Variational Quantum Algorithms

from mpqp.execution.vqa import *

In order to support Variational Quantum Algorithms (VQA for short), the parametrized gates of our circuits accept sympy’s symbolic variable as arguments.

A symbolic variable is a variable aimed at being a numeric value but without the value attributed. It can be created as such:

from sympy import symbols

theta, k = symbols("Θ k")

This concept exists more or less in all quantum circuit libraries: braket has FreeExpression, qiskit has Parameter, qlm has Variable, cirq uses sympy’s Symbol, etc…

Once you define a circuit with variables, you have two options:

  1. either the measure of the circuit is an ExpectationMeasure and can directly feed it in the optimizer;

  2. or you can define a custom cost function for more complicated cases.

Detailed example for those two options can be found in our example notebooks.

minimize(optimizable, method, device=None, init_params=None, nb_params=None, optimizer_options=None)[source]

This function runs an optimization on the parameters of the circuit, in order to minimize the measured expectation value of observables associated with the given circuit. Note that this means that the latter should contain an ExpectationMeasure.

Parameters

  • optimizable (Union[QCircuit, Callable[[Union[list[float], ndarray[Any, dtype[float32]]]], float]]) – Either the circuit, containing symbols and an expectation measure, or the evaluation function.

  • method (Union[Optimizer, Callable[[Callable[[Union[list[float], ndarray[Any, dtype[float32]]]], float], Optional[Union[list[float], ndarray[Any, dtype[float32]]]]], tuple[float, Union[list[float], numpy.ndarray[Any, numpy.dtype[numpy.float32]]]]]]) – The method used to optimize most of those methods come from scipy. If the choices offered in this package are not covering your needs, you can define your own optimizer. This should be a function taking as input a function representing the circuit, with as many inputs as the circuit has parameters, and any optional initialization parameters, and returning the optimal value reached and the parameters used to reach this value.

  • device (Optional[AvailableDevice]) – The device on which the circuit should be run.

  • init_params (Optional[Union[list[float], ndarray[Any, dtype[float32]]]]) – The optional initialization parameters (the value attributed to the symbols in the first loop of the optimizer).

  • nb_params (Optional[int]) – Number of variables to input in optimizable. It is only useful if optimizable is a Callable and if init_params was not given. If not this argument is not taken into account.

  • optimizer_options (Optional[dict[str, Any]]) – Options used to configure the VQA optimizer (maximum iterations, convergence threshold, etc…). These options are passed as is to the minimizer.

Returns

The optimal value reached and the parameters corresponding to this value.

Return type

tuple[float, Union[list[float], numpy.ndarray[Any, numpy.dtype[numpy.float32]]]]

Examples

>>> alpha, beta = symbols("α β")
>>> circuit = QCircuit([
...     H(0),
...     Rx(alpha, 1),
...     CNOT(1,0),
...     Rz(beta, 0),
...     ExpectationMeasure(
...         [0,1],
...         observable=Observable(np.diag([1,2,-3,4])),
...         shots=0,
...     ),
... ])
>>> minimize(
...     circuit,
...     Optimizer.BFGS,
...     ATOSDevice.MYQLM_PYLINALG,
...     optimizer_options={"maxiter":50},
... )
(-0.9999999999999996, array([0., 0.]))

>>> def cost_func(params):
...     run_res = run(
...         circuit,
...         ATOSDevice.MYQLM_PYLINALG,
...         {alpha: params[0], beta: params[1]}
...     )
...     return 1 - run_res.expectation_value ** 2
>>> minimize(
...     cost_func,
...     Optimizer.BFGS,
...     nb_params=2,
...     optimizer_options={"maxiter":50},
... )
(8.881784197001252e-16, array([0., 0.]))

For now, our minimizer is a wrapper around scipy’s minimizer. The Optimizer enum lists all the methods validated with the rest of the library.

class Optimizer(value)[source]

Bases: Enum

Enum used to select the optimizer for the VQA.

BFGS = 1
CMAES = 3
COBYLA = 2