arXiv:2603.14576quant-phcs.LG2026-03被引 9

研究量子生成模型的初始化策略对训练效果的影响,发现数据相关初始化更优。

IQP Born Machines under Data-dependent and Agnostic Initialization Strategies

  • 提出数据依赖初始化策略,改善量子电路优化难度
  • 150量子比特电路在基因组数据上更快收敛到优质解
  • 揭示随机初始化易陷入梯度消失,适合研究量子机器学习冷启动问题

基于瞬时量子多项式(IQP)电路的量子电路玻恩机是量子生成建模的自然候选者,因其概率结构及在某些情形下采样被证明为经典难解。近期工作聚焦于使用基于低阶泡利-Z关联量的均值差异(MMD)损失训练IQP-QCBM,但初始化对优化景观的影响尚不明确。本文首先证明:在全角度随机初始化下,MMD损失景观存在荒原高原。随后建立身份和无偏数据无关初始化下的损失方差下界。进一步考虑与目标分布更匹配的数据依赖初始化,在合理假设下可获得可证明的梯度,并通常更快收敛至良好最小值(在150量子比特电路上对基因组数据的训练中得到验证)。此外,所发展的方差下界框架适用于一类广义非线性损失,为量子机器学习中的热启动分析提供了通用工具。

原文摘要 · Abstract (English)

Quantum circuit Born machines based on instantaneous quantum polynomial-time (IQP) circuits are natural candidates for quantum generative modeling, both because of their probabilistic structure and because IQP sampling is provably classically hard in certain regimes. Recent proposals focus on training IQP-QCBMs using Maximum Mean Discrepancy (MMD) losses built from low-body Pauli-$Z$ correlators, but the effect of initialization on the resulting optimization landscape remains poorly understood. In this work, we address this by first proving that the MMD loss landscape suffers from barren plateaus for random full-angle-range initializations of IQP circuits. We then establish lower bounds on the loss variance for identity and an unbiased data-agnostic initialization. We then additionally consider a data-dependent initialization that is better aligned with the target distribution and, under suitable assumptions, yields provable gradients and generally converges quicker to a good minimum (as indicated by our training of circuits with 150 qubits on genomic data). Finally, as a by-product, the developed variance lower bound framework is applicable to a general class of non-linear losses, offering a broader toolset for analyzing warm-starts in quantum machine learning.

量子生成模型初始化策略梯度消失基因组数据

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