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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.<\/jats:p>","DOI":"10.1007\/s11128-026-05205-1","type":"journal-article","created":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T03:35:37Z","timestamp":1779248137000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Noise-resilient spatial search with lackadaisical quantum walks"],"prefix":"10.1007","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-0341-1929","authenticated-orcid":false,"given":"Gabriel Mauricio","family":"Oswald Vieira","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3897-3356","authenticated-orcid":false,"given":"Nelson","family":"Maculan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9712-1930","authenticated-orcid":false,"given":"Franklin","family":"de Lima Marquezino","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,20]]},"reference":[{"issue":"2","key":"5205_CR1","doi-asserted-by":"publisher","first-page":"1687","DOI":"10.1103\/PhysRevA.48.1687","volume":"48","author":"Y Aharonov","year":"1993","unstructured":"Aharonov, Y., Davidovich, L., Zagury, N.: Quantum random walks. 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