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.

中文翻译：

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克雷洛夫空间绝热的捷径

绝热性的捷径为量子态制备提供了快速协议，其中辅助反绝热控制的使用规避了绝热策略中缓慢驱动的要求。虽然它们的开发在简单系统中得到了很好的发展，但它们的工程和实现在具有多个自由度的多体量子系统中具有挑战性。我们证明了反绝热项的方程（相当于绝热规范势）是通过引入克雷洛夫基来求解的。 Krylov 基跨越了动力学展开的最小算子子空间，并提供了构建反绝热项的有效方法。我们将我们的策略应用于典型的单粒子和多粒子模型。反非绝热项的性质反映在通过算法方法构建克雷洛夫基的过程中获得的兰索斯系数中。我们研究克雷洛夫基础的展开式如何在反非绝热项中纳入多体相互作用。