Custom quantum models

In qadence, the QuantumModel is the central class point for executing QuantumCircuits. The idea of a QuantumModel is to decouple the backend execution from the management of circuit parameters and desired quantum computation output.

In the following, we create a custom QuantumModel instance which introduces some additional optimizable parameters: * an adjustable scaling factor in front of the observable to measured * adjustable scale and shift factors to be applied to the model output before returning the result

This can be easily done using PyTorch flexible model definition, and it will automatically work with the rest of qadence infrastructure.

The custom model can be used like any other QuantumModel:

from qadence import Parameter, RX, CNOT, QuantumCircuit
from qadence import chain, kron, hamiltonian_factory, Z
from sympy import acos

def quantum_circuit(n_qubits):

    x = Parameter("x", trainable=False)
    fm = kron(RX(i, acos(x) * (i+1)) for i in range(n_qubits))

    ansatz = kron(RX(i, f"theta{i}") for i in range(n_qubits))
    ansatz = chain(ansatz, CNOT(0, n_qubits-1))

    block = chain(fm, ansatz)
    block.tag = "circuit"
    return QuantumCircuit(n_qubits, block)

n_qubits = 4
batch_size = 10
circuit = quantum_circuit(n_qubits)
observable = hamiltonian_factory(n_qubits, detuning=Z)  # Total magnetization

model = CustomQuantumModel(circuit, observable, backend="pyqtorch")

values = {"x": torch.rand(batch_size)}
res = model(values)
print("Model output: ", res)
assert len(res) == batch_size

Model output:  tensor([[-0.2319],
        [-1.0448],
        [-1.3911],
        [-1.2497],
        [-1.2542],
        [-1.1644],
        [-1.3818],
        [-1.3643],
        [-1.3341],
        [-0.9175]], grad_fn=<AddBackward0>)

Quantum model with wavefunction overlaps

QuantumModel's can also use different quantum operations in their forward pass, such as wavefunction overlaps described here. Beware that the resulting overlap tensor has to be differentiable to apply gradient-based optimization. This is only applicable to the "EXACT" overlap method.

Here we show how to use overlap calculation when fitting a parameterized quantum circuit to act as a standard Hadamard gate.

from qadence import RY, RX, H, Overlap

# create a quantum model which acts as an Hadamard gate after training
class LearnHadamard(QuantumModel):
    def __init__(
        self,
        train_circuit: QuantumCircuit,
        target_circuit: QuantumCircuit,
        backend="pyqtorch",
    ):
        super().__init__(circuit=train_circuit, backend=backend)
        self.overlap_fn = Overlap(train_circuit, target_circuit, backend=backend, method="exact", diff_mode='ad')

    def forward(self):
        return self.overlap_fn()

    # compute the wavefunction of the associated train circuit
    def wavefunction(self):
        return model.overlap_fn.run({})


train_circuit = QuantumCircuit(1, chain(RX(0, "phi"), RY(0, "theta")))
target_circuit = QuantumCircuit(1, H(0))

model = LearnHadamard(train_circuit, target_circuit)

# get the overlap between model and target circuit wavefunctions
print(model())

tensor([[0.8004]], grad_fn=<UnsqueezeBackward0>)

This model can then be trained with the standard Qadence helper functions.