发表机构
University of Luxembourg; Donostia International Physics Center（卢森堡大学; 圣塞巴斯蒂安国际物理中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种无哈密顿量的绝热规范势理论，适用于参数依赖的幺正算子，通过厄米带状线性系统高效构造，并展示其在踢顶和砖墙电路中的快速收敛，从而将绝热捷径和混沌诊断推广至Floquet系统与量子电路。
AI 中文摘要
反绝热驱动为快速量子控制提供了一条通用途径，但其标准表述预设了一个哈密顿量生成器。我们针对参数依赖的幺正算子 $U_\lambda$ 发展了一种无哈密顿量的绝热规范势（AGP）理论。AGP的精确和正则化版本源自一个厄米、带状线性系统，其成本与厄米情形下的Lanczos构造相当，既不需要对角化，也不需要矩阵对数。我们展示了截断Krylov近似在踢顶（kicked top）以及由幺正 $\check{R}$ 矩阵构建的可积砖墙电路中的快速收敛，而在此类设置中不存在局部有效哈密顿量。我们的结果将绝热捷径以及基于AGP的混沌诊断扩展到Floquet系统和量子电路中。
英文摘要
Counterdiabatic driving provides a universal route to fast quantum control, but its standard formulation presupposes a Hamiltonian generator. We develop a Hamiltonian-free theory of the adiabatic gauge potential (AGP) for parameter-dependent unitary operators $U_λ$. Exact and regularized versions of the AGP follow from a Hermitian, banded linear system at a cost comparable to the Lanczos construction in the Hermitian case, requiring neither diagonalization nor a matrix logarithm. We demonstrate rapid convergence of the truncated Krylov approximation for the kicked top and for an integrable brickwork circuit built from unitary $\check{R}$ matrices, a setting in which no local effective Hamiltonian is available. Our results extend shortcuts to adiabaticity, and AGP-based diagnostics of chaos, to Floquet systems and quantum circuits.
Comments5 pages, 3 figures + supplemental materials
