耗散里德堡原子体系中的量子退火研究

Rydberg quantum system, which has highly-controllable interactions, long coherence times, and large-scale implementing abilities, is now emerging as a competitive platform for quantum simulation. Recently, programmable quantum annealing (QA) architecture based on Rydberg quantum system has been achieved. However, it's worth exploring to implement QA in dissipative experimental systems. On the one hand, dissipation can reduce the coherence time to make QA fail, but on the other hand, dissipation can also export the energy to make the system approach the ground state, which might improve the performances of QA...Based on the mechanism of QA and the properties of Rydberg atoms, this project aims to carry out a QA program in the dissipative Rydberg systems, which can both overcome the adverse impacts and take advantages of the dissipation, so as to farthest improve the performances of QA. The program is divided into two parts, one is to design an iterative QA algorithm which can be realized within the allowed time of the quantum system, and the other one is to design a QA coding scheme to improve the performance of the QA in a dissipative environment. This project is expected to help the experiments to implement large-scale QA to achieve quantum advantages.

里德堡原子体系以其相互作用可控、相干时间较长、容易大规模操作等优势成为实施量子模拟的理想实验平台。近来，基于里德堡原子体系的量子退火研究已经实现可编程的架构设计，而耗散体系中的量子退火还有待研究。这是因为耗散一方面限制了系统的相干时间，使量子退火失效；另一方面也会导致能量输出而使系统更接近基态，从而可能会提升量子退火的性能。..在本项目中，申请人结合量子退火的内在机理和里德堡原子的特殊性质，在有耗散的里德堡原子体系中构建量子退火方案，使其能够克服耗散对量子退火带来的不利影响，同时也尽可能地利用耗散带来的有利因素，以最大程度地提升量子退火的性能。该方案分为两部分，一是设计迭代的量子退火算法，其中每次量子退火都可以在系统允许的时间以内完成；二是利用机器学习辅助设计量子退火编码方案，以显著提升耗散环境下量子退火的性能。预期该项目将为实验上实现大规模的量子退火，从而体现量子优越性提供重要理论基础。

里德堡原子系统因其灵活的可操控性而受到广泛关注，为研究量子多体自旋模型提供了良好的实验平台。我们提出制备格点规范场哈密顿量特定拓扑区域基态的量子退火方案，其具有线性的计算复杂性，可以在当前的里德堡原子系统中实现。此外，我们基于里德堡原子系统，从理论上发现一类由体边响应来刻画的新奇相变。为揭示这类相变的内在机理，我们分别构造了经典和量子的无阻挫哈密顿量，它们的基态与多体系统的动力学有一一对应关系，而从这些基态中可以很好地理解体边响应刻画的相变。我们发现，对于经典系统，这类相变对应着非线性动力系统中的有序到混沌的相变；对于量子系统，这类相变对应着多体周期演化中的热化到多体局域化的相变。我们的理论揭示了动力学相变与平衡系统之间的内在统一。我们的预言可以在里德堡原子阵列中获得实验检验。