iterative_quantum_ae

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

Grinko, D., Gacon, J., Zoufal, C. et al. Iterative Quantum Amplitude Estimation npj Quantum Inf 7, 52 (2021). https://doi.org/10.1038/s41534-021-00379-1

Author: Gonzalo Ferro Costas & Alberto Manzano Herrero

class QQuantLib.AE.iterative_quantum_ae.IQAE(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 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, flag: bool, ratio: float = 2)

This is an implementation of Algorithm 2 from the IQAE 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

  • flag (bool) – flag to keep track of weather we are in the upper or lower half pane

  • ratio (float) – ratio of amplifications between consecutive iterations

Returns:

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

  • flag (bool) – flag to keep track of weather we are in the upper or lower half pane

property index

creating index property

static invert_sector(a_min: float, a_max: float, flag: bool = True)

This function inverts the expression:

\[a = \dfrac{1-\cos(\theta)}{2}\]

for a pair of bounds (a_min,a_max). The result belongs to the domain (0,2pi)

Parameters:

  • a_min (float) – lower bound

  • a_max (float) – upper bound

  • flag (bool) – flag to keep track of weather we are in the upper or lower half pane

Returns:

  • theta_min (float) – lower bound for the associated angle

  • theta_max (float) – upper bound for the associated angle

iqae(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