Noise-Resilient Spatial Search with Lackadaisical Quantum Walks

TL;DR

This paper studies how lackadaisical quantum walks perform in noisy environments with broken links, showing that self-loops help maintain search effectiveness despite decoherence.

Contribution

It demonstrates that self-loops in lackadaisical quantum walks improve robustness against link-breaking noise in spatial search tasks.

Findings

Self-loops mitigate decoherence effects on quantum walks.

Marked vertices remain identifiable under noise with self-loops.

Self-loops extend quantum walk advantages to noisy scenarios.

Abstract

Quantum walks are a powerful framework for the development of quantum algorithms, with lackadaisical quantum walks (LQWs) standing out as an efficient model for spatial search. In this work, we investigate how broken-link decoherence affects the performance of LQW-based search on a two-dimensional toroidal grid. We show through numerical simulations that, while decoherence drives the loopless walk toward a uniform distribution and eliminates its search capability, the inclusion of self-loops significantly mitigates this effect. In particular, even under noise, the marked vertex remains identifiable with probability well above uniform, demonstrating that self-loops enhance the robustness of LQWs in realistic scenarios. These findings extend the known advantages of LQWs from the noiseless setting to noisy environments, consolidating self-loops as a valuable resource for designing resilient quantum search algorithms.