用固定纠缠门构建量子生成模型，仅优化单比特旋转即可高效学习目标分布。
Quantum Scrambling Born Machine
- 用固定纠缠单元作为随机化水库，只优化单比特旋转参数。
- 三种纠缠方案下，只要产生近哈亚典型纠缠，学习效果差异小。
- 将哈密顿量耦合参数可训练，性能媲美经典生成模型。
量子生成建模利用量子态测量的玻恩规则自然定义概率分布，是量子计算的近期重要应用。本文提出量子混沌生成功能机：采用固定纠缠酉矩阵（作为混沌水库）提供多比特纠缠，仅优化单比特旋转。研究了三种纠缠酉——哈亚随机酉及两种物理可实现近似（有限深度砖墙随机电路、近邻自旋链哈密顿量的模拟时间演化），结果表明，在所考虑的基准分布与系统规模下，一旦纠缠器产生近哈亚典型的纠缠，模型对混沌器微观构造的敏感度极低。最后，将哈密顿量耦合参数设为可训练，使生成任务转化为变分哈密顿量问题，在参数量相当条件下，性能可与代表性经典生成模型比肩。
原文摘要 · Abstract (English)
Quantum generative modeling, where the Born rule naturally defines probability distributions through measurement of parameterized quantum states, is a promising near-term application of quantum computing. We propose a Quantum Scrambling Born Machine in which a fixed entangling unitary -- acting as a scrambling reservoir -- provides multi-qubit entanglement, while only single-qubit rotations are optimized. We consider three entangling unitaries -- a Haar random unitary and two physically realizable approximations, a finite-depth brickwork random circuit and analog time evolution under nearest-neighbor spin-chain Hamiltonians -- and show that, for the benchmark distributions and system sizes considered, once the entangler produces near-Haar-typical entanglement the model learns the target distribution with weak sensitivity to the scrambler's microscopic origin. Finally, promoting the Hamiltonian couplings to trainable parameters casts the generative task as a variational Hamiltonian problem, with performance competitive with representative classical generative models at matched parameter count.
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