一维、二维和三维中随机横场伊辛模型的量子退火
Quantum annealing of the random transverse-field Ising model in one, two, and three dimensions
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中文总结 AI 辅助
本文针对随机横场伊辛模型，基于SDRG技术建立标度理论，结合数值分析与精确对角化，揭示误差密度随退火时间对数下降的规律，绘制缺陷形成事件图谱以辅助最优退火路径设计。
中文摘要 AI 辅助
量子退火必须足够缓慢以避免缺陷形成，我们通过绝热定理在随机横场伊辛模型中研究该问题，得到可避免缺陷形成的极限速率。我们基于强无序重正化群（SDRG）技术的方法，将退火过程视为强耦合团簇的逐步聚集，从而获取误差形成的基本事件。我们针对一般维度下这些事件的统计规律建立标度理论，并通过高效实现SDRG方法，将其与一维、二维和三维中的大量数值分析结果进行对比；该方法还通过自由费米子技术在一维中的精确对角化得到验证。我们的结果一致表明，误差密度随退火时间呈对数缓慢下降，其特征由对应模型无限无序不动点的维度相关临界指数决定。此外，我们在激发能-控制参数平面上绘制了潜在缺陷形成的单个事件图谱，这可能有助于最优退火路径的设计。
英文摘要
Quantum annealing must be sufficiently slow to prevent defect formation. We study this problem in the random transverse-field Ising model via the adiabatic theorem to obtain the limiting rate at which defect formation can be avoided. Our approach based on the strong-disorder renormalization group (SDRG) technique views the annealing process as a gradual aggregation of strongly coupled clusters, giving access to the elementary events of error formation. We present a scaling theory of the statistics of these events in general dimensions and confront it to an extensive numerical analysis carried out in one, two, and three dimensions by an efficient implementation of the SDRG method. This approach is also validated by exact diagonalization in one dimension by means of the free-fermion technique. Our results consistently show a logarithmically slow decrease of the error density with the annealing time, characterized by the dimension-dependent critical exponents of the corresponding infinite-disorder fixed point of the model. Furthermore, we provide a map of individual events of potential defect formation in the excitation energy - control parameter plane, which may help in the design of optimal annealing paths.
发表机构
- Northwestern University（西北大学）
- HUN-REN Wigner Research Centre for Physics（匈牙利科学院Wigner物理研究中心）
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