量子玻尔兹曼采样器中的退相干增强响应与相变
Dephasing-Enhanced Response and Phase Transitions in Quantum Boltzmann Samplers
- Nankai University（南开大学）
- National University of Singapore（新加坡国立大学）
- Chern Institute of Mathematics, Nankai University（南开大学陈省身数学研究所）
- National Institute of Education, Nanyang Technological University（南洋理工大学国立教育学院）
- Southwest Minzu University（西南民族大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究退相干如何使量子玻尔兹曼采样器进入有序相，揭示其源于增强的条件响应，并建立全连接耦合下的稳态转变及临界统计，通过调整耗散更新可在任意图上恢复目标概率过程。
AI中文摘要：
退相干可以驱动量子玻尔兹曼采样器进入有序相，而其编程的概率分布仍保持无序。我们将这一转变归因于增强的条件响应：相干性损失改变了每个自旋对其邻居的响应方式，而相互作用放大了这种变化。对于全连接耦合，我们建立了有限退相干下的稳态转变。在临界点附近，磁化分布取决于退相干强度与系统尺寸平方根之比，即使局部相干修正消失，仍保留有限的相干印记。在强退相干极限下的方格晶格上，动力学产生有效的多自旋相互作用和概率流，具有类伊辛的临界统计。调整局部耗散更新可在任意图上恢复目标概率过程。
英文摘要：
Dephasing can drive a quantum Boltzmann sampler into an ordered phase while its programmed probability distribution remains disordered. We trace this transition to an enhanced conditional response: coherence loss changes how each spin responds to its neighbors, and interactions amplify the change. For all-to-all coupling, we establish the stationary transition at finite dephasing. Near criticality, the magnetization distribution depends on the ratio of dephasing strength to the square root of system size, retaining a finite imprint of coherence even as the local coherent correction vanishes. In the strong-dephasing limit on a square lattice, the dynamics generates effective multispin interactions and probability currents, with Ising-like critical statistics. Adjusting the local dissipative update restores the target probability process on arbitrary graphs.
