发表机构
School of Computer Science; Carnegie Mellon University（计算机科学学院; 卡内基梅隆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究离散马尔可夫随机场采样难题中，对小MRF采用幅度编码独立同分布采样，与经典MCMC比较。通过多个实例展示不同方法的ESS比率等，还进行了预处理时间、MPS缩放及VQC与MPS的比较，揭示各方法特点及差距。
AI 中文摘要
从离散马尔可夫随机场（MRF）采样是一个难题。我们研究了对小MRF的幅度编码独立同分布采样，其中\(2^n\)个目标概率通过经典方法预先计算。这消除了量子指数加速，但允许与基于独立电路样本（\(\tau \approx 1\)）的经典MCMC进行清晰比较。在跨越五个图族的60个实例中（1k步预烧，3k个保留样本），量子与单站点吉布斯、块吉布斯、调谐块和平行回火的平均ESS比率分别为\(16.35\)、\(7.29\)、\(1.82\)和\(1.79\)，表明现代经典采样器大大缩小了差距。将\(O(2^n)\)预处理分摊到实际时间中，精确逆CDF采样产生\(17.7\text{M}\) ESS/s，而量子采样器为\(488\text{K}\) ESS/s（平均速率为\(36\times\)，每个实例为\(153\times\)），证实没有实际时间优势。我们表征了MCMC自相关成本，并在\(n \in \{8,10,12\}\)时对幅度编码状态制备进行了基准测试。一个MPS缩放研究（\(n \le 40\)）表明，在\(n = 40\)时，键维度\(\chi = 32\)实现了\(F = 0.721 \pm 0.059\)。最后，在\(n \in \{8,10,12\}\)时，匹配预算的VQC与MPS比较表明，VQC保真度远低于MPS：在压缩率为\(10.7\times\)、\(34.1\times\)和\(113.8\times\)时，\((F_{\mathrm{VQC}}, F_{\mathrm{MPS}}) = (0.31, 0.99), (0.21, 0.96), (0.17, 0.88)\)。
英文摘要
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 $113.8\times$.
Comments9 pages, 7 figures, 9 tables, Accepted to IEEE International Conference of Quantum Computing and Engineering - QCE 2026 in the Quantum End-to-End Hybrid Case Studies (QECS) Technical Papers track
