Choosing a model¶
The following sections provide more information on the various models.
NumpyModel¶
A NumpyModel
uses the unitary and density matrix simulators in the lowlevel lambeq.backend
, 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 a unitary simulator, while circuits containing Encode
, Measure
or Discard
are evaluated using a 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 justintime (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 precompiled 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
.
See also the following use cases:
PennyLaneModel¶
PennyLaneModel
uses PennyLane and PyTorch to allow classicalquantum machine learning experiments. With probabilities=False
, PennyLaneModel
performs a state vector simulation, while with probabilties=True
it performs a probability simulation. The state vector and probability simulations correspond to unitary and density matrix simulations.
To run the model on real quantum hardware, probabilities=True
must be used, so that the lambeq
circuits are optimized using the parametershift rule to calculate the gradients.
PennyLaneModel
can be used to optimize simulated circuits using exact backpropagation with PyTorch, which may give improved results over using NumpyModel
with SPSAOptimizer
. However, this optimization process is not possible on real quantum hardware, so for more realistic results the parametershift rule should be preferred.
To construct a hybrid model that passes the output of a circuit through a classical neural network, it is only necessary to subclass PennyLaneModel
and modify the __init__()
method to store the classical PyTorch parameters, and the forward()
method to pass the result of get_diagram_output()
to the neural network. For example:
import torch
from lambeq import PennyLaneModel
class MyCustomModel(PennyLaneModel):
def __init__(self, **kwargs):
super().__init__(**kwargs)
self.net = torch.nn.Linear(2, 2)
def forward(self, input):
preds = self.get_diagram_output(input)
return self.net(preds)
This neural net can be real or complexvalued, though this affects the nonlinearities that can be used.
PennyLaneModel
can be used with the PytorchTrainer
, or a standard PyTorch training loop.
By using different backend configurations, PennyLaneModel
can be used for several different usecases, listed below:
Use case 
Configurations 

Exact non shotbased simulation with state outputs 

Exact non shotbased simulation with probability outputs 

Noiseless shotbased simulation 

Noisy shotbased simulation on local hardware 

Noisy shotbased simulation on cloudbased emulators 
{'backend': 'qiskit.ibmq', 'device'='ibmq_qasm_simulator', 'shots'=1000, 'probabilities'=True} {'backend': 'honeywell.hqs', device=('H11E' or 'H12E'), 'shots'=1000, 'probabilities'=True} 
Evaluation of quantum circuits on a quantum computer 
{'backend': 'qiskit.ibmq', 'device'='ibmq_hardware_device', 'shots'=1000, 'probabilities'=True} , where ibmq_hardware_device is one that you have access to via your IBMQ account.{'backend': 'honeywell.hqs', device=('H1' or 'H11' or 'H12'), 'shots'=1000, 'probabilities'=True} 
All of these backends are compatible with hybrid quantumclassical models. Note that using quantum hardware or cloudbased emulators are much slower than local simulations.
See also the following use cases:
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 pregroup 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 lambeq.backend.tensor import Dim
parser = BobcatParser()
pregroup_diagram = parser.sentence2diagram('This is a tensor network.')
ansatz = TensorAnsatz({AtomicType.NOUN: Dim(2), AtomicType.SENTENCE: Dim(4)})
tensor_diagram = ansatz(pregroup_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 twodimensional binary labels: [[1,0], [0,1], ...]
. If your data has a different structure, you must implement your custom loss function and evaluation metrics.
See also the following use cases:
TketModel¶
TketModel
uses pytket
to retrieve shotbased 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, architectureaware 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 = 'H11E'
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
.
See also the following use cases: