AQGD#

class AQGD(maxiter=1000, eta=1.0, tol=1e-06, momentum=0.25, param_tol=1e-06, averaging=10, max_evals_grouped=1)[source]#

Bases: Optimizer

Analytic Quantum Gradient Descent (AQGD) with Epochs optimizer. Performs gradient descent optimization with a momentum term, analytic gradients, and customized step length schedule for parameterized quantum gates, i.e. Pauli Rotations. See, for example:

K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii. (2018). Quantum circuit learning. Phys. Rev. A 98, 032309. https://arxiv.org/abs/1803.00745
Maria Schuld, Ville Bergholm, Christian Gogolin, Josh Izaac, Nathan Killoran. (2019). Evaluating analytic gradients on quantum hardware. Phys. Rev. A 99, 032331. https://arxiv.org/abs/1811.11184

for further details on analytic gradients of parameterized quantum gates.

Gradients are computed “analytically” using the quantum circuit when evaluating the objective function.

Performs Analytical Quantum Gradient Descent (AQGD) with Epochs.

Parameters:

maxiter (int | list[int]) – Maximum number of iterations (full gradient steps)
eta (float | list[float]) – The coefficient of the gradient update. Increasing this value results in larger step sizes: param = previous_param - eta * deriv
tol (float) – Tolerance for change in windowed average of objective values. Convergence occurs when either objective tolerance is met OR parameter tolerance is met.
momentum (float | list[float]) – Bias towards the previous gradient momentum in current update. Must be within the bounds: [0,1)
param_tol (float) – Tolerance for change in norm of parameters.
averaging (int) – Length of window over which to average objective values for objective convergence criterion
max_evals_grouped (int) – Max number of default gradient evaluations performed simultaneously.

Raises:

AlgorithmError – If the length of maxiter, momentum`, and eta is not the same.

Attributes

bounds_support_level#: Returns bounds support level

gradient_support_level#: Returns gradient support level

initial_point_support_level#: Returns initial point support level

is_bounds_ignored#: Returns is bounds ignored

is_bounds_required#: Returns is bounds required

is_bounds_supported#: Returns is bounds supported

is_gradient_ignored#: Returns is gradient ignored

is_gradient_required#: Returns is gradient required

is_gradient_supported#: Returns is gradient supported

is_initial_point_ignored#: Returns is initial point ignored

is_initial_point_required#: Returns is initial point required

is_initial_point_supported#: Returns is initial point supported

setting#: Return setting

settings#

Methods

get_support_level()[source]#

Support level dictionary

Returns:

gradient, bounds and initial point: support information that is ignored/required.

Return type:

Dict[str, int]

static gradient_num_diff(x_center, f, epsilon, max_evals_grouped=None)#

We compute the gradient with the numeric differentiation in the parallel way, around the point x_center.

Parameters:

x_center (ndarray) – point around which we compute the gradient
f (func) – the function of which the gradient is to be computed.
epsilon (float) – the epsilon used in the numeric differentiation.
max_evals_grouped (int) – max evals grouped, defaults to 1 (i.e. no batching).

Returns:

the gradient computed

Return type:

grad

minimize(fun, x0, jac=None, bounds=None)[source]#

Minimize the scalar function.

Parameters:

fun (Callable[[POINT], float]) – The scalar function to minimize.
x0 (POINT) – The initial point for the minimization.
jac (Callable[[POINT], POINT] | None) – The gradient of the scalar function fun.
bounds (list[tuple[float, float]] | None) – Bounds for the variables of fun. This argument might be ignored if the optimizer does not support bounds.

Returns:

The result of the optimization, containing e.g. the result as attribute x.

Return type:

OptimizerResult

print_options()#: Print algorithm-specific options.

set_max_evals_grouped(limit)#: Set max evals grouped

set_options(**kwargs)#

Sets or updates values in the options dictionary.

The options dictionary may be used internally by a given optimizer to pass additional optional values for the underlying optimizer/optimization function used. The options dictionary may be initially populated with a set of key/values when the given optimizer is constructed.

Parameters:: kwargs (dict) – options, given as name=value.

static wrap_function(function, args)#

Wrap the function to implicitly inject the args at the call of the function.

Parameters:

function (func) – the target function
args (tuple) – the args to be injected

Returns:

wrapper

Return type:

function_wrapper