Optimizing the walk coin in the quantum random walk search algorithm through machine learning

TL;DR

This paper investigates how machine learning techniques can optimize the phase parameters of the walk coin in quantum random walk search algorithms, enhancing their stability against phase inaccuracies, especially on hypercube structures.

Contribution

It introduces a machine learning-based approach to optimize the walk coin phases, improving the stability of quantum search algorithms against phase errors.

Findings

Optimized phase differences improve stability of the quantum walk search.

Machine learning methods effectively identify stable phase configurations.

Stability gains are demonstrated for hypercubes with 1-3 qubits.

Abstract

This paper examines the stability of the quantum random walk search algorithm, when the walk coin is constructed by generalized Householder reflection and additional phase shift, against inaccuracies in the phases used to construct the coin. The optimization of the algorithm is done by numerical methods - Monte Carlo, neural networks, and supervised machine learning. The results of numerical simulations show that, with such a construction of the Householder reflection, the algorithm is more stable to inaccuracies in the specific values of these phases, as long as it is possible to control the phase difference between the phase shift and the phase involved in the Householder reflection. This paper explicitly shows as an example, how achieving a properly designed phase difference would make quantum random walk search on a hypercube more stable for coin register consisting of one, two, and three qubits.