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arXiv · 2508.13462

Noise-Resilient Spatial Search with Lackadaisical Quantum Walks

Gabriel Mauricio Oswald Vieira·Nelson Maculan·Franklin de Lima Marquezino
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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.

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Gabriel Mauricio Oswald Vieira, Nelson Maculan, Franklin de Lima Marquezino. 2025-08-19. Noise-Resilient Spatial Search with Lackadaisical Quantum Walks. https://doi.org/10.1007/s11128-026-05205-1

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