Building Equivariant Models

By default, when a trainable Circuit is passed to a QuantumModel through the circuit_structure, all its parameters are considered independent. In some cases, however, one might want to just have a handful of independent parameters that are recombined in several different location inside the gates of your trainable quantum circuit.

For this reason Qiboml allows for the definition of custom circuits by means of user-defined functions, that can be added together with encoders and plain circuits to the circuit_structure. For example, one can define a circuit with only three independent parameters that are recombined in several gates:

import torch

# this defines 3 independent parameters
def my_equivariant_circuit(th, phi, lam):
   c = Circuit(2)
   delta = 2 * torch.cos(phi) + lam**2
   gamma = lam * torch.exp(th / 2)
   c.add([gates.RZ(i, theta=th) for i in range(2)])
   c.add([gates.RX(i, theta=lam) for i in range(2)])
   c.add([gates.RY(i, theta=phi) for i in range(2)])
   c.add(gates.RZ(0, theta=delta))
   c.add(gates.RX(1, theta=gamma))
   return c

and then pass it to the QuantumModel through its circuit_structure argument:

from qiboml.interfaces.pytorch import QuantumModel

model = QuantumModel(
   circuit_structure = [my_encoder, my_equivariant_circuit, my_plain_circuit],
   decoding = my_decoding,
)

Note that, first, inside of your function you should use only operations that are compatible with the interface you are planning to use. Therefore, torch operations with the torch interface and keras or tensorflow operations with the keras interface. Second, that the each input to your custom function has to be a scalar, thus one argument is expected, for each independent parameter you wish to declare.