Random sampling of permutations through quantum circuits

TL;DR

This paper presents a novel quantum algorithm for sampling permutations, inspired by classical methods, and demonstrates its application in statistical testing and graph generation within quantum computing frameworks.

Contribution

It introduces a quantum analogue of a classical permutation sampling algorithm and applies it to statistical tests and graph models, advancing quantum permutation sampling techniques.

Findings

Quantum permutation sampling algorithm developed

Application to two-sample mean difference testing

Proposal of a quantum-based graph generative model

Abstract

In this paper, we introduce a classical algorithm for random sampling of permutations, drawing inspiration from the Steinhaus-Johnson-Trotter algorithm. Our approach takes a comprehensive view of permutation sampling by expressing them as products of adjacent transpositions. Building on this, we develop a quantum analogue of the classical algorithm using a quantum circuit model for random sampling of permutations. As an application, we present a quantum algorithm for the two-sample randomization test to assess the difference of means in classical data. Finally, we propose a nested corona product graph generative model for symmetric groups, which facilitates random sampling of permutations from specific sets of permutations through a quantum circuit model.