AQGD
class AQGD(maxiter=1000, eta=3.0, tol=1e-06, disp=False, momentum=0.25)
Analytic Quantum Gradient Descent (AQGD) optimizer.
Performs gradient descent optimization with a momentum term and analytic gradients for parametrized 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 parametrized quantum gates.
Gradients are computed “analytically” using the quantum circuit when evaluating the objective function.
Parameters
- maxiter (
int) – Maximum number of iterations, each iteration evaluation gradient. - eta (
float) – The coefficient of the gradient update. Increasing this value results in larger step sizes: param = previous_param - eta * deriv - tol (
float) – The convergence criteria that must be reached before stopping. Optimization stops when: absolute(loss - previous_loss) < tol - disp (
bool) – Set to True to display convergence messages. - momentum (
float) – Bias towards the previous gradient momentum in current update. Must be within the bounds: [0,1)
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
Methods
converged
AQGD.converged(objval, n=2)
Determines if the objective function has converged by finding the difference between the current value and the previous n values.
Parameters
- objval (float) – Current value of the objective function.
- n (int) – Number of previous steps which must be within the convergence criteria in order to be considered converged. Using a larger number will prevent the optimizer from stopping early.
Returns
Whether or not the optimization has converged.
Return type
bool
deriv
AQGD.deriv(j, params, obj)
Obtains the analytical quantum derivative of the objective function with respect to the jth parameter.
Parameters
- j (int) – Index of the parameter to compute the derivative of.
- params (array) – Current value of the parameters to evaluate the objective function at.
- obj (callable) – Objective function.
Returns
The derivative of the objective function w.r.t. j
Return type
float
get_support_level
AQGD.get_support_level()
Return support level dictionary
gradient_num_diff
static AQGD.gradient_num_diff(x_center, f, epsilon, max_evals_grouped=1)
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
Returns
the gradient computed
Return type
grad
optimize
AQGD.optimize(num_vars, objective_function, gradient_function=None, variable_bounds=None, initial_point=None)
Perform optimization.
Parameters
- num_vars (int) – Number of parameters to be optimized.
- objective_function (callable) – A function that computes the objective function.
- gradient_function (callable) – A function that computes the gradient of the objective function, or None if not available.
- variable_bounds (list[(float, float)]) – List of variable bounds, given as pairs (lower, upper). None means unbounded.
- initial_point (numpy.ndarray[float]) – Initial point.
Returns
point, value, nfev
point: is a 1D numpy.ndarray[float] containing the solution value: is a float with the objective function value nfev: number of objective function calls made if available or None
Raises
ValueError – invalid input
print_options
AQGD.print_options()
Print algorithm-specific options.
set_max_evals_grouped
AQGD.set_max_evals_grouped(limit)
Set max evals grouped
set_options
AQGD.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.
update
AQGD.update(j, params, deriv, mprev)
Updates the jth parameter based on the derivative and previous momentum
Parameters
- j (int) – Index of the parameter to compute the derivative of.
- params (array) – Current value of the parameters to evaluate the objective function at.
- deriv (float) – Value of the derivative w.r.t. the jth parameter
- mprev (array) – Array containing all of the parameter momentums
Returns
params, new momentums
Return type
tuple
wrap_function
static AQGD.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