Decoherence on Staggered Quantum Walks

TL;DR

This paper models decoherence in staggered quantum walks using percolation-inspired noise, analyzes its effects on quantum walk algorithms on 2D grids, and explores how tessellation intersection expansion enhances robustness.

Contribution

It introduces two novel decoherence models for staggered quantum walks and demonstrates their impact on quantum search algorithms and robustness improvements.

Findings

Decoherence modeled by breaking polygons and vertices affects quantum walk dynamics.

Expanding tessellations intersection increases robustness against decoherence.

Numerical analysis shows how decoherence impacts search efficiency.

Abstract

Decoherence phenomenon has been widely studied in different types of quantum walks. In this work we show how to model decoherence inspired by percolation on staggered quantum walks. Two models of unitary noise are described: breaking polygons and breaking vertices. The evolution operators subject to these noises are obtained and the equivalence to the coined quantum walk model is presented. Further, we numerically analyze the effect of these decoherence models on the two-dimensional grid of $4$-cliques. We examine how these perturbations affect the quantum walk based search algorithm in this graph and how expanding the tessellations intersection can make it more robust against decoherence.