Minimal action control method in quantum critical models

TL;DR

This paper introduces a control protocol for quantum systems that minimizes adiabatic action, enabling high-fidelity ground state control in critical quantum models with minimal spectral gap knowledge.

Contribution

It proposes a geometry-based control method using quantum adiabatic brachistochrone, applicable to various critical quantum systems, improving control fidelity with limited spectral gap information.

Findings

High-fidelity ground state control achieved in critical models

Method applicable to Landau-Zener, Ising, and spin models

Requires only approximate spectral gap knowledge

Abstract

We present a general protocol to control closed quantum systems that is based on minimising the adiabatic action. Using tools based on the geometry of quantum evolutions through the quantum adiabatic brachistochrone, we show that high fidelity control of the ground state of critical quantum systems can be achieved and requires only a reasonable approximation for the ground state spectral gap. We demonstrate our results for three widely applicable systems: the Landau-Zener, Ising, and fully connected spin models.