modified_iterative_quantum_ae

This module contains the mIQAE class. Given a quantum oracle operator, this class estimates the probability of a given target state using a modification of the IQAE algorithm based on the paper:

Fukuzawa, Shion and Ho, Christopher and Irani, Sandy and Zion, Jasen Modified Iterative Quantum Amplitude Estimation is Asymptotically Optimal. Society for Industrial and Applied Mathematics. 2023 Proceedings of the Symposium on Algorithm Engineering and Experiments (ALENEX). 2023

Author: Gonzalo Ferro Costas & Alberto Manzano Herrero

class QQuantLib.AE.modified_iterative_quantum_ae.mIQAE(oracle: qat.lang.AQASM.QRoutine, target: list, index: list, **kwargs)

Class for Iterative Quantum Amplitude Estimation (IQAE) algorithm

Parameters:

  • oracle (QLM gate) – QLM gate with the Oracle for implementing the Grover operator

  • target (list of ints) – python list with the target for the amplitude estimation

  • index (list of ints) – qubits which mark the register to do the amplitude estimation

  • kwargs (dictionary) – dictionary that allows the configuration of the IQAE algorithm: Implemented keys:

  • qpu (kwargs, QLM solver) – solver for simulating the resulting circuits

  • epsilon (kwargs, float) – precision

  • alpha (kwargs, float) – accuracy

  • shots (kwargs, int) – number of measurements on each iteration

  • mcz_qlm (kwargs, bool) – for using or not QLM implementation of the multi controlled Z gate

static chebysev_bound(n_samples: int, gamma: float)

Computes the length of the confidence interval for a given number of samples n_samples and an accuracy gamma:

\[\epsilon = \dfrac{1}{\sqrt{2N}}\log\left(\dfrac{2}{\gamma} \ \right)\]
Parameters:

  • n_samples (int) – number of samples

  • gamma (float) – accuracy

Returns:

length of the confidence interval

Return type:

float

static compute_info(epsilon: float = 0.01, shots: int = 100, alpha: float = 0.05)

This function computes theoretical values of the IQAE algorithm.

Parameters:

  • epsilon (float) – precision

  • alpha (float) – accuracy

  • shots (int) – number of measurements on each iteration

Returns:

info – python dictionary with the computed information

Return type:

dict

static confidence_intervals(a_min: float, a_max: float, ri: int)

Computes the confidence intervals

Parameters:

  • a_min (float) – minimum amplitude measured in the round

  • a_max (float) – maximum amplitude measured in the round

  • ri (int) – number of quadrants passed to get the current angle

static display_information(epsilon: float = 0.01, shots: int = 100, alpha: float = 0.05)

This function displays information of the properties of the method for a given set of parameters

Parameters:

  • epsilon (float) – precision

  • alpha (float) – accuracy

  • shots (int) – number of measurements on each iteration

static find_next_k(k: int, theta_lower: float, theta_upper: float)

This is an implementation of Algorithm 2 from the mIQAE paper. This function computes the next suitable k.

Parameters:

  • k (int) – number of times to apply the grover operator to the quantum circuit

  • theta_lower (float) – lower bound for the estimation of the angle

  • theta_upper (float) – upper bound for the estimation of the angle

Returns:

k – number of times to apply the grover operator to the quantum circuit

Return type:

int

property index

creating index property

miqae(epsilon: float = 0.01, shots: int = 100, alpha: float = 0.05)

This function implements Algorithm 1 from the IQAE paper. The result is an estimation of the desired probability with precision at least epsilon and accuracy at least alpha.

Parameters:

  • epsilon (float) – precision

  • alpha (float) – accuracy

  • shots (int) – number of measurements on each iteration

Returns:

  • a_l (float) – lower bound for the probability to be estimated

  • a_u (float) – upper bound for the probability to be estimated

property oracle

creating oracle property

quantum_step(k)

Create the quantum routine needed for the iqae step

Parameters:

k (int) – number of Grover operator applications

Returns:

routine – qlm routine for the iqae step

Return type:

qlm routine

run()

run method for the class.

Returns:

amplitude estimation parameter

Return type:

self.ae

property target

creating target property