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

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 $17.7\text{M}$ ESS/s versus $488\text{K}$ 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 $113.8\times$.

Quantum Physics (quant-ph); Machine Learning (cs.LG)

arXiv:2607.09893 [quant-ph]

(or arXiv:2607.09893v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.09893 Focus to learn more arXiv-issued DOI via DataCite

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.