可整合的数字量子模拟:一般化的吉布斯集和Trotter过渡
Eric Vernier1, Bruno Bertini2,3, Giuliano Giudici4,5
1CNRS and Université Paris Cité, Laboratoire de Probabilités, Statistique et Modélisation, F-75013 Paris, France.
Physical review letters
|July 14, 2023
概括
数字量子模拟 (DQS) 错误通常无法控制. 然而,对于可整合的系统,错误仍然是有限的,揭示了与保存量和分阶磁化相关的新型Trotter过渡.
科学领域:
- 量子信息科学 量子信息科学
- 凝聚物质物理学 凝聚物质物理学
- 计算物理 计算物理
背景情况:
- 数字量子模拟 (DQS) 使用离散的Trotter步骤近似连续动态.
- 以前的研究表明,由于量子混乱,错误变得无法控制的急剧Trotter过渡.
- 可整合的系统,拥有精确的保存规律,为DQS忠实性提供了不同的视角.
研究的目的:
- 为了研究一个可整合的系统中Trotterized进化的行为,特别是XXZ海森伯格旋转链.
- 将典型的Trotter过渡与可整合DQS中观察到的现象进行对比.
- 在可整合模型的数字量子模拟中识别Trotter过渡的新型签名.
主要方法:
- 专注于XXZ海森堡旋转链中的自旋波状态的火.
- 分析可整合的Trotterized进化作为Trotter步骤持续时间 (τ) 的函数.
- 采用精确的计算来确定晚时动态的属性,由离散的一般化吉布斯集团 (dGGE) 描述.
主要成果:
- 对于小的 τ,dGGE 在分析上依赖于Trotter 步骤,保持离谱化误差的界限.
- 一个新的Trotter过渡发生在一个值 τ_{th},在那里dGGE突然变化.
- 这种过渡可以通过依赖于t的非零分级磁化的出现在本地检测到.
结论:
- 可整合的DQS不一定会导致不受控制的错误,挑战以前关于Trotter过渡的假设.
- 在可集成系统中存在一种新型的Trotter过渡,其特点是dGGE的突然变化.
- 离散的GGE代表了数字量子平台特有的独特的不平衡状态.
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