对比量子与经典采样在离散马尔可夫随机场中的表现，发现量子无实际速度优势。
An End-to-End Hybrid Quantum--Classical Sampling Workflow for Discrete Markov Random Fields: A Reproducible Case Study
- 用经典预计算概率，实现量子幅度编码采样以公平比较
- 量子采样每秒有效样本数仅为经典方法的1/36，无时钟时间优势
- 量子变分电路在高压缩下性能远差于张量网络模型，适合研究者参考
离散马尔可夫随机场（MRFs）的采样是一个难题。本文研究小规模MRF上基于幅度编码的独立同分布采样，其中2^n个目标概率通过经典方式预先计算。这虽消除量子指数加速，但能与经典MCMC方法进行清晰对比。在涵盖五类图结构的60个实例中（1000步预烧、3000个保留样本），量子采样相对于单点吉布斯、块吉布斯、调优块和并行退火的平均有效样本数（ESS）比分别为16.35、7.29、1.82和1.79，表明现代经典采样器已大幅缩小差距。将O(2^n)预处理开销摊入真实时间后，精确逆累积分布函数采样达到1770万ESS/s，而量子采样仅48.8万ESS/s（平均快36倍，单实例快153倍），确认无真实时间优势。我们分析了MCMC自相关代价，并对n∈{8,10,12}的幅度编码态制备进行了基准测试。针对n≤40的矩阵乘积态（MPS）缩放研究显示，当χ=32时，n=40处保真度为0.721±0.059。最后，在相同预算下对n∈{8,10,12}的变分量子电路（VQC）与MPS进行比较，结果表明：对应压缩比10.7×、34.1×、113.8×时，保真度分别为(0.31, 0.99)、(0.21, 0.96)、(0.17, 0.88)，表明VQC性能显著落后。
原文摘要 · Abstract (English)
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 ($τ\approx 1$). 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 $χ=32$ 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 $113.8\times$.
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