Quantum Hash Function Based on Spectral Properties of Graphs and Discrete Walker Dynamics

Quantum Physics arXiv:2512.03581 (quant-ph) [Submitted on 3 Dec 2025] Title:Quantum Hash Function Based on Spectral Properties of Graphs and Discrete Walker Dynamics Authors:Mohana Priya Thinesh Kumar, Pranavishvar Hariprakash View a PDF of the paper titled Quantum Hash Function Based on Spectral Properties of Graphs and Discrete Walker Dynamics, by Mohana Priya Thinesh Kumar and 1 other authors View PDF HTML (experimental) Abstract:We present Quantum Graph Hash (QGH-256), a novel quantum spectral hashing algorithm that generates high-entropy fingerprints from message-induced graphs. Each input message is mapped to a weighted graph via a discrete random walk on an n X n toroidal grid, where the walk dynamics determine the edge weights.

Quantum Phase Estimation (QPE) is then used to extract the phase spectrum of the graph Laplacian. Unlike standard QPE settings, the phase estimation is performed with respect to a superposition state (a uniform superposition over all node basis states) rather than an eigenvector, ensuring that all eigencomponents contribute to the resulting spectrum. This yields spectral features that distinguish even co-spectral but non-isomorphic message-induced graphs. The final spectral fingerprint is converted into a 256-bit digest, producing a compact representation of the input. As the fingerprint encodes both spectral and dynamical properties of the message-induced graph, the resulting hash exhibits strong sensitivity to input perturbations and provides a structurally rich foundation for post-quantum hashing. To demonstrate the feasibility of the approach, we implement QGH-256 on a 4 X 4 toroidal grid, chosen empirically: smaller grids exhibit collisions, whereas larger grids significantly increase execution time. The entire pipeline is implemented in Qiskit, and we use a seeded statevector simulator to obtain stable, noise-free results. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2512.03581 [quant-ph] (or arXiv:2512.03581v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.03581 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mohana Priya Thinesh Kumar [view email] [v1] Wed, 3 Dec 2025 09:05:27 UTC (1,092 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Hash Function Based on Spectral Properties of Graphs and Discrete Walker Dynamics, by Mohana Priya Thinesh Kumar and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)