Evolution of Quantum Resources in Quantum-walk-based Search Algorithm

TL;DR

This paper investigates how quantum coherence and entanglement evolve during quantum walk-based search algorithms on bipartite graphs, highlighting their interplay, effects of noise, and theoretical insights into their dynamics.

Contribution

It provides a combined numerical and theoretical analysis of quantum resources in quantum walk search algorithms, especially under noise influence.

Findings

Quantum coherence and entanglement show a complementary relationship during the search process.

Generalized depolarizing noise significantly affects success probability and quantum coherence.

Theoretical analysis supports numerical findings on resource dynamics and noise effects.

Abstract

Quantum walk is fundamental to designing many quantum algorithms. Here we consider the effects of quantum coherence and quantum entanglement for the quantum walk search on the complete bipartite graph. First, we numerically show the complementary relationship between the success probability and the two quantum resources (quantum coherence and quantum entanglement). We also provide theoretical analysis in the asymptotic scenarios. At last, we discuss the role played by generalized depolarizing noises and find that it would influence the dynamics of success probability and quantum coherence sharply, which is demonstrated by theoretical derivation and numerical simulation.