# Copyright 2021-2024 Cambridge Quantum Computing Ltd.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
Circuit Ansatz
==============
A circuit ansatz converts a DisCoCat diagram into a quantum circuit.
This work is based on DisCoPy (https://discopy.org/) which is released
under the BSD 3-Clause "New" or "Revised" License.
"""
from __future__ import annotations
__all__ = ['CircuitAnsatz',
'IQPAnsatz',
'Sim4Ansatz',
'Sim14Ansatz',
'Sim15Ansatz',
'StronglyEntanglingAnsatz']
from abc import abstractmethod
from collections.abc import Callable, Mapping
from itertools import cycle
from typing import Type
import numpy as np
from sympy import Symbol, symbols
from lambeq.ansatz import BaseAnsatz
from lambeq.backend.grammar import Box, Diagram, Functor, Ty
from lambeq.backend.quantum import (
Bra,
CRz,
Diagram as Circuit,
Discard,
H,
Id,
Ket,
quantum,
qubit,
Rotation,
Rx, Ry, Rz
)
computational_basis = Id(qubit)
[docs]class CircuitAnsatz(BaseAnsatz):
"""Base class for circuit ansatz."""
[docs] def __init__(self,
ob_map: Mapping[Ty, int],
n_layers: int,
n_single_qubit_params: int,
circuit: Callable[[int, np.ndarray], Circuit],
discard: bool = False,
single_qubit_rotations: list[Type[Rotation]] | None = None,
postselection_basis: Circuit = computational_basis) -> None:
"""Instantiate a circuit ansatz.
Parameters
----------
ob_map : dict
A mapping from :py:class:`lambeq.backend.grammar.Ty` to
the number of qubits it uses in a circuit.
n_layers : int
The number of layers used by the ansatz.
n_single_qubit_params : int
The number of single qubit rotations used by the ansatz.
It only affects wires that `ob_map` maps to a single
qubit.
circuit : callable
Circuit generator used by the ansatz. This is a function
(or a class constructor) that takes a number of qubits and
a numpy array of parameters, and returns the ansatz of that
size, with parameterised boxes.
discard : bool, default: False
Discard open wires instead of post-selecting.
postselection_basis: Circuit, default: Id(qubit)
Basis to post-select in, by default the computational basis.
single_qubit_rotations: list of Circuit, optional
The rotations to be used for a single qubit. When only a
single qubit is present, the ansatz defaults to applying a
series of rotations in a cycle, determined by this parameter
and `n_single_qubit_params`.
"""
self.ob_map = {src: qubit ** ty if isinstance(ty, int) else ty
for src, ty in ob_map.items()}
self.n_layers = n_layers
self.n_single_qubit_params = n_single_qubit_params
self.circuit = circuit
self.discard = discard
self.postselection_basis = postselection_basis
self.single_qubit_rotations = single_qubit_rotations or []
self.functor = Functor(target_category=quantum,
ob=self._ob,
ar=self._ar)
[docs] def __call__(self, diagram: Diagram) -> Circuit:
"""Convert a lambeq diagram into a lambeq circuit."""
return self.functor(diagram) # type: ignore[return-value]
[docs] def ob_size(self, pg_type: Ty) -> int:
"""Calculate the number of qubits used for a given type."""
return sum(map(len, map(self.functor, pg_type)))
[docs] @abstractmethod
def params_shape(self, n_qubits: int) -> tuple[int, ...]:
"""Calculate the shape of the parameters required."""
def _ob(self, _: Functor, ty: Ty) -> Ty:
return self.ob_map[ty]
def _ar(self, _: Functor, box: Box) -> Circuit:
label = self._summarise_box(box)
dom, cod = self.ob_size(box.dom), self.ob_size(box.cod)
n_qubits = max(dom, cod)
if n_qubits == 0:
circuit = Id()
elif n_qubits == 1:
syms = symbols(f'{label}_0:{self.n_single_qubit_params}',
cls=Symbol)
circuit = Id(qubit)
for rot, sym in zip(cycle(self.single_qubit_rotations), syms):
circuit >>= rot(sym)
else:
params_shape = self.params_shape(n_qubits)
syms = symbols(f'{label}_0:{np.prod(params_shape)}', cls=Symbol)
params: np.ndarray = np.array(syms).reshape(params_shape)
circuit = self.circuit(n_qubits, params)
if cod > dom:
circuit = Id(dom) @ Ket(*[0]*(cod - dom)) >> circuit
elif cod < dom:
if self.discard:
circuit >>= Id(cod) @ Id().tensor(
*[Discard() for _ in range(dom - cod)]
)
else:
circuit >>= Id(cod).tensor(
*[self.postselection_basis] * (dom-cod))
circuit >>= Id(cod) @ Bra(*[0]*(dom - cod))
return circuit
[docs]class IQPAnsatz(CircuitAnsatz):
"""Instantaneous Quantum Polynomial ansatz.
An IQP ansatz interleaves layers of Hadamard gates with diagonal
unitaries. This class uses :py:obj:`n_layers-1` adjacent CRz gates
to implement each diagonal unitary.
Code adapted from DisCoPy.
"""
[docs] def __init__(self,
ob_map: Mapping[Ty, int],
n_layers: int,
n_single_qubit_params: int = 3,
discard: bool = False) -> None:
"""Instantiate an IQP ansatz.
Parameters
----------
ob_map : dict
A mapping from :py:class:`lambeq.backend.grammar.Ty` to
the number of qubits it uses in a circuit.
n_layers : int
The number of layers used by the ansatz.
n_single_qubit_params : int, default: 3
The number of single qubit rotations used by the ansatz.
It only affects wires that `ob_map` maps to a single
qubit.
discard : bool, default: False
Discard open wires instead of post-selecting.
"""
super().__init__(ob_map,
n_layers,
n_single_qubit_params,
self.circuit,
discard,
[Rx, Rz])
[docs] def params_shape(self, n_qubits: int) -> tuple[int, ...]:
return (self.n_layers, n_qubits - 1)
[docs] def circuit(self, n_qubits: int, params: np.ndarray) -> Circuit:
if n_qubits == 1:
circuit = Rx(params[0]) >> Rz(params[1]) >> Rx(params[2])
else:
circuit = Id(n_qubits)
hadamards = Id().tensor(*(n_qubits * [H]))
for thetas in params:
rotations = Id(n_qubits).then(*(
Id(i) @ CRz(thetas[i]) @ Id(n_qubits - 2 - i)
for i in range(n_qubits - 1)))
circuit >>= hadamards >> rotations
if self.n_layers > 0: # Final layer of Hadamards
circuit >>= hadamards
return circuit # type: ignore[return-value]
[docs]class Sim14Ansatz(CircuitAnsatz):
"""Modification of circuit 14 from Sim et al.
Replaces circuit-block construction with two rings of CRx gates, in
opposite orientation.
Paper at: https://arxiv.org/abs/1905.10876
Code adapted from DisCoPy.
"""
[docs] def __init__(self,
ob_map: Mapping[Ty, int],
n_layers: int,
n_single_qubit_params: int = 3,
discard: bool = False) -> None:
"""Instantiate a Sim 14 ansatz.
Parameters
----------
ob_map : dict
A mapping from :py:class:`lambeq.backend.grammar.Ty` to
the number of qubits it uses in a circuit.
n_layers : int
The number of layers used by the ansatz.
n_single_qubit_params : int, default: 3
The number of single qubit rotations used by the ansatz.
It only affects wires that `ob_map` maps to a single
qubit.
discard : bool, default: False
Discard open wires instead of post-selecting.
"""
super().__init__(ob_map,
n_layers,
n_single_qubit_params,
self.circuit,
discard,
[Rx, Rz])
[docs] def params_shape(self, n_qubits: int) -> tuple[int, ...]:
return (self.n_layers, 4 * n_qubits)
[docs] def circuit(self, n_qubits: int, params: np.ndarray) -> Circuit:
if n_qubits == 1:
circuit = Rx(params[0]) >> Rz(params[1]) >> Rx(params[2])
else:
circuit = Id(n_qubits)
for thetas in params:
sublayer1 = Id().tensor(*map(Ry, thetas[:n_qubits]))
for i in range(n_qubits):
tgt = (i - 1) % n_qubits
sublayer1 = sublayer1.CRx(thetas[n_qubits + i], i, tgt)
sublayer2 = Id().tensor(
*map(Ry, thetas[2 * n_qubits: 3 * n_qubits]))
for i in range(n_qubits, 0, -1):
src = i % n_qubits
tgt = (i + 1) % n_qubits
sublayer2 = sublayer2.CRx(thetas[-i], src, tgt)
circuit >>= sublayer1 >> sublayer2
return circuit # type: ignore[return-value]
[docs]class Sim15Ansatz(CircuitAnsatz):
"""Modification of circuit 15 from Sim et al.
Replaces circuit-block construction with two rings of CNOT gates, in
opposite orientation.
Paper at: https://arxiv.org/abs/1905.10876
Code adapted from DisCoPy.
"""
[docs] def __init__(self,
ob_map: Mapping[Ty, int],
n_layers: int,
n_single_qubit_params: int = 3,
discard: bool = False) -> None:
"""Instantiate a Sim 15 ansatz.
Parameters
----------
ob_map : dict
A mapping from :py:class:`lambeq.backend.grammar.Ty` to
the number of qubits it uses in a circuit.
n_layers : int
The number of layers used by the ansatz.
n_single_qubit_params : int, default: 3
The number of single qubit rotations used by the ansatz.
It only affects wires that `ob_map` maps to a single
qubit.
discard : bool, default: False
Discard open wires instead of post-selecting.
"""
super().__init__(ob_map,
n_layers,
n_single_qubit_params,
self.circuit,
discard,
[Rx, Rz])
[docs] def params_shape(self, n_qubits: int) -> tuple[int, ...]:
return (self.n_layers, 2 * n_qubits)
[docs] def circuit(self, n_qubits: int, params: np.ndarray) -> Circuit:
if n_qubits == 1:
circuit = Rx(params[0]) >> Rz(params[1]) >> Rx(params[2])
else:
circuit = Id(n_qubits)
for thetas in params:
sublayer1 = Id().tensor(*map(Ry, thetas[:n_qubits]))
for i in range(n_qubits):
tgt = (i - 1) % n_qubits
sublayer1 = sublayer1.CX(i, tgt)
sublayer2 = Id().tensor(*map(Ry, thetas[n_qubits:]))
for i in range(n_qubits, 0, -1):
src = i % n_qubits
tgt = (i + 1) % n_qubits
sublayer2 = sublayer2.CX(src, tgt)
circuit >>= sublayer1 >> sublayer2
return circuit # type: ignore[return-value]
[docs]class Sim4Ansatz(CircuitAnsatz):
"""Circuit 4 from Sim et al.
Ansatz with a layer of Rx and Rz gates, followed by a
ladder of CRxs.
Paper at: https://arxiv.org/abs/1905.10876
"""
[docs] def __init__(self,
ob_map: Mapping[Ty, int],
n_layers: int,
n_single_qubit_params: int = 3,
discard: bool = False) -> None:
"""Instantiate a Sim 4 ansatz.
Parameters
----------
ob_map : dict
A mapping from :py:class:`lambeq.backend.grammar.Ty` to
the number of qubits it uses in a circuit.
n_layers : int
The number of layers used by the ansatz.
n_single_qubit_params : int, default: 3
The number of single qubit rotations used by the ansatz.
It only affects wires that `ob_map` maps to a single
qubit.
discard : bool, default: False
Discard open wires instead of post-selecting.
"""
super().__init__(ob_map,
n_layers,
n_single_qubit_params,
self.circuit,
discard,
[Rx, Rz])
[docs] def params_shape(self, n_qubits: int) -> tuple[int, ...]:
return (self.n_layers, 3 * n_qubits - 1)
[docs] def circuit(self, n_qubits: int, params: np.ndarray) -> Circuit:
if n_qubits == 1:
circuit = Rx(params[0]) >> Rz(params[1]) >> Rx(params[2])
else:
circuit = Id(n_qubits)
for thetas in params:
circuit >>= Id().tensor(*map(Rx, thetas[:n_qubits]))
circuit >>= Id().tensor(*map(Rz,
thetas[n_qubits:2 * n_qubits]))
crxs = Id(n_qubits)
for i in range(n_qubits - 1):
crxs = crxs.CRx(thetas[2 * n_qubits + i], i, i + 1)
circuit >>= crxs
return circuit # type: ignore[return-value]
[docs]class StronglyEntanglingAnsatz(CircuitAnsatz):
"""Strongly entangling ansatz.
Ansatz using three single qubit rotations (RzRyRz) followed by a
ladder of CNOT gates with different ranges per layer.
This is adapted from the PennyLane implementation of the
:py:class:`pennylane.StronglyEntanglingLayers`, pursuant to `Apache
2.0 licence <https://www.apache.org/licenses/LICENSE-2.0.html>`_.
The original paper which introduces the architecture can be found
`here <https://arxiv.org/abs/1804.00633>`_.
"""
[docs] def __init__(self,
ob_map: Mapping[Ty, int],
n_layers: int,
n_single_qubit_params: int = 3,
ranges: list[int] | None = None,
discard: bool = False) -> None:
"""Instantiate a strongly entangling ansatz.
Parameters
----------
ob_map : dict
A mapping from :py:class:`lambeq.backend.grammar.Ty` to
the number of qubits it uses in a circuit.
n_layers : int
The number of circuit layers used by the ansatz.
n_single_qubit_params : int, default: 3
The number of single qubit rotations used by the ansatz.
It only affects wires that `ob_map` maps to a single
qubit.
ranges : list of int, optional
The range of the CNOT gate between wires in each layer. By
default, the range starts at one (i.e. adjacent wires) and
increases by one for each subsequent layer.
discard : bool, default: False
Discard open wires instead of post-selecting.
"""
super().__init__(ob_map,
n_layers,
n_single_qubit_params,
self.circuit,
discard,
[Rz, Ry])
self.ranges = ranges
if self.ranges is not None and len(self.ranges) != self.n_layers:
raise ValueError('The number of ranges must match the number of '
'layers.')
[docs] def params_shape(self, n_qubits: int) -> tuple[int, ...]:
return (self.n_layers, 3 * n_qubits)
[docs] def circuit(self, n_qubits: int, params: np.ndarray) -> Circuit:
circuit = Id(qubit**n_qubits)
for layer in range(self.n_layers):
for j in range(n_qubits):
syms = params[layer][j*3:j*3+3]
circuit = circuit.Rz(syms[0], j).Ry(syms[1], j).Rz(syms[2], j)
if self.ranges is None:
step = layer % (n_qubits - 1) + 1
elif self.ranges[layer] >= n_qubits:
raise ValueError('The maximum range must be smaller '
'than the number of qubits.')
else:
step = self.ranges[layer]
for j in range(n_qubits):
circuit = circuit.CX(j, (j+step) % n_qubits)
return circuit