Shortcuts to Adiabaticity in Krylov Space

TL;DR

This paper introduces a Krylov space method to efficiently construct counterdiabatic terms for shortcuts to adiabaticity, enabling faster quantum state preparation in many-body systems.

Contribution

It develops a Krylov basis approach to solve for counterdiabatic controls, simplifying implementation in complex quantum systems.

Findings

Krylov basis efficiently constructs counterdiabatic terms

Lanczos coefficients reveal properties of counterdiabatic controls

Method incorporates many-body interactions effectively

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.