Choosing a model

The following sections provide more information on the various models.

NumpyModel

A NumpyModel uses the unitary and density matrix simulators in DisCoPy, which convert quantum circuits into a tensor network. The resulting tensor network is efficiently contracted using opt_einsum.

Circuits containing only Bra, Ket and unitary gates are evaluated using DisCoPy’s unitary simulator, while circuits containing Encode, Measure or Discard are evaluated using DisCoPy’s density matrix simulator.

Note

Note that the unitary simulator converts a circuit with n output qubits into a tensor of shape (2, ) * n, while the density matrix simulator converts a circuit with n output qubits and m output bits into a tensor of shape (2, ) * (2 * n + m).

In the common use case of using a stairs_reader or a TreeReader with discarding for binary classification, the process involves measuring (Measure) one of the “open” qubits, and discarding (Discard) the rest of them.

One advantage that the NumpyModel has over the TketModel is that it supports the just-in-time (jit) compilation provided by the library jax. This speeds up the model’s diagram evaluation by an order of magnitude. The NumpyModel with jit mode enabled can be instantiated with the following command:

from lambeq import NumpyModel

model = NumpyModel.from_diagrams(circuits, use_jit=True)

Note

Using the NumpyModel with jit mode enabled is not recommended for large models, as it requires a large amount of memory to store the pre-compiled functions for each circuit.

To use the NumpyModel with jit mode, you need to install lambeq with the extra packages by running the following command:

pip install lambeq[extras]

Note

To enable GPU support for jax, follow the installation instructions on the JAX GitHub repository.

NumpyModel should be used with the QuantumTrainer.

PytorchModel

PytorchModel is the right choice for classical experiments. Here, string diagrams are treated as tensor networks, where boxes represent tensors and edges define the specific tensor contractions. Tensor contractions are optimised by the python package opt_einsum.

To prepare the diagrams for the computation, we use a TensorAnsatz that converts a rigid diagram into a tensor diagram. Subclasses of TensorAnsatz include the SpiderAnsatz and the MPSAnsatz, which reduce the size of large tensors by spliting them into chains of many smaller boxes. To prepare a tensor diagram for a sentence, for example:

from lambeq import AtomicType, BobcatParser, TensorAnsatz
from discopy import Dim

parser = BobcatParser()
rigid_diagram = parser.sentence2diagram('This is a tensor network.')

ansatz = TensorAnsatz({AtomicType.NOUN: Dim(2), AtomicType.SENTENCE: Dim(4)})
tensor_diagram = ansatz(rigid_diagram)

After preparing a list of tensor diagrams, we can initialise the model through:

from lambeq import PytorchModel

model = PytorchModel.from_diagrams(tensor_diagrams)

The PytorchModel is capable of combining tensor networks and neural network architectures. For example, it is possible to feed the output of a tensor diagram into a neural network, by subclassing and modifying the forward() method:

import torch
from lambeq import PytorchModel

class MyCustomModel(PytorchModel):
   def __init__(self):
      super().__init__()
      self.net = torch.nn.Linear(2, 2)

   def forward(self, input):
      """define a custom forward pass here"""
      preds = self.get_diagram_output(input)  # performs tensor contraction
      return self.net(preds)

To simplify training, the PytorchModel can be used with the PytorchTrainer. A comprehensive tutorial can be found here.

Note

The loss function and the accuracy metric in the tutorial are defined for two-dimensional binary labels: [[1,0], [0,1], ...]. If your data has a different structure, you must implement your custom loss function and evaluation metrics.

TketModel

TketModel uses pytket to retrieve shot-based results from a quantum computer, then uses the shot counts to build the resulting tensor.

The AerBackend can be used with TketModel to perform a noisy, architecture-aware simulation of an IBM machine. Other backends supported by pytket can also be used. To run an experiment on a real quantum computer, for example:

from lambeq import TketModel
from pytket.extensions.quantinuum import QuantinuumBackend

machine = 'H1-1E'
backend = QuantinuumBackend(device_name=machine)
backend.login()

backend_config = {
 'backend': backend,
 'compilation': backend.default_compilation_pass(2),
 'shots': 2048
}

model = TketModel.from_diagrams(all_circuits, backend_config=backend_config)

Note

Note that you need user accounts and allocated resources to run experiments on real machines. However, IBM Quantum provides some limited resources for free.

For initial experiments we recommend using a NumpyModel, as it performs noiseless simulations and is orders of magnitude faster.

TketModel should be used with the QuantumTrainer.