An End-to-End Hybrid Quantum--Classical Sampling Workflow for Discrete Markov Random Fields: A Reproducible Case Study

[2607.09893] An End-to-End Hybrid Quantum-Classical Sampling Workflow for Discrete Markov Random Fields: A Reproducible Case Study Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2607.09893 (quant-ph) [Submitted on 10 Jul 2026 ( v1 ), last revised 9 Oct 2026 (this version, v3)] Title: An End-to-End Hybrid Quantum-Classical Sampling Workflow for Discrete Markov Random Fields: A Reproducible Case Study Authors: Arul Rhik Mazumder , Elias Towe View PDF HTML (experimental) Abstract: Sampling from discrete Markov random fields (MRFs) is a hard problem. We study amplitude-encoded i.i.d. sampling for small MRFs where $2^n$ target probabilities are precomputed classically. This removes quantum exponential speedup but allows a clean comparison against classical MCMC based on independent circuit samples ($\tau \approx 1$). Across 60 instances spanning five graph families (1k-step burn-in, 3k retained samples), the mean ESS ratios of Quantum to Single-Site Gibbs, Block Gibbs, Tuned-Block, and Parallel Tempering are $16.35$, $7.29$, $1.82$, and $1.79$, showing modern classical samplers substantially close this gap. Amortizing $O(2^n)$ preprocessing into wall-clock time, exact inverse-CDF sampling yields $17.7$M ESS/s versus $488$K ESS/s for the quantum sampler ($36\times$ mean rate, $153\times$ per-instance), confirming no wall-clock advantage. We characterize MCMC autocorrelation costs and benchmark amplitude-encoded state preparation at $n \in \{8,10,12\}$. An MPS scaling study ($n \le 40$) shows bond dimension $\chi=32$ achieves $F=0.721\pm0.059$ at $n=40$. Finally, a matched-budget VQC vs. MPS comparison at $n \in \{8,10,12\}$ shows VQC fidelities fall far below MPS: $(F_{\mathrm{VQC}}, F_{\mathrm{MPS}}) = (0.31, 0.99), (0.21, 0.96), (0.17, 0.88)$ at compressions $10.7\times$, $34.1\times$, and $113.8\times$. Comments: 9 pages, 7 figures, 9 tables. Accepted to the IEEE International Conference on Quantum Computing and Engineering (QCE 2026), Quantum End-to-End Hybrid Case Studies (QECS) Technical Papers track Subjects: Quantum Physics (quant-ph) ; Machine Learning (cs.LG) MSC classes: 81P68, 65C05, 60J22 ACM classes: G.3; F.1.2 Cite as: arXiv:2607.09893 [quant-ph] (or arXiv:2607.09893v3 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.09893 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Arul Mazumder [ view email ] [v1] Fri, 10 Jul 2026 18:33:14 UTC (607 KB) [v2] Fri, 28 Aug 2026 03:08:23 UTC (607 KB) [v3] Fri, 9 Oct 2026 02:43:00 UTC (59 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2026-07 Change to browse by: cs cs.LG References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation 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? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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