发表机构
University of Michigan; Virginia Tech（密歇根大学; 弗吉尼亚理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出通用量子分数匹配框架，用于学习热态，在高温区实现最优样本复杂度，并在IBM硬件上将参数误差从64%降至约10%，无需误差缓解。
AI 中文摘要
分数匹配推动了经典生成学习的重大进展，它使模型能够在不计算难处理的归一化常数（即配分函数）的情况下从数据中学习。然而，将这一原理扩展到量子学习需要重新思考其基础，因为量子态由非对易的密度算符描述，而非标量概率。非对易性不仅在定义量子分数时带来根本性挑战，而且在开发具有高效电路实现和严格理论保证的训练框架时也带来挑战。在这项工作中，我们通过建立一个具有端到端理论保证的通用量子分数匹配框架来弥合这一差距。应用于吉布斯态学习时，我们的方法避免了额外的热态制备，并在高温区域对具有有界局域性和相互作用度的哈密顿量实现了信息论上最优的样本复杂度。这使得分数匹配成为学习量子吉布斯态达到最先进性能的新途径。除这些理论结果外，数值模拟表明，即使在有限测量预算下梯度估计不准确，我们的方法仍然有效。在IBM量子硬件上的实验进一步证明，量子分数匹配是NISQ友好的：无需任何误差缓解或校正，它就能将相对哈密顿量参数误差从64%降低到约10%。这些结果共同将分数匹配扩展为一种实验上可实现的量子态学习范式。
英文摘要
Score matching has driven major advances in classical generative learning by enabling models to learn from data without evaluating intractable normalization constants, or partition functions. Yet, extending this principle to quantum learning requires rethinking its foundations, as quantum states are described by noncommuting density operators rather than scalar probabilities. The noncommutativity creates fundamental challenges not only in defining quantum scores, but also in developing a training framework with efficient circuit implementations and rigorous theoretical guarantees. In this work, we bridge this gap by establishing a general quantum score-matching framework with end-to-end theoretical guarantees. Applied to Gibbs-state learning, our approach avoids additional thermal-state preparation and achieves information-theoretically optimal sample complexity in the high-temperature regime for Hamiltonians with bounded locality and interaction degree. This positions score matching as a new route to state-of-the-art performance in learning quantum Gibbs states. Beyond these theoretical results, numerical simulations show that our method remains effective even when gradients are estimated inaccurately under limited measurement budgets. Experiments on IBM quantum hardware further demonstrate that quantum score matching is NISQ-friendly: without any error mitigation or correction, it reduces the relative Hamiltonian-parameter error from 64% to approximately 10%. Together, these results extend score matching into an experimentally realizable paradigm for quantum-state learning.
Comments57 pages, 5 figures, 3 tables, with an accompanying GitHub repository at https://github.com/dongsnaq/Quantum-Score-Matching
