Gate-level Implementation and Resource Analysis of Lackadaisical Quantum Walk Search

Quantum Physics arXiv:2608.17136 (quant-ph) [Submitted on 17 Aug 2026] Title:Gate-level Implementation and Resource Analysis of Lackadaisical Quantum Walk Search Authors:Amit Saha, Debanjan Kola, Nishanka Das, Amlan Chakrabarti View a PDF of the paper titled Gate-level Implementation and Resource Analysis of Lackadaisical Quantum Walk Search, by Amit Saha and 3 other authors View PDF HTML (experimental) Abstract:Lackadaisical quantum walks (LQW) extend discrete-time quantum walks (DTQW) by introducing weighted self-loops, enabling improved spatial-search performance through controlled localization of the walker. Although their theoretical properties and algorithmic advantages have been studied extensively, practical gate-level realizations suitable for execution on quantum hardware remain largely unexplored. This gap limits the assessment of lackadaisical quantum walk search under realistic architectural constraints, noise processes, and resource requirements. In this work, we present a gate-level implementation framework for lackadaisical quantum walk search. The proposed construction encodes the position and coin spaces into qubit registers, and realizes the walk dynamics through oracle, coin, and flip-flop shift operations. We validate the circuit by reproducing the expected search behavior for single and multiple marked vertices and by analyzing the effect of the self-loop weight on the success probability. We further evaluate the implementation under realistic noisy settings using superconducting hardware's noise models and apply noise-mitigation techniques to improve the measured search performance. Logical-resource analysis shows that, for grids ranging from $8\times8$ to $64\times64$, the algorithmic register increases from 9 to 15 qubits, while the transpiled gate count increases from $3.63\times10^{5}$ to $4.38\times10^{6}$ and the circuit depth from $2.13\times10^{5}$ to $2.56\times10^{6}$. Finally, fault-tolerant resource estimates based on a surface-code model using the Microsoft Quantum Resource Estimator demonstrate the substantial space-time trade-off associated with magic-state production. Comments: Subjects: Quantum Physics (quant-ph); Emerging Technologies (cs.ET) Cite as: arXiv:2608.17136 [quant-ph] (or arXiv:2608.17136v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.17136 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Amit Saha [view email] [v1] Mon, 17 Aug 2026 21:08:36 UTC (1,988 KB) Full-text links: Access Paper: View a PDF of the paper titled Gate-level Implementation and Resource Analysis of Lackadaisical Quantum Walk Search, by Amit Saha and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 Change to browse by: cs cs.ET References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)