Abstract
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.
- Received 16 February 2023
- Revised 17 October 2023
- Accepted 19 January 2024
DOI:https://doi.org/10.1103/PhysRevX.14.011032
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
In noisy quantum devices, the prospects of implementing exact adiabatic control protocols are dim. One promising alternative is known as “shortcuts to adiabaticity” (STA); it removes the requirement for slow driving in adiabatic protocols, leading to the preparation of the same target state in a shorter time. Of the techniques developed to engineer STA, counterdiabatic (CD) driving stands out by providing a universal approach for any system in isolation. While its development is well established in simple systems, many-body quantum systems remain challenging. Here, we present an efficient way to construct the CD term that is required to guide the system’s dynamics along a prescribed trajectory.
Specifically, we identify the minimal subspace in which the dynamics unfolds, known as the Krylov space. Our formalism provides a significant advance beyond the state of the art, which currently focuses on the use of variational methods to find an approximate CD control. Our results show that the CD term admits a closed-form expansion in Krylov space.
Beyond its use for quantum control, the CD term has fundamental significance in the theoretical foundation of nonequilibrium physics. Our results are therefore of broad relevance to foundations of physics, nonequilibrium statistical mechanics, quantum control, and quantum algorithms. As a prospect, we expect our findings to have a transformative impact leading to a new generation of digitized CD quantum algorithms.
