Predicting Resource Efficient Hamiltonian Decomposition for Continuous-Time Quantum Walk Simulations

Quantum Physics arXiv:2608.20660 (quant-ph) [Submitted on 21 Aug 2026] Title:Predicting Resource Efficient Hamiltonian Decomposition for Continuous-Time Quantum Walk Simulations Authors:Mostafa Atallah, Rebekah Herrman, Zain H. Saleem View a PDF of the paper titled Predicting Resource Efficient Hamiltonian Decomposition for Continuous-Time Quantum Walk Simulations, by Mostafa Atallah and 2 other authors View PDF HTML (experimental) Abstract:Simulating a continuous-time quantum walk (CTQW) on a graph in the circuit model of quantum computing requires decomposing its Hamiltonian into terms that can be Trotterized into hardware-native gates. We consider two such decompositions: the standard Pauli decomposition and the recently introduced matching decomposition. Prior work suggests that the matching decomposition uses fewer CX gates on sparse graphs, while the Pauli decomposition uses fewer on denser graphs. Since CX gates dominate error and runtime on current hardware, we train machine learning models to predict, for a given graph, which of the two decompositions produces the smaller CX gate count. We train and evaluate on the complete population of all 11,117 connected eight-vertex graphs from Brendan McKay's database, so the class balance and overlap are measured directly rather than estimated. We use twelve features: ten topological properties of the graph and two that count the terms the Pauli and matching decompositions produce (n_Pauli and n_match), both computable without transpiling the simulation circuit. Standard topological properties alone provide little predictive power. Instead, the dominant signal comes from n_Pauli, a property of the Hamiltonian decomposition rather than an intrinsic property of the graph; degree variance is the only other feature that carries signal. Across a range of models the Matthews correlation coefficient (MCC) falls in a narrow band, from 0.569 untuned to 0.593 after tuning, so no single architecture stands out. We adopt a single-hidden-layer neural network at MCC 0.593. Applied frozen to a held-out, class-balanced test set of larger graphs (up to 256 vertices) from structured and Erdos-Renyi families, the model transfers, with MCC rising from 0.785 at N=8 to 1 at N>=64. Comments: Subjects: Quantum Physics (quant-ph); Machine Learning (cs.LG) Cite as: arXiv:2608.20660 [quant-ph] (or arXiv:2608.20660v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.20660 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mostafa Atallah [view email] [v1] Fri, 21 Aug 2026 01:34:17 UTC (326 KB) Full-text links: Access Paper: View a PDF of the paper titled Predicting Resource Efficient Hamiltonian Decomposition for Continuous-Time Quantum Walk Simulations, by Mostafa Atallah and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 Change to browse by: cs cs.LG 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?)