arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2302.05460quant-phcond-mat.stat-mechcond-mat.str-el
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Krylov空间中的绝热捷径

Shortcuts to Adiabaticity in Krylov Space

Kazutaka Takahashi, Adolfo del Campo

AI总结:

本研究针对多体量子系统中绝热捷径实现困难的问题,提出利用Krylov基求解反绝热项方程的高效方法,通过典型模型验证了其可行性,并探究了多体相互作用的纳入机制。

摘要:

绝热捷径为量子态制备提供了快速协议,其中借助辅助反绝热控制的运用,规避了绝热策略中对慢驱动的要求。尽管这类方法在简单系统中已发展成熟,但在具有多自由度的多体量子系统中,其设计与实现仍颇具挑战。我们证明,通过引入Krylov基,可求解反绝热项(等价于绝热规范势)的方程。Krylov基张成了动力学演化所在的最小算子子空间,为构建反绝热项提供了一种高效途径。我们将该策略应用于典型的单粒子与多粒子模型。反绝热项的性质可通过算法方法构建Krylov基过程中得到的Lanczos系数体现。我们还探究了Krylov基展开如何将多体相互作用纳入反绝热项之中。

英文摘要:

Shortcuts to adiabaticity provide fast protocols for quantum state preparation in which the use of auxiliary counterdiabatic controls circumvents the requirement of slow driving in adiabatic strategies. While their development is well established in simple systems, their engineering and implementation are challenging in many-body quantum systems with many degrees of freedom. We show that the equation for the counterdiabatic term, equivalently the adiabatic gauge potential, is solved by introducing a Krylov basis. The Krylov basis spans the minimal operator subspace in which the dynamics unfolds and provides an efficient way to construct the counterdiabatic term. We apply our strategy to paradigmatic single- and many-particle models. The properties of the counterdiabatic term are reflected in the Lanczos coefficients obtained in the course of the construction of the Krylov basis by an algorithmic method. We examine how the expansion in the Krylov basis incorporates many-body interactions in the counterdiabatic term.

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