Noise-Resilient Spatial Search with Lackadaisical Quantum Walks
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915754277863424 |
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| author | Vieira, Gabriel Mauricio Oswald Maculan, Nelson Marquezino, Franklin de Lima |
| author_facet | Vieira, Gabriel Mauricio Oswald Maculan, Nelson Marquezino, Franklin de Lima |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13462 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Noise-Resilient Spatial Search with Lackadaisical Quantum Walks Vieira, Gabriel Mauricio Oswald Maculan, Nelson Marquezino, Franklin de Lima Quantum Physics 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. |
| title | Noise-Resilient Spatial Search with Lackadaisical Quantum Walks |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2508.13462 |