混合IQP-QCBM的可训练性与模式分离
Trainability and Mode Separation of Mixed IQP-QCBMs
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中文总结 AI 辅助
该研究提出混合IQP-QCBM模型，证明其可避免局部贫瘠高原，提出聚类初始化方法，在四个基准任务中表现最优，分支可捕获不同数据特征。
中文摘要 AI 辅助
基于瞬时量子多项式时间（IQP）电路的量子电路玻尔兹曼机（QCBM）是具有经典可训练性的有潜力量子生成模型。已知其无辅助量子比特（ancilla-free）形式在特定初始化下避免贫瘠高原，但仍非通用模型。虽然添加辅助量子比特提升了表达能力，但扩展辅助量子比特的模型是否保留局部可训练性仍未知。我们提出混合IQP-QCBM，其将扩展辅助量子比特的电路泛化为无辅助IQP电路的加权混合，每个无辅助IQP电路称为一个分支。对于多项式数量的分支，我们证明其在与数据无关的初始化下可避免局部贫瘠高原，且在特定假设下与数据相关的初始化也可避免。我们进一步证明，混合IQP-QCBM仅当其分支生成大量不同分布时，才能超越最优无辅助IQP电路。特别地，我们关注一种称为“模式分离”的行为，即每个分支捕获目标的特定特征。从分支生成相同分布的初始化中实现模式分离十分困难：分离分支的梯度被抑制，且分支生成的分布仍保持接近。这促使我们提出“聚类初始化”，其为每个分支分配不同的无监督数据聚类，提供初始程度的模式分离。对两个16位数据集的精确计算支持贫瘠高原和梯度抑制的结论。在四个基准任务（二元聚类、二维伊辛模型、二值化MNIST和484自旋玻璃）上，聚类初始化收敛最快且达到最低的平均测试MMD²。我们观察到，当达到最低测试MMD²时，混合IQP-QCBM包含专门用于可区分数据特征的分支，如斑点模式、磁化区或数字形状。
英文摘要
Quantum circuit Born machines (QCBMs) based on instantaneous quantum polynomial-time (IQP) circuits are promising quantum generative models for their classical trainability. It is known that their ancilla-free form avoids barren plateaus under certain initializations, but remains non-universal. Although adding ancilla qubits raises the expressivity, whether the ancilla-extended model retains local trainability remains unknown. We propose the mixed IQP-QCBM, which generalizes the ancilla-extended circuit as a weighted mixture of ancilla-free IQP circuits, called branches. For a polynomial number of branches, we prove local barren-plateau avoidance from data-agnostic and, under certain assumptions, data-dependent initializations. We further show that the mixed IQP-QCBM can surpass the best ancilla-free IQP circuit only if its branches generate a number of distinct distributions. In particular, we focus on a behavior we call \emph{mode separation}, in which each branch captures a particular feature of the target. Mode separation is hard to attain from an initialization whose branches generate the same distribution: the gradients that would separate them are suppressed while the distributions they generate remain close. This motivates \emph{cluster initialization}, which assigns a different unsupervised data cluster to each branch and provides an initial degree of mode separation. Exact calculations on two 16-bit datasets support the barren-plateau and gradient-suppression claims. On four benchmarks, binary clusters, a two-dimensional Ising model, binarized MNIST, and a 484-spin glass, cluster initialization converges fastest and reaches the lowest mean test $\mathrm{MMD}^2$. We observe that, when achieving the lowest test $\mathrm{MMD}^2$, the mixed IQP-QCBM contains branches specialized to distinguishable data features such as blob patterns, magnetization sectors, or digit shapes.
