Efficient Simulation of Szegedy Quantum Walk Formulations and Algorithms

Quantum Physics arXiv:2606.14226 (quant-ph) [Submitted on 12 Jun 2026] Title:Efficient Simulation of Szegedy Quantum Walk Formulations and Algorithms Authors:Sergio A. Ortega, Daniel K. Park View a PDF of the paper titled Efficient Simulation of Szegedy Quantum Walk Formulations and Algorithms, by Sergio A. Ortega and 1 other authors View PDF HTML (experimental) Abstract:Quantum walks provide a versatile framework for quantum algorithms across a wide range of applications. We develop efficient classical simulation methods for Szegedy quantum walks that avoid explicit construction of the full unitary evolution operator. Unlike previous approaches restricted to a particular walk formulation, our framework is built from fundamental update and reflection operators, enabling the simulation of a broader class of Szegedy walk formulations. We further extend these methods to phase-estimation-based algorithms coupled to the walk, including implementations suitable for large sparse graphs. The resulting methods achieve optimal $O(N^2)$ complexity for dense graphs with $N$ nodes. For sparse graphs, the computational cost scales linearly with the number of edges, which is $O(N)$ in many cases. We implement the framework in the Python package SQWLib and illustrate its capabilities through simulations of representative algorithms, including quantum simulated annealing and quantum search on graphs. These results provide a practical tool for studying Szegedy-walk-based algorithms numerically beyond purely analytical treatments. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.14226 [quant-ph] (or arXiv:2606.14226v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.14226 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Sergio A. Ortega [view email] [v1] Fri, 12 Jun 2026 08:06:45 UTC (488 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient Simulation of Szegedy Quantum Walk Formulations and Algorithms, by Sergio A. Ortega and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?)