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a SWAP gate on the wires for the specified qubits.

Returns:

the new Circuit

2. SWAP(self: pytket._tket.circuit.Circuit, qubit_0: pytket._tket.unit_id.Qubit, qubit_1: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a SWAP gate on the wires for the specified qubits.

Returns:

the new Circuit

SX(*args, **kwargs)

Overloaded function.

1. SX(self: pytket._tket.circuit.Circuit, qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a SX gate (equivalent to Rx(0.5,-) up to a 0.25 global phase).

Returns:

the new Circuit

2. SX(self: pytket._tket.circuit.Circuit, qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a SX gate (equivalent to Rx(0.5,-) up to a 0.25 global phase).

Returns:

the new Circuit

SXdg(*args, **kwargs)

Overloaded function.

1. SXdg(self: pytket._tket.circuit.Circuit, qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a SXdg gate (equivalent to Rx(-0.5,-) up to a -0.25 global phase).

Returns:

the new Circuit

2. SXdg(self: pytket._tket.circuit.Circuit, qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a SXdg gate (equivalent to Rx(-0.5,-) up to a -0.25 global phase).

Returns:

the new Circuit

Sdg(*args, **kwargs)

Overloaded function.

1. Sdg(self: pytket._tket.circuit.Circuit, qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends an S-dagger gate (equivalent to U1(-0.5,-)).

Returns:

the new Circuit

2. Sdg(self: pytket._tket.circuit.Circuit, qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends an S-dagger gate (equivalent to Rz(-0.5,-)).

Returns:

the new Circuit

Sycamore(*args, **kwargs)

Overloaded function.

1. Sycamore(self: pytket._tket.circuit.Circuit, qubit0: int, qubit1: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a Sycamore gate on the wires for the specified qubits.

Returns:

the new Circuit

2. Sycamore(self: pytket._tket.circuit.Circuit, qubit0: pytket._tket.unit_id.Qubit, qubit1: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a Sycamore gate on the wires for the specified qubits.

Returns:

the new Circuit

T(*args, **kwargs)

Overloaded function.

1. T(self: pytket._tket.circuit.Circuit, qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a T gate (equivalent to U1(0.25,-)).

Returns:

the new Circuit

2. T(self: pytket._tket.circuit.Circuit, qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a T gate (equivalent to Rz(0.25,-)).

Returns:

the new Circuit

TK1(*args, **kwargs)

Overloaded function.

1. TK1(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], angle2: typing.Union[sympy.Expr, float], qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a TK1 gate with possibly symbolic angles (specified in half-turns).

Returns:

the new Circuit

2. TK1(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], angle2: typing.Union[sympy.Expr, float], qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a TK1 gate with possibly symbolic angles (specified in half-turns).

Returns:

the new Circuit

TK2(*args, **kwargs)

Overloaded function.

1. TK2(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], angle2: typing.Union[sympy.Expr, float], qubit0: int, qubit1: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a TK2 gate with possibly symbolic angles (specified in half-turns).

Returns:

the new Circuit

2. TK2(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], angle2: typing.Union[sympy.Expr, float], qubit0: pytket._tket.unit_id.Qubit, qubit1: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a TK2 gate with possibly symbolic angles (specified in half-turns).

Returns:

the new Circuit

Tdg(*args, **kwargs)

Overloaded function.

1. Tdg(self: pytket._tket.circuit.Circuit, qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a T-dagger gate (equivalent to U1(-0.25,-)).

Returns:

the new Circuit

2. Tdg(self: pytket._tket.circuit.Circuit, qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a T-dagger gate (equivalent to Rz(-0.25,-)).

Returns:

the new Circuit

U1(*args, **kwargs)

Overloaded function.

1. U1(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a U1 gate with a possibly symbolic angle (specified in half-turns).

Returns:

the new Circuit

2. U1(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a U1 gate with a possibly symbolic angle (specified in half-turns).

Returns:

the new Circuit

U2(*args, **kwargs)

Overloaded function.

1. U2(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a U2 gate with possibly symbolic angles (specified in half-turns).

Returns:

the new Circuit

2. U2(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a U2 gate with possibly symbolic angles (specified in half-turns).

Returns:

the new Circuit

U3(*args, **kwargs)

Overloaded function.

1. U3(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], angle2: typing.Union[sympy.Expr, float], qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a U3 gate with possibly symbolic angles (specified in half-turns).

Returns:

the new Circuit

2. U3(self: pytket._tket.circuit.Circuit, angle0: typing.Union[sympy.Expr, float], angle1: typing.Union[sympy.Expr, float], angle2: typing.Union[sympy.Expr, float], qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a U3 gate with possibly symbolic angles (specified in half-turns).

Returns:

the new Circuit

V(*args, **kwargs)

Overloaded function.

1. V(self: pytket._tket.circuit.Circuit, qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a V gate (equivalent to Rx(0.5,-)).

Returns:

the new Circuit

2. V(self: pytket._tket.circuit.Circuit, qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a V gate (equivalent to Rx(0.5,-)).

Returns:

the new Circuit

Vdg(*args, **kwargs)

Overloaded function.

1. Vdg(self: pytket._tket.circuit.Circuit, qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a V-dagger gate (equivalent to Rx(-0.5,-)).

Returns:

the new Circuit

2. Vdg(self: pytket._tket.circuit.Circuit, qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a V-dagger gate (equivalent to Rx(-0.5,-)).

Returns:

the new Circuit

X(*args, **kwargs)

Overloaded function.

1. X(self: pytket._tket.circuit.Circuit, qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Returns:

the new Circuit

2. X(self: pytket._tket.circuit.Circuit, qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends an X gate.

Returns:

the new Circuit

XXPhase(*args, **kwargs)

Overloaded function.

1. XXPhase(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit0: int, qubit1: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a XX gate with a possibly symbolic angle (specified in half-turns) on the wires for the specified two qubits.

Returns:

the new Circuit

2. XXPhase(self: pytket._tket.circuit.Circuit, qubit0: typing.Union[sympy.Expr, float], qubit1: pytket._tket.unit_id.Qubit, angle: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a XX gate with a symbolic angle (specified in half-turns) on the wires for the specified two qubits.

Returns:

the new Circuit

XXPhase3(*args, **kwargs)

Overloaded function.

1. XXPhase3(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit0: int, qubit1: int, qubit2: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a 3-qubit XX gate with a possibly symbolic angle (specified in half-turns) on the wires for the specified three qubits.

Returns:

the new Circuit

2. XXPhase3(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit0: pytket._tket.unit_id.Qubit, qubit1: pytket._tket.unit_id.Qubit, qubit2: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a 3-qubit XX gate with a symbolic angle (specified in half-turns) on the wires for the specified three qubits.

Returns:

the new Circuit

Y(*args, **kwargs)

Overloaded function.

1. Y(self: pytket._tket.circuit.Circuit, qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Returns:

the new Circuit

2. Y(self: pytket._tket.circuit.Circuit, qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a Y gate.

Returns:

the new Circuit

YYPhase(*args, **kwargs)

Overloaded function.

1. YYPhase(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit0: int, qubit1: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a YY gate with a possibly symbolic angle (specified in half-turns) on the wires for the specified two qubits.

Returns:

the new Circuit

2. YYPhase(self: pytket._tket.circuit.Circuit, qubit0: typing.Union[sympy.Expr, float], qubit1: pytket._tket.unit_id.Qubit, angle: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a YY gate with a symbolic angle (specified in half-turns) on the wires for the specified two qubits.

Returns:

the new Circuit

Z(*args, **kwargs)

Overloaded function.

1. Z(self: pytket._tket.circuit.Circuit, qubit: int, **kwargs) -> pytket._tket.circuit.Circuit

Returns:

the new Circuit

2. Z(self: pytket._tket.circuit.Circuit, qubit: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a Z gate.

Returns:

the new Circuit

ZZMax(*args, **kwargs)

Overloaded function.

1. ZZMax(self: pytket._tket.circuit.Circuit, qubit0: int, qubit1: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a ZZMax gate on the wires for the specified two qubits.

Returns:

the new Circuit

2. ZZMax(self: pytket._tket.circuit.Circuit, qubit0: pytket._tket.unit_id.Qubit, qubit1: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a ZZMax gate on the wires for the specified two qubits.

Returns:

the new Circuit

ZZPhase(*args, **kwargs)

Overloaded function.

1. ZZPhase(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit0: int, qubit1: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a ZZ gate with a possibly symbolic angle (specified in half-turns) on the wires for the specified two qubits.

Returns:

the new Circuit

2. ZZPhase(self: pytket._tket.circuit.Circuit, angle: typing.Union[sympy.Expr, float], qubit0: pytket._tket.unit_id.Qubit, qubit1: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a ZZ gate with a symbolic angle (specified in half-turns) on the wires for the specified two qubits.

Returns:

the new Circuit

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: pytket._tket.circuit.Circuit) -> None

Constructs a circuit with a completely empty DAG.

2. __init__(self: pytket._tket.circuit.Circuit, name: str) -> None

Constructs a named circuit with a completely empty DAG.

Parameters:

name – name for the circuit

3. __init__(self: pytket._tket.circuit.Circuit, n_qubits: int, name: Optional[str] = None) -> None

Constructs a circuit with a given number of qubits/blank wires.

>>> c = Circuit()
>>> c.add_blank_wires(3)

is equivalent to

>>> c = Circuit(3)

Parameters:

• n_qubits – The number of qubits in the circuit

• name – Optional name for the circuit.

4. __init__(self: pytket._tket.circuit.Circuit, n_qubits: int, n_bits: int, name: Optional[str] = None) -> None

Constructs a circuit with a given number of quantum and classical bits

Parameters:

• n_qubits – The number of qubits in the circuit

• n_bits – The number of classical bits in the circuit

• name – Optional name for the circuit.

add_assertion(*args, **kwargs)

Overloaded function.

1. add_assertion(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.ProjectorAssertionBox, qubits: Sequence[int], ancilla: Optional[int] = None, name: Optional[str] = None) -> pytket._tket.circuit.Circuit

Append a ProjectorAssertionBox to the circuit.

Parameters:

• box – ProjectorAssertionBox to append

• qubits – indices of target qubits

• ancilla – index of ancilla qubit

• name – name used to identify this assertion

Returns:

the new Circuit

2. add_assertion(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.ProjectorAssertionBox, qubits: Sequence[pytket._tket.unit_id.Qubit], ancilla: Optional[pytket._tket.unit_id.Qubit] = None, name: Optional[str] = None) -> pytket._tket.circuit.Circuit

Append a ProjectorAssertionBox to the circuit.

Parameters:

• box – ProjectorAssertionBox to append

• qubits – target qubits

• ancilla – ancilla qubit

• name – name used to identify this assertion

Returns:

the new Circuit

3. add_assertion(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.StabiliserAssertionBox, qubits: Sequence[int], ancilla: int, name: Optional[str] = None) -> pytket._tket.circuit.Circuit

Append a StabiliserAssertionBox to the circuit.

Parameters:

• box – StabiliserAssertionBox to append

• qubits – indices of target qubits

• ancilla – index of ancilla qubit

• name – name used to identify this assertion

Returns:

the new Circuit

4. add_assertion(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.StabiliserAssertionBox, qubits: Sequence[pytket._tket.unit_id.Qubit], ancilla: pytket._tket.unit_id.Qubit, name: Optional[str] = None) -> pytket._tket.circuit.Circuit

Append a StabiliserAssertionBox to the circuit.

Parameters:

• box – StabiliserAssertionBox to append

• qubits – target qubits

• ancilla – ancilla qubit

• name – name used to identify this assertion

Returns:

the new Circuit

add_barrier(*args, **kwargs)

Overloaded function.

1. add_barrier(self: pytket._tket.circuit.Circuit, qubits: Sequence[int], bits: Sequence[int] = [], data: str = ‘’) -> pytket._tket.circuit.Circuit

Append a Barrier on the given units

Parameters:

data – additional data stored in the barrier

Returns:

the new Circuit

2. add_barrier(self: pytket._tket.circuit.Circuit, units: Sequence[pytket._tket.unit_id.UnitID], data: str = ‘’) -> pytket._tket.circuit.Circuit

Append a Barrier on the given units

Parameters:

data – additional data stored in the barrier

Returns:

the new Circuit

add_bit(unit, offset=None) → None

Add a bit, update post_processing.

add_blank_wires(self: pytket._tket.circuit.Circuit, number: int) → None

Adds a number of new qubits to the circuit. These will be added to the default register (‘q’) if possible, filling out the unused indices from 0.

Parameters:

number – Number of qubits to add

add_c_and(*args, **kwargs)

Overloaded function.

1. add_c_and(self: pytket._tket.circuit.Circuit, arg0_in: int, arg1_in: int, arg_out: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a binary AND operation to the end of the circuit.

Parameters:

• arg0_in – first input bit

• arg1_in – second input bit

• arg_out – output bit

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

2. add_c_and(self: pytket._tket.circuit.Circuit, arg0_in: pytket._tket.unit_id.Bit, arg1_in: pytket._tket.unit_id.Bit, arg_out: pytket._tket.unit_id.Bit, **kwargs) -> pytket._tket.circuit.Circuit

See add_c_and().

add_c_and_to_registers(self: pytket._tket.circuit.Circuit, reg0_in: pytket._tket.unit_id.BitRegister, reg1_in: pytket._tket.unit_id.BitRegister, reg_out: pytket._tket.unit_id.BitRegister, **kwargs) → pytket._tket.circuit.Circuit

Applies bitwise AND to linear registers.

The operation is applied to the bits with indices 0, 1, 2, … in each register, up to the size of the smallest register.

Parameters:

• reg0_in – first input register

• reg1_in – second input register

• reg_out – output register

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

add_c_copybits(*args, **kwargs)

Overloaded function.

1. add_c_copybits(self: pytket._tket.circuit.Circuit, args_in: Sequence[int], args_out: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Appends a classical copy operation

Parameters:

• args_in – source bits

• args_out – destination bits

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

2. add_c_copybits(self: pytket._tket.circuit.Circuit, args_in: Sequence[pytket._tket.unit_id.Bit], args_out: Sequence[pytket._tket.unit_id.Bit], **kwargs) -> pytket._tket.circuit.Circuit

See add_c_copybits().

add_c_copyreg(self: pytket._tket.circuit.Circuit, input_reg: pytket._tket.unit_id.BitRegister, output_reg: pytket._tket.unit_id.BitRegister, **kwargs) → pytket._tket.circuit.Circuit

Copy a classical register to another. Copying is truncated to the size of the smaller of the two registers.

add_c_modifier(*args, **kwargs)

Overloaded function.

1. add_c_modifier(self: pytket._tket.circuit.Circuit, values: Sequence[bool], args_in: Sequence[int], arg_inout: int, name: str = ‘ExplicitModifier’, **kwargs) -> pytket._tket.circuit.Circuit

Parameters:

• name – operation name

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

2. add_c_modifier(self: pytket._tket.circuit.Circuit, values: Sequence[bool], args_in: Sequence[pytket._tket.unit_id.Bit], arg_inout: pytket._tket.unit_id.Bit, name: str = ‘ExplicitModifier’, **kwargs) -> pytket._tket.circuit.Circuit

See add_c_modifier().

add_c_not(*args, **kwargs)

Overloaded function.

1. add_c_not(self: pytket._tket.circuit.Circuit, arg_in: int, arg_out: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a NOT operation to the end of the circuit.

Parameters:

• arg_in – input bit

• arg_out – output bit

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

2. add_c_not(self: pytket._tket.circuit.Circuit, arg_in: pytket._tket.unit_id.Bit, arg_out: pytket._tket.unit_id.Bit, **kwargs) -> pytket._tket.circuit.Circuit

See add_c_not().

add_c_not_to_registers(self: pytket._tket.circuit.Circuit, reg_in: pytket._tket.unit_id.BitRegister, reg_out: pytket._tket.unit_id.BitRegister, **kwargs) → pytket._tket.circuit.Circuit

Applies bitwise NOT to linear registers.

The operation is applied to the bits with indices 0, 1, 2, … in each register, up to the size of the smallest register.

Parameters:

• reg_in – input register

• reg_out – name of output register

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

add_c_or(*args, **kwargs)

Overloaded function.

1. add_c_or(self: pytket._tket.circuit.Circuit, arg0_in: int, arg1_in: int, arg_out: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a binary OR operation to the end of the circuit.

Parameters:

• arg0_in – first input bit

• arg1_in – second input bit

• arg_out – output bit

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

2. add_c_or(self: pytket._tket.circuit.Circuit, arg0_in: pytket._tket.unit_id.Bit, arg1_in: pytket._tket.unit_id.Bit, arg_out: pytket._tket.unit_id.Bit, **kwargs) -> pytket._tket.circuit.Circuit

See add_c_or().

add_c_or_to_registers(self: pytket._tket.circuit.Circuit, reg0_in: pytket._tket.unit_id.BitRegister, reg1_in: pytket._tket.unit_id.BitRegister, reg_out: pytket._tket.unit_id.BitRegister, **kwargs) → pytket._tket.circuit.Circuit

Applies bitwise OR to linear registers.

The operation is applied to the bits with indices 0, 1, 2, … in each register, up to the size of the smallest register.

Parameters:

• reg0_in – first input register

• reg1_in – second input register

• reg_out – output register

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

add_c_predicate(*args, **kwargs)

Overloaded function.

1. add_c_predicate(self: pytket._tket.circuit.Circuit, values: Sequence[bool], args_in: Sequence[int], arg_out: int, name: str = ‘ExplicitPredicate’, **kwargs) -> pytket._tket.circuit.Circuit

Parameters:

• name – operation name

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

2. add_c_predicate(self: pytket._tket.circuit.Circuit, values: Sequence[bool], args_in: Sequence[pytket._tket.unit_id.Bit], arg_out: pytket._tket.unit_id.Bit, name: str = ‘ExplicitPredicate’, **kwargs) -> pytket._tket.circuit.Circuit

See add_c_predicate().

add_c_range_predicate(*args, **kwargs)

Overloaded function.

1. add_c_range_predicate(self: pytket._tket.circuit.Circuit, minval: int, maxval: int, args_in: Sequence[int], arg_out: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a range-predicate operation to the end of the circuit.

Parameters:

• minval – lower bound of input in little-endian encoding

• maxval – upper bound of input in little-endian encoding

• args_in – input bits

• arg_out – output bit (distinct from input bits)

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

2. add_c_range_predicate(self: pytket._tket.circuit.Circuit, minval: int, maxval: int, args_in: Sequence[pytket._tket.unit_id.Bit], arg_out: pytket._tket.unit_id.Bit, **kwargs) -> pytket._tket.circuit.Circuit

Appends a range-predicate operation to the end of the circuit.

Parameters:

• minval – lower bound of input in little-endian encoding

• maxval – upper bound of input in little-endian encoding

• args_in – input bits

• arg_out – output bit (distinct from input bits)

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

add_c_register(*args, **kwargs)

Overloaded function.

1. add_c_register(self: pytket._tket.circuit.Circuit, name: str, size: int) -> pytket._tket.unit_id.BitRegister

Constructs a new classical register with a given name and number of bits.

Parameters:

• name – Unique readable name for the register

• size – Number of bits required

Returns:

a map from index to the corresponding UnitIDs

2. add_c_register(self: pytket._tket.circuit.Circuit, register: pytket._tket.unit_id.BitRegister) -> pytket._tket.unit_id.BitRegister

Adds BitRegister to Circuit

Parameters:

register – BitRegister

add_c_setbits(*args, **kwargs)

Overloaded function.

1. add_c_setbits(self: pytket._tket.circuit.Circuit, values: Sequence[bool], args: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Appends an operation to set some bit values.

Parameters:

• values – values to set

• args – bits to set

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

2. add_c_setbits(self: pytket._tket.circuit.Circuit, values: Sequence[bool], args: Sequence[pytket._tket.unit_id.Bit], **kwargs) -> pytket._tket.circuit.Circuit

See add_c_setbits().

add_c_setreg(self: pytket._tket.circuit.Circuit, value: int, arg: pytket._tket.unit_id.BitRegister, **kwargs) → pytket._tket.circuit.Circuit

Set a classical register to an unsigned integer value. The little-endian bitwise representation of the integer is truncated to the register size, up to _TKET_REG_WIDTH bit width. It is zero-padded if the width of the register is greater than _TKET_REG_WIDTH.

add_c_transform(*args, **kwargs)

Overloaded function.

1. add_c_transform(self: pytket._tket.circuit.Circuit, values: Sequence[int], args: Sequence[int], name: str = ‘ClassicalTransform’, **kwargs) -> pytket._tket.circuit.Circuit

Appends a purely classical transformation, defined by a table of values, to the end of the circuit.

Parameters:

• values – table of values: bit \(j\) (in little-endian order) of the term indexed by \(sum_i a_i 2^i\) is output \(j\) of the transform applied to inputs \((a_i)\).

• args – bits to which the transform is applied

• name – operation name

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

2. add_c_transform(self: pytket._tket.circuit.Circuit, values: Sequence[int], args: Sequence[pytket._tket.unit_id.Bit], name: str = ‘ClassicalTransform’, **kwargs) -> pytket._tket.circuit.Circuit

See add_c_transform().

add_c_xor(*args, **kwargs)

Overloaded function.

1. add_c_xor(self: pytket._tket.circuit.Circuit, arg0_in: int, arg1_in: int, arg_out: int, **kwargs) -> pytket._tket.circuit.Circuit

Appends a binary XOR operation to the end of the circuit.

Parameters:

• arg0_in – first input bit

• arg1_in – second input bit

• arg_out – output bit

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

2. add_c_xor(self: pytket._tket.circuit.Circuit, arg0_in: pytket._tket.unit_id.Bit, arg1_in: pytket._tket.unit_id.Bit, arg_out: pytket._tket.unit_id.Bit, **kwargs) -> pytket._tket.circuit.Circuit

See add_c_xor().

add_c_xor_to_registers(self: pytket._tket.circuit.Circuit, reg0_in: pytket._tket.unit_id.BitRegister, reg1_in: pytket._tket.unit_id.BitRegister, reg_out: pytket._tket.unit_id.BitRegister, **kwargs) → pytket._tket.circuit.Circuit

Applies bitwise XOR to linear registers.

The operation is applied to the bits with indices 0, 1, 2, … in each register, up to the size of the smallest register.

Parameters:

• reg0_in – first input register

• reg1_in – second input register

• reg_out – output register

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

add_circbox(*args, **kwargs)

Overloaded function.

1. add_circbox(self: pytket._tket.circuit.Circuit, circbox: pytket._tket.circuit.CircBox, args: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append a CircBox to the circuit.

The qubits and bits of the CircBox are wired into the circuit in lexicographic order. Bits follow qubits in the order of arguments.

Parameters:

• circbox – The box to append

• args – Indices of the (default-register) qubits/bits to append the box to

Returns:

the new Circuit

2. add_circbox(self: pytket._tket.circuit.Circuit, circbox: pytket._tket.circuit.CircBox, args: Sequence[pytket._tket.unit_id.UnitID], **kwargs) -> pytket._tket.circuit.Circuit

Append a CircBox to the circuit.

The qubits and bits of the CircBox are wired into the circuit in lexicographic order. Bits follow qubits in the order of arguments.

Parameters:

• circbox – The box to append

• args – The qubits/bits to append the box to

Returns:

the new Circuit

add_circbox_regwise(self: pytket._tket.circuit.Circuit, circbox: pytket._tket.circuit.CircBox, qregs: Sequence[pytket._tket.unit_id.QubitRegister], cregs: Sequence[pytket._tket.unit_id.BitRegister], **kwargs) → pytket._tket.circuit.Circuit

Append a CircBox to the circuit, wiring whole registers together.

Parameters:

• circbox – The box to append

• qregs – Sequence of QubitRegister from the outer Circuit, the order corresponding to the lexicographic order of corresponding registers in the CircBox

• cregs – Sequence of BitRegister from the outer Circuit, the order corresponding to the lexicographic order of corresponding registers in the CircBox

Returns:

the new Circuit

add_circbox_with_regmap(self: pytket._tket.circuit.Circuit, circbox: pytket._tket.circuit.CircBox, qregmap: dict[str, str], cregmap: dict[str, str], **kwargs) → pytket._tket.circuit.Circuit

Append a CircBox to the circuit, wiring whole registers together.

This method expects two maps (one for qubit registers and one for bit registers), which must have keys corresponding to all register names in the box. The box may not contain any qubits or bits that do not belong to a register, i.e. all must be single-indexed contiguously from zero.

Parameters:

• circbox – The box to append

• qregmap – Map specifying which qubit register in the CircBox (the map’s keys) matches which register in the outer circuit (the map’s values)

• cregmap – Map specifying which bit register in the CircBox (the map’s keys) matches which register in the outer circuit (the map’s values)

Returns:

the new Circuit

add_circuit(*args, **kwargs)

Overloaded function.

1. add_circuit(self: pytket._tket.circuit.Circuit, circuit: pytket._tket.circuit.Circuit, qubits: Sequence[pytket._tket.unit_id.Qubit], bits: Sequence[pytket._tket.unit_id.Bit] = []) -> pytket._tket.circuit.Circuit

In-place sequential composition of circuits, appending a copy of the argument onto the end of the circuit. Connects qubits and bits with the same behaviour as add_gate().

Parameters:

• circuit – The circuit to be appended to the end of self

• qubits – List mapping the (default register) qubits of circuit to the qubits of self

• bits – List mapping the (default register) bits of circuit to the bits of self

Returns:

the new Circuit

2. add_circuit(self: pytket._tket.circuit.Circuit, circuit: pytket._tket.circuit.Circuit, qubits: Sequence[int], bits: Sequence[int] = []) -> pytket._tket.circuit.Circuit

In-place sequential composition of circuits, appending a copy of the argument onto the end of the circuit. Connects qubits and bits with the same behaviour as add_gate().

Parameters:

• circuit – The circuit to be appended to the end of self

• qubits – List mapping the (default register) qubits of circuit to the (default register) qubits of self

• bits – List mapping the (default register) bits of circuit to the (default register) bits of self

Returns:

the new Circuit

add_classicalexpbox_bit(self: pytket._tket.circuit.Circuit, expression: pytket.circuit.logic_exp.BitLogicExp, target: Sequence[pytket._tket.unit_id.Bit], **kwargs) → pytket._tket.circuit.Circuit

Append a ClassicalExpBox over Bit to the circuit.

Parameters:

• classicalexpbox – The box to append

• args – Indices of the qubits to append the box to

Returns:

the new Circuit

add_classicalexpbox_register(self: pytket._tket.circuit.Circuit, expression: pytket.circuit.logic_exp.RegLogicExp, target: Sequence[pytket._tket.unit_id.Bit], **kwargs) → pytket._tket.circuit.Circuit

Append a ClassicalExpBox over BitRegister to the circuit.

Parameters:

• classicalexpbox – The box to append

• args – Indices of the qubits to append the box to

Returns:

the new Circuit

add_conditional_barrier(*args, **kwargs)

Overloaded function.

1. add_conditional_barrier(self: pytket._tket.circuit.Circuit, barrier_qubits: Sequence[int], barrier_bits: Sequence[int], condition_bits: Sequence[int], value: int, data: str = ‘’) -> pytket._tket.circuit.Circuit

Append a Conditional Barrier on the given barrier qubits and barrier bits, conditioned on the given condition bits.

Parameters:

• barrier_qubits – Qubit in Barrier operation.

• barrier_bits – Bit in Barrier operation.

• condition_bits – Bit covering classical control condition of barrier operation.

• value – Value that classical condition must have to hold (little-endian).

• data – Additional data stored in Barrier operation.

Returns:

the new Circuit

2. add_conditional_barrier(self: pytket._tket.circuit.Circuit, barrier_args: Sequence[pytket._tket.unit_id.UnitID], condition_bits: Sequence[pytket._tket.unit_id.Bit], value: int, data: str = ‘’) -> pytket._tket.circuit.Circuit

Append a Conditional Barrier on the given barrier qubits and barrier bits, conditioned on the given condition bits.

Parameters:

• barrier_args – Qubit and Bit in Barrier operation.

• condition_bits – Bit covering classical control condition of barrier operation.

• value – Value that classical condition must have to hold (little-endian).

• data – Additional data stored in Barrier operation.

Returns:

the new Circuit

add_conjugation_box(*args, **kwargs)

Overloaded function.

1. add_conjugation_box(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.ConjugationBox, args: Sequence[pytket._tket.unit_id.UnitID], **kwargs) -> pytket._tket.circuit.Circuit

Append a ConjugationBox to the circuit.

Parameters:

• box – The box to append

• args – The qubits to append the box to

Returns:

the new Circuit

2. add_conjugation_box(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.ConjugationBox, args: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append a ConjugationBox to the circuit.

Parameters:

• box – The box to append

• args – Indices of the qubits to append the box to

Returns:

the new Circuit

add_custom_gate(*args, **kwargs)

Overloaded function.

1. add_custom_gate(self: pytket._tket.circuit.Circuit, definition: pytket._tket.circuit.CustomGateDef, params: Sequence[typing.Union[sympy.Expr, float]], qubits: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append an instance of a CustomGateDef to the circuit.

Parameters:

• def – The custom gate definition

• params – List of parameters to instantiate the gate with, in halfturns

• qubits – Indices of the qubits to append the box to

Returns:

the new Circuit

2. add_custom_gate(self: pytket._tket.circuit.Circuit, definition: pytket._tket.circuit.CustomGateDef, params: Sequence[typing.Union[sympy.Expr, float]], qubits: Sequence[pytket._tket.unit_id.Qubit], **kwargs) -> pytket._tket.circuit.Circuit

Append an instance of a CustomGateDef to the circuit.

Parameters:

• def – The custom gate definition

• params – List of parameters to instantiate the gate with, in halfturns

• qubits – The qubits to append the box to

Returns:

the new Circuit

add_diagonal_box(*args, **kwargs)

Overloaded function.

1. add_diagonal_box(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.DiagonalBox, args: Sequence[pytket._tket.unit_id.UnitID], **kwargs) -> pytket._tket.circuit.Circuit

Append a DiagonalBox to the circuit.

Parameters:

• box – The box to append

• args – The qubits to append the box to

Returns:

the new Circuit

2. add_diagonal_box(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.DiagonalBox, args: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append a DiagonalBox to the circuit.

Parameters:

• box – The box to append

• args – Indices of the qubits to append the box to

Returns:

the new Circuit

add_dummybox(*args, **kwargs)

Overloaded function.

1. add_dummybox(self: pytket._tket.circuit.Circuit, dummybox: pytket._tket.circuit.DummyBox, qubits: Sequence[int], bits: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append a DummyBox to the circuit.

Parameters:

• dummybox – The box to append

• qubits – Indices (in the default register) of the qubits to append the box to

• bits – Indices of the bits (in the default register) to append the box to

Returns:

the new Circuit

2. add_dummybox(self: pytket._tket.circuit.Circuit, dummybox: pytket._tket.circuit.DummyBox, qubits: Sequence[pytket._tket.unit_id.Qubit], bits: Sequence[pytket._tket.unit_id.Bit], **kwargs) -> pytket._tket.circuit.Circuit

Append a DummyBox to the circuit.

Parameters:

• dummybox – The box to append

• qubits – Qubits to append the box to

• bits – Bits to append the box to

Returns:

the new Circuit

add_expbox(*args, **kwargs)

Overloaded function.

1. add_expbox(self: pytket._tket.circuit.Circuit, expbox: pytket._tket.circuit.ExpBox, qubit_0: int, qubit_1: int, **kwargs) -> pytket._tket.circuit.Circuit

Append an ExpBox to the circuit.

The matrix representation is ILO-BE.

Parameters:

• expbox – The box to append

• qubit_0 – Index of the first target qubit

• qubit_1 – Index of the second target qubit

Returns:

the new Circuit

2. add_expbox(self: pytket._tket.circuit.Circuit, expbox: pytket._tket.circuit.ExpBox, qubit_0: pytket._tket.unit_id.Qubit, qubit_1: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Append an ExpBox to the circuit.

The matrix representation is ILO-BE.

Parameters:

• expbox – The box to append

• qubit_0 – The first target qubit

• qubit_1 – The second target qubit

Returns:

the new Circuit

add_gate(*args, **kwargs)

Overloaded function.

1. add_gate(self: pytket._tket.circuit.Circuit, Op: pytket._tket.circuit.Op, args: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Appends a single operation to the end of the circuit on some particular qubits/bits. The number of qubits/bits specified must match the arity of the gate.

2. add_gate(self: pytket._tket.circuit.Circuit, Op: pytket._tket.circuit.Op, args: Sequence[pytket._tket.unit_id.UnitID], **kwargs) -> pytket._tket.circuit.Circuit

Appends a single operation to the end of the circuit on some particular qubits/bits. The number of qubits/bits specified must match the arity of the gate.

3. add_gate(self: pytket._tket.circuit.Circuit, type: pytket._tket.circuit.OpType, args: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Appends a single (non-parameterised) gate to the end of the circuit on some particular qubits from the default register (‘q’). The number of qubits specified must match the arity of the gate. For OpType.Measure operations the bit from the default register should follow the qubit.

>>> c.add_gate(OpType.H, [0]) # equivalent to c.H(0)
>>> c.add_gate(OpType.CX, [0,1]) # equivalent to c.CX(0,1)

Parameters:

• type – The type of operation to add

• args – The list of indices for the qubits/bits to which the operation is applied

• kwargs – Additional properties for classical conditions

Returns:

the new Circuit

4. add_gate(self: pytket._tket.circuit.Circuit, type: pytket._tket.circuit.OpType, args: Sequence[pytket._tket.unit_id.UnitID], **kwargs) -> pytket._tket.circuit.Circuit

Appends a single (non-parameterised) gate to the end of the circuit on some particular qubits from the default register (‘q’). The number of qubits specified must match the arity of the gate. For OpType.Measure operations the bit from the default register should follow the qubit.

>>> c.add_gate(OpType.H, [0]) # equivalent to c.H(0)
>>> c.add_gate(OpType.CX, [0,1]) # equivalent to c.CX(0,1)

Parameters:

• type – The type of operation to add

• args – The qubits/bits to apply the gate to

• kwargs – Additional properties for classical conditions

Returns:

the new Circuit

5. add_gate(self: pytket._tket.circuit.Circuit, type: pytket._tket.circuit.OpType, angle: typing.Union[sympy.Expr, float], args: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Appends a single gate, parameterised by an expression, to the end of circuit on some particular qubits from the default register (‘q’).

Parameters:

• type – The type of gate to add

• angle – The parameter for the gate in halfturns

• args – The list of indices for the qubits to which the operation is applied

• kwargs – Additional properties for classical conditions

Returns:

the new Circuit

6. add_gate(self: pytket._tket.circuit.Circuit, type: pytket._tket.circuit.OpType, angle: typing.Union[sympy.Expr, float], args: Sequence[pytket._tket.unit_id.UnitID], **kwargs) -> pytket._tket.circuit.Circuit

Appends a single gate, parameterised by an expression, to the end of circuit on some particular qubits from the default register (‘q’).

Parameters:

• type – The type of gate to add

• angle – The parameter for the gate in halfturns

• args – The qubits/bits to apply the gate to

• kwargs – Additional properties for classical conditions

Returns:

the new Circuit

7. add_gate(self: pytket._tket.circuit.Circuit, type: pytket._tket.circuit.OpType, angles: Sequence[typing.Union[sympy.Expr, float]], args: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Appends a single gate, parameterised with a vector of expressions corresponding to halfturns, to the end of circuit on some particular qubits from the default register (‘q’).

Parameters:

• type – The type of gate to add

• angles – The parameters for the gate in halfturns

• args – The list of indices for the qubits to which the operation is applied

• kwargs – Additional properties for classical conditions

Returns:

the new Circuit

8. add_gate(self: pytket._tket.circuit.Circuit, type: pytket._tket.circuit.OpType, angles: Sequence[typing.Union[sympy.Expr, float]], args: Sequence[pytket._tket.unit_id.UnitID], **kwargs) -> pytket._tket.circuit.Circuit

Appends a single gate to the end of the circuit

Parameters:

• type – The type of gate to add

• params – The parameters for the gate in halfturns

• args – The qubits/bits to apply the gate to

• kwargs – Additional properties for classical conditions

Returns:

the new Circuit

add_multiplexed_tensored_u2(*args, **kwargs)

Overloaded function.

1. add_multiplexed_tensored_u2(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.MultiplexedTensoredU2Box, args: Sequence[pytket._tket.unit_id.UnitID], **kwargs) -> pytket._tket.circuit.Circuit

Append a MultiplexedTensoredU2Box to the circuit.

Parameters:

• box – The box to append

• args – The qubits to append the box to

Returns:

the new Circuit

2. add_multiplexed_tensored_u2(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.MultiplexedTensoredU2Box, args: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append a MultiplexedTensoredU2Box to the circuit.

Parameters:

• box – The box to append

• args – Indices of the qubits to append the box to

Returns:

the new Circuit

add_multiplexedrotation(*args, **kwargs)

Overloaded function.

1. add_multiplexedrotation(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.MultiplexedRotationBox, args: Sequence[pytket._tket.unit_id.UnitID], **kwargs) -> pytket._tket.circuit.Circuit

Append a MultiplexedRotationBox to the circuit.

Parameters:

• box – The box to append

• args – The qubits to append the box to

Returns:

the new Circuit

2. add_multiplexedrotation(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.MultiplexedRotationBox, args: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append a MultiplexedRotationBox to the circuit.

Parameters:

• box – The box to append

• args – Indices of the qubits to append the box to

Returns:

the new Circuit

add_multiplexedu2(*args, **kwargs)

Overloaded function.

1. add_multiplexedu2(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.MultiplexedU2Box, args: Sequence[pytket._tket.unit_id.UnitID], **kwargs) -> pytket._tket.circuit.Circuit

Append a MultiplexedU2Box to the circuit.

Parameters:

• box – The box to append

• args – The qubits to append the box to

Returns:

the new Circuit

2. add_multiplexedu2(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.MultiplexedU2Box, args: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append a MultiplexedU2Box to the circuit.

Parameters:

• box – The box to append

• args – Indices of the qubits to append the box to

Returns:

the new Circuit

add_multiplexor(*args, **kwargs)

Overloaded function.

1. add_multiplexor(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.MultiplexorBox, args: Sequence[pytket._tket.unit_id.UnitID], **kwargs) -> pytket._tket.circuit.Circuit

Append a MultiplexorBox to the circuit.

Parameters:

• box – The box to append

• args – The qubits to append the box to

Returns:

the new Circuit

2. add_multiplexor(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.MultiplexorBox, args: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append a MultiplexorBox to the circuit.

Parameters:

• box – The box to append

• args – Indices of the qubits to append the box to

Returns:

the new Circuit

add_pauliexpbox(*args, **kwargs)

Overloaded function.

1. add_pauliexpbox(self: pytket._tket.circuit.Circuit, pauliexpbox: pytket._tket.circuit.PauliExpBox, qubits: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append a PauliExpBox to the circuit.

Parameters:

• pauliexpbox – The box to append

• qubits – Indices of the qubits to append the box to

Returns:

the new Circuit

2. add_pauliexpbox(self: pytket._tket.circuit.Circuit, pauliexpbox: pytket._tket.circuit.PauliExpBox, qubits: Sequence[pytket._tket.unit_id.Qubit], **kwargs) -> pytket._tket.circuit.Circuit

Append a PauliExpBox to the circuit.

Parameters:

• pauliexpbox – The box to append

• qubits – The qubits to append the box to

Returns:

the new Circuit

add_pauliexpcommutingsetbox(*args, **kwargs)

Overloaded function.

1. add_pauliexpcommutingsetbox(self: pytket._tket.circuit.Circuit, pauliexpcommutingsetbox: pytket._tket.circuit.PauliExpCommutingSetBox, qubits: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append a PauliExpCommutingSetBox to the circuit.

Parameters:

• pauliexpcommutingsetbox – The box to append

• qubits – Indices of the qubits to append the box to

Returns:

the new Circuit

2. add_pauliexpcommutingsetbox(self: pytket._tket.circuit.Circuit, pauliexpcommutingsetbox: pytket._tket.circuit.PauliExpCommutingSetBox, qubits: Sequence[pytket._tket.unit_id.Qubit], **kwargs) -> pytket._tket.circuit.Circuit

Append a PauliExpCommutingSetBox to the circuit.

Parameters:

• pauliexpcommutingsetbox – The box to append

• qubits – The qubits to append the box to

Returns:

the new Circuit

add_pauliexppairbox(*args, **kwargs)

Overloaded function.

1. add_pauliexppairbox(self: pytket._tket.circuit.Circuit, pauliexppairbox: pytket._tket.circuit.PauliExpPairBox, qubits: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append a PauliExpPairBox to the circuit.

Parameters:

• pauliexppairbox – The box to append

• qubits – Indices of the qubits to append the box to

Returns:

the new Circuit

2. add_pauliexppairbox(self: pytket._tket.circuit.Circuit, pauliexppairbox: pytket._tket.circuit.PauliExpPairBox, qubits: Sequence[pytket._tket.unit_id.Qubit], **kwargs) -> pytket._tket.circuit.Circuit

Append a PauliExpPairBox to the circuit.

Parameters:

• pauliexppairbox – The box to append

• qubits – The qubits to append the box to

Returns:

the new Circuit

add_phase(self: pytket._tket.circuit.Circuit, a: Union[sympy.Expr, float]) → pytket._tket.circuit.Circuit

Add a global phase to the circuit.

Parameters:

a – Phase to add, in halfturns

Returns:

circuit with added phase

add_phasepolybox(*args, **kwargs)

Overloaded function.

1. add_phasepolybox(self: pytket._tket.circuit.Circuit, phasepolybox: pytket._tket.circuit.PhasePolyBox, qubits: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append a PhasePolyBox to the circuit.

Parameters:

• phasepolybox – The box to append

• qubits – Indices of the qubits to append the box to

Returns:

the new Circuit

2. add_phasepolybox(self: pytket._tket.circuit.Circuit, phasepolybox: pytket._tket.circuit.PhasePolyBox, qubits: Sequence[pytket._tket.unit_id.Qubit], **kwargs) -> pytket._tket.circuit.Circuit

Append a PhasePolyBox to the circuit.

Parameters:

• phasepolybox – The box to append

• qubits – The qubits to append the box to

Returns:

the new Circuit

add_q_register(*args, **kwargs)

Overloaded function.

1. add_q_register(self: pytket._tket.circuit.Circuit, name: str, size: int) -> pytket._tket.unit_id.QubitRegister

Constructs a new quantum register with a given name and number of qubits.

Parameters:

• name – Unique readable name for the register

• size – Number of qubits required

Returns:

a map from index to the corresponding UnitIDs

2. add_q_register(self: pytket._tket.circuit.Circuit, register: pytket._tket.unit_id.QubitRegister) -> pytket._tket.unit_id.QubitRegister

Adds QubitRegister to Circuit

Parameters:

register – QubitRegister

add_qcontrolbox(*args, **kwargs)

Overloaded function.

1. add_qcontrolbox(self: pytket._tket.circuit.Circuit, qcontrolbox: pytket._tket.circuit.QControlBox, args: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append a QControlBox to the circuit.

Parameters:

• qcontrolbox – The box to append

• args – Indices of the qubits to append the box to

Returns:

the new Circuit

2. add_qcontrolbox(self: pytket._tket.circuit.Circuit, qcontrolbox: pytket._tket.circuit.QControlBox, args: Sequence[pytket._tket.unit_id.UnitID], **kwargs) -> pytket._tket.circuit.Circuit

Append a QControlBox to the circuit.

Parameters:

• qcontrolbox – The box to append

• args – The qubits to append the box to

Returns:

the new Circuit

add_qubit(self: pytket._tket.circuit.Circuit, id: pytket._tket.unit_id.Qubit, reject_dups: bool = True) → None

Constructs a single qubit with the given id.

Parameters:

• id – Unique id for the qubit

• reject_dups – Fail if there is already a qubit in this circuit with the id. Default to True

add_state_preparation_box(*args, **kwargs)

Overloaded function.

1. add_state_preparation_box(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.StatePreparationBox, args: Sequence[pytket._tket.unit_id.UnitID], **kwargs) -> pytket._tket.circuit.Circuit

Append a StatePreparationBox to the circuit.

Parameters:

• box – The box to append

• args – The qubits to append the box to

Returns:

the new Circuit

2. add_state_preparation_box(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.StatePreparationBox, args: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append a StatePreparationBox to the circuit.

Parameters:

• box – The box to append

• args – Indices of the qubits to append the box to

Returns:

the new Circuit

add_termsequencebox(*args, **kwargs)

Overloaded function.

1. add_termsequencebox(self: pytket._tket.circuit.Circuit, termsequencebox: pytket._tket.circuit.TermSequenceBox, qubits: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append a TermSequenceBox to the circuit.

Parameters:

• termsequencebox – The box to append

• qubits – Indices of the qubits to append the box to

Returns:

the new Circuit

2. add_termsequencebox(self: pytket._tket.circuit.Circuit, termsequencebox: pytket._tket.circuit.TermSequenceBox, qubits: Sequence[pytket._tket.unit_id.Qubit], **kwargs) -> pytket._tket.circuit.Circuit

Append a TermSequenceBox to the circuit.

Parameters:

• termsequencebox – The box to append

• qubits – The qubits to append the box to

Returns:

the new Circuit

add_toffolibox(*args, **kwargs)

Overloaded function.

1. add_toffolibox(self: pytket._tket.circuit.Circuit, toffolibox: pytket._tket.circuit.ToffoliBox, qubits: Sequence[int], **kwargs) -> pytket._tket.circuit.Circuit

Append a ToffoliBox to the circuit.

Parameters:

• toffolibox – The box to append

• qubits – Indices of the qubits to append the box to

Returns:

the new Circuit

2. add_toffolibox(self: pytket._tket.circuit.Circuit, toffolibox: pytket._tket.circuit.ToffoliBox, qubits: Sequence[pytket._tket.unit_id.Qubit], **kwargs) -> pytket._tket.circuit.Circuit

Append a ToffoliBox to the circuit.

Parameters:

• toffolibox – The box to append

• qubits – Indices of the qubits to append the box to

Returns:

the new Circuit

add_unitary1qbox(*args, **kwargs)

Overloaded function.

1. add_unitary1qbox(self: pytket._tket.circuit.Circuit, unitarybox: pytket._tket.circuit.Unitary1qBox, qubit_0: int, **kwargs) -> pytket._tket.circuit.Circuit

Append a Unitary1qBox to the circuit.

Parameters:

• unitarybox – The box to append

• qubit_0 – Index of the qubit to append the box to

Returns:

the new Circuit

2. add_unitary1qbox(self: pytket._tket.circuit.Circuit, unitarybox: pytket._tket.circuit.Unitary1qBox, qubit_0: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Append a Unitary1qBox to the circuit.

Parameters:

• unitarybox – The box to append

• qubit_0 – The qubit to append the box to

Returns:

the new Circuit

add_unitary2qbox(*args, **kwargs)

Overloaded function.

1. add_unitary2qbox(self: pytket._tket.circuit.Circuit, unitarybox: pytket._tket.circuit.Unitary2qBox, qubit_0: int, qubit_1: int, **kwargs) -> pytket._tket.circuit.Circuit

Append a Unitary2qBox to the circuit.

The matrix representation is ILO-BE.

Parameters:

• unitarybox – The box to append

• qubit_0 – Index of the first target qubit

• qubit_1 – Index of the second target qubit

Returns:

the new Circuit

2. add_unitary2qbox(self: pytket._tket.circuit.Circuit, unitarybox: pytket._tket.circuit.Unitary2qBox, qubit_0: pytket._tket.unit_id.Qubit, qubit_1: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Append a Unitary2qBox to the circuit.

The matrix representation is ILO-BE.

Parameters:

• unitarybox – The box to append

• qubit_0 – The first target qubit

• qubit_1 – The second target qubit

Returns:

the new Circuit

add_unitary3qbox(*args, **kwargs)

Overloaded function.

1. add_unitary3qbox(self: pytket._tket.circuit.Circuit, unitarybox: pytket._tket.circuit.Unitary3qBox, qubit_0: int, qubit_1: int, qubit_2: int, **kwargs) -> pytket._tket.circuit.Circuit

Append a Unitary3qBox to the circuit.

Parameters:

• unitarybox – box to append

• qubit_0 – index of target qubit 0

• qubit_1 – index of target qubit 1

• qubit_2 – index of target qubit 2

Returns:

the new Circuit

2. add_unitary3qbox(self: pytket._tket.circuit.Circuit, unitarybox: pytket._tket.circuit.Unitary3qBox, qubit_0: pytket._tket.unit_id.Qubit, qubit_1: pytket._tket.unit_id.Qubit, qubit_2: pytket._tket.unit_id.Qubit, **kwargs) -> pytket._tket.circuit.Circuit

Append a Unitary3qBox to the circuit.

Parameters:

• unitarybox – box to append

• qubit_0 – index of target qubit 0

• qubit_1 – index of target qubit 1

• qubit_2 – index of target qubit 2

Returns:

the new Circuit

add_wasm(funcname: str, filehandler: WasmFileHandler, list_i: Sequence[int], list_o: Sequence[int], args: Sequence[int] | Sequence[Bit], args_wasm: Sequence[int] | None = None, **kwargs: Any) → Circuit

Add a classical function call from a wasm file to the circuit.

Parameters:

• funcname – name of the function that is called

• filehandler – wasm file handler to identify the wasm file

• list_i – list of the number of bits in the input variables

• list_o – list of the number of bits in the output variables

• args – vector of circuit bits the wasm op should be added to

• args_wasm – vector of wasmstates the wasm op should be added to

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

add_wasm_to_reg(funcname: str, filehandler: WasmFileHandler, list_i: Sequence[BitRegister], list_o: Sequence[BitRegister], args_wasm: Sequence[int] | None = None, **kwargs: Any) → Circuit

Add a classical function call from a wasm file to the circuit.

Parameters:

• funcname – name of the function that is called

• filehandler – wasm file handler to identify the wasm file

• list_i – list of the classical registers assigned to the input variables of the function call

• list_o – list of the classical registers assigned to the output variables of the function call

• args_wasm – vector of wasmstates the wasm op should be added to

• kwargs – additional arguments passed to add_gate_method . Allowed parameters are opgroup, condition , condition_bits, condition_value

Returns:

the new Circuit

append(self: pytket._tket.circuit.Circuit, circuit: pytket._tket.circuit.Circuit) → None

In-place sequential composition of circuits, appending a copy of the argument onto the end of the circuit. Inputs and Outputs are unified if they share the same id, defaulting to parallel composition if there is no match.

Parameters:

circuit – The circuit to be appended to the end of self

property bit_readout

A map from bit to its (left-to-right) index in readouts from backends (following the increasing lexicographic order convention)

property bits

A list of all classical bit ids in the circuit

property c_registers

Get all classical registers.

The list only includes registers that are singly-indexed contiguously from zero.

Returns:

List of BitRegister

commands_of_type(self: pytket._tket.circuit.Circuit, optype: pytket._tket.circuit.OpType) → list[pytket._tket.circuit.Command]

Get all commands in a circuit of a given type.

The order is consistent with the causal order of the operations in the circuit.

Parameters:

optype – operation type

Returns:

list of Command

copy(self: pytket._tket.circuit.Circuit) → pytket._tket.circuit.Circuit

Returns:

an identical copy of the circuit

property created_qubits

A list of qubits whose input is a Create operation

dagger(self: pytket._tket.circuit.Circuit) → pytket._tket.circuit.Circuit

Given a pure circuit (i.e. without any measurements or conditional gates), produces a new circuit for the inverse/adjoint operation.

Returns:

a new Circuit corresponding to the inverse operation

depth(self: pytket._tket.circuit.Circuit) → int

Returns the number of interior vertices on the longest path through the DAG, excluding vertices representing barrier operations.

>>> c = Circuit(3)
>>> c.depth()
0
>>> c.CX(0,1)
>>> c.CX(1,2)
>>> c.CX(2,0)
>>> c.depth()
3

Returns:

the circuit depth

depth_2q(self: pytket._tket.circuit.Circuit) → int

Returns the number of vertices in the longest path through the sub-DAG consisting of vertices with 2 quantum wires,excluding vertices representing barrier operations.

>>> c = Circuit(3)
>>> c.CZ(0,1)
>>> c.Z(0)
>>> c.Z(1)
>>> c.ZZMax(1,2)
>>> c.CX(1,2)
>>> c.depth_2q()
3
:return: the circuit depth with respect to 2-qubit operations.

depth_by_type(*args, **kwargs)

Overloaded function.

1. depth_by_type(self: pytket._tket.circuit.Circuit, type: pytket._tket.circuit.OpType) -> int

Returns the number of vertices in the longest path through the sub-DAG consisting of vertices representing operations of the given type.

>>> c = Circuit(3)
>>> c.CX(0,1)
>>> c.Z(1)
>>> c.CX(1,2)
>>> c.depth_by_type(OpType.CX)
2

Parameters:

type – the operation type of interest

Returns:

the circuit depth with respect to operations matching type

2. depth_by_type(self: pytket._tket.circuit.Circuit, types: set[pytket._tket.circuit.OpType]) -> int

Returns the number of vertices in the longest path through the sub-DAG consisting of vertices representing operations of the given types.

>>> c = Circuit(3)
>>> c.CZ(0,1)
>>> c.Z(1)
>>> c.CX(1,2)
>>> c.depth_by_type({OpType.CZ, OpType.CX})
2

Parameters:

types – the set of operation types of interest

Returns:

the circuit depth with respect to operations matching an element of types

property discarded_qubits

A list of qubits whose output is a Discard operation

flatten_registers(self: pytket._tket.circuit.Circuit) → dict[pytket._tket.unit_id.UnitID, pytket._tket.unit_id.UnitID]

Combines all qubits into a single register namespace with the default name, and likewise for bits

free_symbols(self: pytket._tket.circuit.Circuit) → set[sympy.Symbol]

Returns:

set of symbolic parameters in the circuit

static from_dict(arg0: dict) → pytket._tket.circuit.Circuit

Construct Circuit instance from JSON serializable dictionary representation of the Circuit.

get_c_register(self: pytket._tket.circuit.Circuit, name: str) → pytket._tket.unit_id.BitRegister

Get the classical register with the given name.

Parameters:

name – name for the register

Returns:

the retrieved BitRegister

get_commands(self: pytket._tket.circuit.Circuit) → list[pytket._tket.circuit.Command]

Returns:

a list of all the Commands in the circuit

get_counts(*others: Circuit, backend=None, **params) → list[numpy.ndarray]

Runs a circuit on a backend and returns the counts.

get_q_register(self: pytket._tket.circuit.Circuit, name: str) → pytket._tket.unit_id.QubitRegister

Get the quantum register with the given name.

Parameters:

name – name for the register

Returns:

the retrieved QubitRegister

get_resources(self: pytket._tket.circuit.Circuit) → pytket._tket.circuit.ResourceData

Calculate the overall resources of the circuit.

This takes account of the data stored in each py:class:DummyBox within the circuit, as well as other gates, to compute upper and lower bounds.

Returns:

bounds on resources of the circuit

>>> resource_data0 = ResourceData(
...     op_type_count={
...         OpType.T: ResourceBounds(1, 2),
...         OpType.H: ResourceBounds(0, 1),
...         OpType.CX: ResourceBounds(1, 2),
...         OpType.CZ: ResourceBounds(3, 3),
...     },
...     gate_depth=ResourceBounds(5, 8),
...     op_type_depth={
...         OpType.T: ResourceBounds(0, 10),
...         OpType.H: ResourceBounds(0, 10),
...         OpType.CX: ResourceBounds(1, 2),
...         OpType.CZ: ResourceBounds(3, 3),
...     },
...     two_qubit_gate_depth=ResourceBounds(4, 5),
... )
>>> dbox0 = DummyBox(n_qubits=2, n_bits=0, resource_data=resource_data0)
>>> resource_data1 = ResourceData(
...     op_type_count={
...         OpType.T: ResourceBounds(2, 2),
...         OpType.H: ResourceBounds(1, 1),
...         OpType.CX: ResourceBounds(2, 3),
...         OpType.CZ: ResourceBounds(3, 5),
...     },
...     gate_depth=ResourceBounds(5, 10),
...     op_type_depth={
...         OpType.T: ResourceBounds(1, 2),
...         OpType.H: ResourceBounds(2, 4),
...         OpType.CX: ResourceBounds(1, 1),
...         OpType.CZ: ResourceBounds(3, 4),
...     },
...     two_qubit_gate_depth=ResourceBounds(3, 5),
... )
>>> dbox1 = DummyBox(n_qubits=3, n_bits=0, resource_data=resource_data1)
>>> c = (
...     Circuit(3)
...     .H(0)
...     .CX(1, 2)
...     .CX(0, 1)
...     .T(2)
...     .H(1)
...     .add_dummybox(dbox0, [0, 1], [])
...     .CZ(1, 2)
...     .add_dummybox(dbox1, [0, 1, 2], [])
...     .H(2)
... )
>>> resource_data = c.get_resources()
>>> print(resource_data)
ResourceData(op_type_count={OpType.T: ResourceBounds(4, 5), OpType.H: ResourceBounds(4, 5), OpType.CX: ResourceBounds(5, 7), OpType.CZ: ResourceBounds(7, 9), }, gate_depth=ResourceBounds(15, 23), op_type_depth={OpType.T: ResourceBounds(2, 12), OpType.H: ResourceBounds(5, 17), OpType.CX: ResourceBounds(4, 5), OpType.CZ: ResourceBounds(7, 8), }, two_qubit_gate_depth=ResourceBounds(10, 13))

get_statevector(self: pytket._tket.circuit.Circuit) → numpy.ndarray[numpy.complex128[m, 1]]

Calculate the unitary matrix of the circuit, using ILO-BE convention, applied to the column vector (1,0,0…), which is thus another column vector. Due to pybind11 and numpy peculiarities, to treat the result as a genuine column vector and perform further matrix multiplication, you need to call .reshape(rows,1) to get a 2D matrix with the correct dimensions.

Returns:

The calculated vector.

get_unitary(self: pytket._tket.circuit.Circuit) → numpy.ndarray[numpy.complex128[m, n]]

Returns:

The numerical unitary matrix of the circuit, using ILO-BE convention.

get_unitary_times_other(self: pytket._tket.circuit.Circuit, matr: numpy.ndarray[numpy.complex128[m, n]]) → numpy.ndarray[numpy.complex128[m, n]]

Calculate UM, where U is the numerical unitary matrix of the circuit, with ILO-BE convention, and M is another matrix. This is more efficient than calculating U separately, if M has fewer columns than U.

Parameters:

matr – The matrix to be multiplied.

Returns:

The product of the circuit unitary and the given matrix.

implicit_qubit_permutation(self: pytket._tket.circuit.Circuit) → dict[pytket._tket.unit_id.Qubit, pytket._tket.unit_id.Qubit]

Returns:

dictionary mapping input qubit to output qubit on the same path

property is_simple

Checks that the circuit has only 1 quantum and 1 classic register using the default names (‘q’ and ‘c’). This means it is suitable to refer to qubits simply by their integer indices.

is_symbolic(self: pytket._tket.circuit.Circuit) → bool

Returns:

True if the circuit contains any free symbols, False otherwise.

measure_all(self: pytket._tket.circuit.Circuit) → pytket._tket.circuit.Circuit

Appends a measure gate to all qubits, storing the results in the default classical register. Bits are added to the circuit if they do not already exist.

Returns:

the new Circuit

measure_register(self: pytket._tket.circuit.Circuit, arg0: pytket._tket.unit_id.QubitRegister, arg1: str) → pytket._tket.circuit.Circuit

Appends a measure gate to all qubits in the given register, storing the results in the given classical register with matching indices.The classical register will be created if it doesn’t exist.

Parameters:

• qreg – the QubitRegister to be measured

• creg_name – the name of the BitRegister to store the results

Returns:

the new Circuit

n_1qb_gates(self: pytket._tket.circuit.Circuit) → int

Returns the number of vertices in the dag with one quantum edge.Ignores Input, Create, Output, Discard, Reset, Measure and Barrier vertices.

n_2qb_gates(self: pytket._tket.circuit.Circuit) → int

Returns the number of vertices in the dag with two quantum edges.Ignores Input, Create, Output, Discard, Reset, Measure and Barrier vertices.

property n_bits: int

Number of bits in a circuit.

property n_gates

Returns:

the number of gates in the Circuit

n_gates_of_type(self: pytket._tket.circuit.Circuit, type: pytket._tket.circuit.OpType) → int

Returns the number of vertices in the dag of a given operation type.

>>> c.CX(0,1)
>>> c.H(0)
>>> c.CX(0,1)
>>> c.n_gates_of_type(OpType.CX)
2

Parameters:

type – The operation type to search for

Returns:

the number of operations matching type

n_nqb_gates(self: pytket._tket.circuit.Circuit, size: int) → int

Returns the number of vertices in the dag with given number of quantum edges.Ignores Input, Create, Output, Discard, Reset, Measure and Barrier vertices.

property n_qubits

Returns:

the number of qubits in the circuit

property name

property opgroups

A set of all opgroup names in the circuit

ops_of_type(self: pytket._tket.circuit.Circuit, optype: pytket._tket.circuit.OpType) → list[pytket._tket.circuit.Op]

Get all operations in the circuit of a given type.

The order is not guaranteed.

Parameters:

optype – operation type

Returns:

list of Op

property phase

Returns:

the global phase applied to the circuit, in halfturns (not meaningful for circuits with classical interactions)

post_process(process: Diagram) → Self

Classical post-processing.

post_select(post_selection: dict[int, int]) → Self

Post-select bits on a a given value.

property q_registers

Get all quantum registers.

The list only includes registers that are singly-indexed contiguously from zero.

Returns:

List of QubitRegister

qubit_create(self: pytket._tket.circuit.Circuit, arg0: pytket._tket.unit_id.Qubit) → None

Make a quantum input a Create operation (initialized to 0

qubit_create_all(self: pytket._tket.circuit.Circuit) → None

Make all quantum inputs Create operations (initialized to 0)

qubit_discard(self: pytket._tket.circuit.Circuit, arg0: pytket._tket.unit_id.Qubit) → None

Make a quantum output a Discard operation

qubit_discard_all(self: pytket._tket.circuit.Circuit) → None

Make all quantum outputs Discard operations

qubit_is_created(self: pytket._tket.circuit.Circuit, arg0: pytket._tket.unit_id.Qubit) → bool

Query whether a qubit has its initial state set to zero

qubit_is_discarded(self: pytket._tket.circuit.Circuit, arg0: pytket._tket.unit_id.Qubit) → bool

Query whether a qubit has its final state discarded

property qubit_readout

A map from qubit to its (left-to-right) index in readouts from backends. A qubit will feature in this map if it is measured and neither it nor the bit containing the measurement result is subsequently acted on

property qubit_to_bit_map

A map from qubit to the bit it is measured to. A qubit will feature in this map if it is measured and neither it nor the bit containing the measurement result is subsequently acted on

property qubits

A list of all qubit ids in the circuit

remove_blank_wires(self: pytket._tket.circuit.Circuit, keep_blank_classical_wires: bool = False) → None

Removes any Input-Output pairs in the DAG with no intervening operations, i.e. removes untouched qubits/bits from the circuit. This may occur when optimisations recognise that the operations on a qubit reduce to the identity, or when routing adds wires to “fill out” the architecture. This operation will only remove empty classical wires if there are no used bits with a higher index in the same register.

Parameters:

keep_blank_classical_wires – select if empty classical wires should not be removed

rename_units(renaming)

Rename units in a circuit.

replace_SWAPs(self: pytket._tket.circuit.Circuit) → None

Replace all SWAP gates with implicit wire swaps.

replace_implicit_wire_swaps(self: pytket._tket.circuit.Circuit) → None

Replace all implicit wire swaps with SWAP gates.

scale(number: float) → Self

Scale a circuit by a given number.

substitute_named(*args, **kwargs)

Overloaded function.

1. substitute_named(self: pytket._tket.circuit.Circuit, op: pytket._tket.circuit.Op, opgroup: str) -> bool

Substitute all ops with the given name for the given op.The replacement operations retain the same name.

Parameters:

• op – the replacement operation

• opgroup – the name of the operations group to replace

Returns:

whether any replacements were made

2. substitute_named(self: pytket._tket.circuit.Circuit, repl: pytket._tket.circuit.Circuit, opgroup: str) -> bool

Substitute all ops with the given name for the given circuit.Named operations in the replacement circuit must not match any named operations in the circuit being modified.

Parameters:

• repl – the replacement circuit

• opgroup – the name of the operations group to replace

Returns:

whether any replacements were made

3. substitute_named(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.CircBox, opgroup: str) -> bool

Substitute all ops with the given name for the given box.The replacement boxes retain the same name.

Parameters:

• box – the replacement CircBox

• opgroup – the name of the operations group to replace

Returns:

whether any replacements were made

4. substitute_named(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.Unitary1qBox, opgroup: str) -> bool

Substitute all ops with the given name for the given box.The replacement boxes retain the same name.

Parameters:

• box – the replacement Unitary1qBox

• opgroup – the name of the operations group to replace

Returns:

whether any replacements were made

5. substitute_named(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.Unitary2qBox, opgroup: str) -> bool

Substitute all ops with the given name for the given box.The replacement boxes retain the same name.

Parameters:

• box – the replacement Unitary2qBox

• opgroup – the name of the operations group to replace

Returns:

whether any replacements were made

6. substitute_named(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.Unitary3qBox, opgroup: str) -> bool

Substitute all ops with the given name for the given box.The replacement boxes retain the same name.

Parameters:

• box – the replacement Unitary3qBox

• opgroup – the name of the operations group to replace

Returns:

whether any replacements were made

7. substitute_named(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.ExpBox, opgroup: str) -> bool

Substitute all ops with the given name for the given box.The replacement boxes retain the same name.

Parameters:

• box – the replacement ExpBox

• opgroup – the name of the operations group to replace

Returns:

whether any replacements were made

8. substitute_named(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.PauliExpBox, opgroup: str) -> bool

Substitute all ops with the given name for the given box.The replacement boxes retain the same name.

Parameters:

• box – the replacement PauliExpBox

• opgroup – the name of the operations group to replace

Returns:

whether any replacements were made

9. substitute_named(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.ToffoliBox, opgroup: str) -> bool

Substitute all ops with the given name for the given box.The replacement boxes retain the same name.

Parameters:

• box – the replacement ToffoliBox

• opgroup – the name of the operations group to replace

Returns:

whether any replacements were made

10. substitute_named(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.DummyBox, opgroup: str) -> bool

Substitute all ops with the given name for the given box.The replacement boxes retain the same name.

Parameters:

• box – the replacement DummyBox

• opgroup – the name of the operations group to replace

Returns:

whether any replacements were made

11. substitute_named(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.QControlBox, opgroup: str) -> bool

Substitute all ops with the given name for the given box.The replacement boxes retain the same name.

Parameters:

• box – the replacement QControlBox

• opgroup – the name of the operations group to replace

Returns:

whether any replacements were made

12. substitute_named(self: pytket._tket.circuit.Circuit, box: pytket._tket.circuit.CustomGate, opgroup: str) -> bool

Substitute all ops with the given name for the given box.The replacement boxes retain the same name.

Parameters:

• box – the replacement CustomGate

• opgroup – the name of the operations group to replace

Returns:

whether any replacements were made

symbol_substitution(*args, **kwargs)

Overloaded function.

1. symbol_substitution(self: pytket._tket.circuit.Circuit, symbol_map: dict[sympy.Symbol, typing.Union[sympy.Expr, float]]) -> None

In-place substitution for symbolic expressions; iterates through each parameterised gate/box and performs the substitution.

Parameters:

symbol_map – A map from SymPy symbols to SymPy expressions

2. symbol_substitution(self: pytket._tket.circuit.Circuit, symbol_map: dict[sympy.Symbol, float]) -> None

In-place substitution for symbolic expressions; iterates through each gate/box and performs the substitution.

Parameters:

symbol_map – A map from SymPy symbols to floating-point values

to_dict(self: pytket._tket.circuit.Circuit) → dict

Returns:

a JSON serializable dictionary representation of the Circuit

to_latex_file(self: pytket._tket.circuit.Circuit, filename: str) → None

Produces a latex file with a visualisation of the circuit using the Quantikz package.

Parameters:

filename – Name of file to write output to (must end in “.tex”)

transpose(self: pytket._tket.circuit.Circuit) → pytket._tket.circuit.Circuit

Given a pure circuit (i.e. without any measurements or conditional gates), produces a new circuit for the transpose operation.

Returns:

a new Circuit corresponding to the transpose operation

static upgrade(tk_circuit) → Circuit

Takes a pytket.Circuit, returns a Circuit.

valid_connectivity(self: pytket._tket.circuit.Circuit, arch: pytket._tket.architecture.Architecture, directed: bool, allow_bridge: bool = False) → bool

Confirms whether all two qubit gates in given circuit are along some edge of the architecture.

Parameters:

• arch – The architecture capturing the desired connectivity

• directed – If true, also checks that CX or ECR gates are in the same direction as the edges of the architecture

• allow_bridge – Accept BRIDGEs as valid, assuming the middle qubit neighbours the others

Returns:

True or False

lambeq.backend.converters.tk.from_tk(tk_circuit: Circuit) → Diagram

Translates from tket to a lambeq Diagram.

lambeq.backend.converters.tk.to_tk(circuit: Diagram)

Takes a lambeq.quantum.Diagram, returns a Circuit.

lambeq.backend.pennylane

PennyLane interface

Lambeq’s interface with Pennylane circuits. This work is based on DisCoPy (https://discopy.org/) which is released under the BSD 3-Clause ‘New’ or ‘Revised’ License.

Notes

If probabilities is set to False, the output states of the PennyLane circuit will be exactly equivalent to those of the lambeq circuit (for the same parameters).

If probabilities is set to True, the output states of the PennyLane circuit will be the probabilities of the output states, equivalent to appending lambeq.backend.quantum.Measure to all the open wires in the lambeq circuit.

Once a PennyLaneCircuit has been constructed, it can be evaluated with eval(). If the circuit contains only concrete parameters (i.e. no symbolic parameters), no arguments should be passed to eval(). If the circuit contains symbolic parameters, a list of the symbolic parameters and a list of their associated weights should be passed to eval() as symbols= and weights=.

class lambeq.backend.pennylane.PennyLaneCircuit(ops, symbols, params, wires, probabilities, post_selection, scale, n_qubits, backend_config, diff_method)

Bases: object

Implement a pennylane circuit with post-selection.

__init__(ops, symbols, params, wires, probabilities, post_selection, scale, n_qubits, backend_config, diff_method)

contains_sympy()

Determine if the circuit parameters are concrete or contain SymPy symbols.

Returns:

bool

Whether the circuit parameters contain SymPy symbols.

draw()

Print a string representation of the circuit similar to qml.draw, but including post-selection.

Parameters:

symbolslist of sympy.core.symbol.Symbol, default: None

The symbols from the original lambeq circuit.

weightslist of torch.FloatTensor, default: None

The weights to substitute for the symbols.

eval()

Evaluate the circuit. The symbols should be those from the original lambeq diagram, which will be substituted for the concrete parameters in weights.

Parameters:

symbolslist of sympy.core.symbol.Symbol, default: None

The symbols from the original lambeq circuit.

weightslist of torch.FloatTensor, default: None

The weights to substitute for the symbols.

Returns:

torch.Tensor

The post-selected output of the circuit.

get_device(backend_config)

Return a PennyLane device with the specified backend configuration.

get_valid_states()

Determine which of the output states of the circuit are compatible with the post-selections.

Returns:

list of int

The indices of the circuit output that are compatible with the post-selections.

initialise_concrete_params(symbol_weight_map)

Given concrete values for each of the SymPy symbols, substitute the symbols for the values to obtain concrete parameters, via the param_substitution method.

initialise_device_and_circuit()

Initialise the PennyLane device and circuit when instantiating the PennyLaneCirucit, or loading from disk.

make_circuit()

Construct the qml.Qnode, a circuit that can be used with autograd to construct hybrid models.

Returns:

qml.Qnode

A Pennylane circuit without post-selection.

param_substitution(weights)

Substitute symbolic parameters (SymPy symbols) with floats.

Parameters:

weightslist of torch.FloatTensor

The weights to substitute for the symbols.

Returns:

torch.FloatTensor

The concrete (non-symbolic) parameters for the circuit.

post_selected_circuit(params)

Run the circuit with the given parameters and return the post-selected output.

Parameters:

paramstorch.FloatTensor

The concrete parameters for the gates in the circuit.

Returns:

torch.Tensor

The post-selected output of the circuit.

lambeq.backend.pennylane.extract_ops_from_tk(tk_circ)

Extract the operations, and corresponding parameters and wires, from a pytket Circuit. Return these as lists to use in constructing PennyLane circuit.

Parameters:

tk_circlambeq.backend.converters.tk.Circuit

The pytket circuit to extract the operations from.

Returns:

list of qml.operation.Operation

The PennyLane operations extracted from the pytket circuit.

list of list of (torch.FloatTensor or

sympy.core.symbol.Symbol)

The corresponding parameters of the operations.

list of list of int

The corresponding wires of the operations.

set of sympy.core.symbol.Symbol

The free symbols in the parameters of the tket circuit.

lambeq.backend.pennylane.get_post_selection_dict(tk_circ)

Return post-selections based on qubit indices.

Parameters:

tk_circlambeq.backend.converters.tk.Circuit

The pytket circuit to extract the post-selections from.

Returns:

dict of int

A mapping from qubit indices to pytket classical indices.

lambeq.backend.pennylane.tk_op_to_pennylane(tk_op)

Extract the operation, parameters and wires from a pytket Op, and return the corresponding PennyLane operation.

Parameters:

tk_oppytket.circuit.Op

The pytket Op to convert.

Returns:

qml.operation.Operation

The PennyLane operation equivalent to the input pytket Op.

list of (torch.FloatTensor or

sympy.core.symbol.Symbol)

The parameters of the operation.

list of sympy.core.symbol.Symbol

The free symbols in the parameters of the operation.

list of int

The wires/qubits to apply the operation to.

lambeq.backend.pennylane.to_pennylane(lambeq_circuit: Diagram, probabilities=False, backend_config=None, diff_method='best')

Return a PennyLaneCircuit equivalent to the input lambeq circuit. probabilities determines whether the PennyLaneCircuit returns states (as in lambeq), or probabilities (to be more compatible with automatic differentiation in PennyLane).

Parameters:

lambeq_circuitlambeq.backend.quantum.Diagram

The lambeq circuit to convert to PennyLane.

probabilitiesbool, default: False

Determines whether the PennyLane circuit outputs states or un-normalized probabilities. Probabilities can be used with more PennyLane backpropagation methods.

backend_configdict, default: None

A dictionary of PennyLane backend configration options, including the provider (e.g. IBM or Honeywell), the device, the number of shots, etc. See the PennyLane plugin documentation for more details.

diff_methodstr, default: “best”

The differentiation method to use to obtain gradients for the PennyLane circuit. Some gradient methods are only compatible with simulated circuits. See the PennyLane documentation for more details.

Returns:

PennyLaneCircuit

The PennyLane circuit equivalent to the input lambeq circuit.

lambeq.backend.drawing

lambeq’s drawing module.

class lambeq.backend.drawing.DrawableDiagram(boxes: list[lambeq.backend.drawing.drawable.BoxNode] = <factory>, wire_endpoints: list[lambeq.backend.drawing.drawable.WireEndpoint] = <factory>, wires: list[tuple[int, int]] = <factory>)

Bases: object

Representation of a lambeq diagram carrying all information necessary to render it.

Attributes:

boxes: list of BoxNode

Boxes in the diagram.

wire_endpoints: list of WireEndpoint

Endpoints for all wires in the diagram.

wires: list of tuple of the form (int, int)

The wires in a diagram, each represented by the indices of its 2 endpoints in wire_endpoints.

__init__(boxes: list[lambeq.backend.drawing.drawable.BoxNode] = <factory>, wire_endpoints: list[lambeq.backend.drawing.drawable.WireEndpoint] = <factory>, wires: list[tuple[int, int]] = <factory>) → None

boxes: list[lambeq.backend.drawing.drawable.BoxNode]

classmethod from_diagram(diagram: Diagram, foliated: bool = False) → Self

Builds a graph representation of the diagram, calculating coordinates for each box and wire.

Parameters:

diagramgrammar Diagram

A lambeq diagram.

foliatedbool, default: False

If true, each box of the diagram is drawn in a separate layer. By default boxes are compressed upwards into available space.

Returns:

drawableDrawableDiagram

Representation of diagram including all coordinates necessary to draw it.

scale_and_pad(scale: tuple[float, float], pad: tuple[float, float])

Scales and pads the diagram as specified.

Parameters:

scaletuple of 2 floats

Scaling factors for x and y axes respectively.

padtuple of 2 floats

Padding values for x and y axes respectively.

wire_endpoints: list[lambeq.backend.drawing.drawable.WireEndpoint]

wires: list[tuple[int, int]]

lambeq.backend.drawing.draw(diagram: Diagram, **params) → None

Draw a grammar diagram.

Parameters:

diagram: Diagram

Diagram to draw.

draw_as_nodesbool, optional

Whether to draw boxes as nodes, default is False.

colorstring, optional

Color of the box or node, default is white (‘#ffffff’) for boxes and red (‘#ff0000’) for nodes.

textpadpair of floats, optional

Padding between text and wires, default is (0.1, 0.1).

draw_type_labelsbool, optional

Whether to draw type labels, default is True.

draw_box_labelsbool, optional

Whether to draw box labels, default is True.

aspectstring, optional

Aspect ratio, one of [‘auto’, ‘equal’].

marginstuple, optional

Margins, default is (0.05, 0.05).

nodesizefloat, optional

BoxNode size for spiders and controlled gates.

fontsizeint, optional

Font size for the boxes, default is 12.

fontsize_typesint, optional

Font size for the types, default is 12.

figsizetuple, optional

Figure size.

pathstr, optional

Where to save the image, if None we call plt.show().

to_tikzbool, optional

Whether to output tikz code instead of matplotlib.

asymmetryfloat, optional

Make a box and its dagger mirror images, default is .25 * any(box.is_dagger for box in diagram.boxes).

foliatedbool, default: False

If true, each box of the diagram is drawn in a separate layer. By default boxes are compressed upwards into available space.

lambeq.backend.drawing.draw_equation(*terms: Diagram, symbol: str = '=', space: float = 1, path: str | None = None, **params) → None

Draw an equation with multiple diagrams.

Parameters:

terms: list of Diagrams

Diagrams in equation.

symbol: str

Symbol separating equations. ‘=’ by default.

space: float

Amount of space between adjacent diagrams.

pathstr, optional

Where to save the image, if None we call plt.show().

**params:

Additional drawing parameters, passed to draw().

lambeq.backend.drawing.draw_pregroup(diagram: Diagram, **params) → None

Draw a pregroup grammar diagram.

A pregroup diagram is structured as:

(State @ State … State) >> (Cups and Swaps)

Parameters:

diagram: Diagram

Diagram to draw.

draw_as_nodesbool, optional

Whether to draw boxes as nodes, default is False.

colorstring, optional

Color of the box or node, default is white (‘#ffffff’) for boxes and red (‘#ff0000’) for nodes.

textpadpair of floats, optional

Padding between text and wires, default is (0.1, 0.1).

aspectstring, optional

Aspect ratio, one of [‘auto’, ‘equal’].

marginstuple, optional

Margins, default is (0.05, 0.05).

fontsizeint, optional

Font size for the boxes, default is 12.

fontsize_typesint, optional

Font size for the types, default is 12.

figsizetuple, optional

Figure size.

pathstr, optional

Where to save the image, if None we call plt.show().

to_tikzbool, optional

Whether to output tikz code instead of matplotlib.

lambeq.backend.drawing.render_as_str(diagram: Diagram, word_spacing: int = 2, use_at_separator: bool = False, compress_layers: bool = True, use_ascii: bool = False) → str

Render a grammar diagram as text.

Presently only implemented for pregroup diagrams.

Parameters:

diagram: Diagram

Diagram to draw.

word_spacingint, default: 2

The number of spaces between the words of the diagrams.

use_at_separatorbool, default: False

Whether to represent types using @ as the monoidal product. Otherwise, use the unicode dot character.

compress_layersbool, default: True

Whether to draw boxes in the same layer when they can occur simultaneously, otherwise, draw one box per layer.

use_ascii: bool, default: False

Whether to draw using ASCII characters only, for compatibility reasons.

Returns:

str

Drawing of diagram in string format.

lambeq.backend.drawing.to_gif(diagrams: list[Diagram], path: str | None = None, timestep: int = 500, loop: bool = False, **params) → str | HTML_ty

Build a GIF stepping through the given diagrams.

Parameters:

diagrams: list of Diagrams

Sequence of diagrams to draw.

pathstr

Where to save the image, if None a gif gets created.

timestepint, optional

Time step in milliseconds, default is 500.

loopbool, optional

Whether to loop, default is False

paramsany, optional

Passed to Diagram.draw.

Returns:

IPython.display.HTML or str

HTML to display the generated GIF

lambeq.backend.snake_removal

Snake removal

This module contains a function for removing snakes from diagrams. This work is based on DisCoPy (https://discopy.org/) which is released under the BSD 3-Clause “New” or “Revised” License.

exception lambeq.backend.snake_removal.InterchangerError(box0: Box, box1: Box)

Bases: Exception

This is raised when we try to interchange conected boxes.

__init__(box0: Box, box1: Box) → None

add_note()

Exception.add_note(note) – add a note to the exception

args

with_traceback()

Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.

lambeq.backend.snake_removal.interchange(diagram: Diagram, i: int, j: int, left: bool = False) → Diagram

Returns a new diagram with boxes i and j interchanged.

Gets called recursively whenever i < j + 1 or j < i - 1.

Parameters:

diagramDiagram

The diagram to interchange boxes in.

iint

Index of the box to interchange.

jint

Index of the new position for the box.

leftbool, optional

Whether to apply left interchangers.

Notes

By default, we apply only right exchange moves:

top >> Id(left @ box1.dom @ mid) @ box0 @ Id(right)
    >> Id(left) @ box1 @ Id(mid @ box0.cod @ right)
    >> bottom

gets rewritten to:

top >> Id(left) @ box1 @ Id(mid @ box0.dom @ right)
    >> Id(left @ box1.cod @ mid) @ box0 @ Id(right)
    >> bottom

lambeq.backend.snake_removal.normalize(diagram: Diagram, left: bool = False) → Iterator[Diagram]

Implements normalization of diagrams, see arXiv:1804.07832.

Parameters:

diagramDiagram

The diagram to normalize.

leftbool, optional

Passed to interchange().

Yields:

diagramDiagram

Rewrite steps.

Examples

>>> from lambeq.backend.grammar import Ty, Box
>>> s0, s1 = Box('s0', Ty(), Ty()), Box('s1', Ty(), Ty())
>>> gen = normalize(s0 @ s1)
>>> for _ in range(3): print(next(gen))
|Ty() @ [s1; Ty() -> Ty()] @ Ty()| >> |Ty() @ [s0; Ty() -> Ty()] @ Ty()|
|Ty() @ [s0; Ty() -> Ty()] @ Ty()| >> |Ty() @ [s1; Ty() -> Ty()] @ Ty()|
|Ty() @ [s1; Ty() -> Ty()] @ Ty()| >> |Ty() @ [s0; Ty() -> Ty()] @ Ty()|

lambeq.backend.snake_removal.snake_removal(diagram: Diagram, left: bool = False) → Iterator[Diagram]

Returns a generator which yields normalization steps.

Parameters:

leftbool, optional

Whether to apply left interchangers.

Yields:

diagramDiagram

Rewrite steps.

Examples

>>> from lambeq.backend.grammar import Ty, Box, Cup, Cap, Id
>>> n, s = Ty('n'), Ty('s')
>>> cup, cap = Cup(n, n.r), Cap(n.r, n)
>>> f = Box('f', n, n)
>>> g = Box('g', s @ n, n)
>>> h = Box('h', n, n @ s)
>>> diagram = g @ cap >> f.dagger() @ Id(n.r) @ f >> cup @ h
>>> for d in snake_removal(diagram):
...     print(d)  
|Ty... >> |Ty() @ [CUP; Ty(n) @ Ty(n).r -> Ty()] @ Ty(n)| >>...
|Ty... >> |Ty(n) @ [CAP; Ty() -> Ty(n).r @ Ty(n)] @ Ty()| >> |Ty() @ [CUP; Ty(n) @ Ty(n).r -> Ty()] @ Ty(n)| >>...
|Ty() @ [g; Ty(s) @ Ty(n) -> Ty(n)] @ Ty()| >> |Ty() @ [f†; Ty(n) -> Ty(n)] @ Ty()| >> |Ty() @ [f; Ty(n) -> Ty(n)] @ Ty()| >> |Ty() @ [h; Ty(n) -> Ty(n) @ Ty(s)] @ Ty()|