Suppressing excitations using quantum-Brachistochrone and nearest-neighbour interactions

TL;DR

This paper introduces a local, time-dependent control protocol for the transverse-field Ising model that suppresses excitations more effectively and robustly than traditional counterdiabatic methods, even in noisy environments.

Contribution

It proposes a novel, experimentally feasible control scheme using local modulation of the Hamiltonian to improve excitation suppression in quantum critical dynamics.

Findings

Higher fidelity in excitation suppression compared to approximate counterdiabatic driving.

Enhanced robustness against noise in the proposed protocol.

Analytical demonstration of anti-Kibble-Zurek scaling with noise presence.

Abstract

We examine excitation suppression in the transverse-field Ising model (TFIM), where finite-time drive across a quantum critical point is assisted by the presence of a time-dependent coupling parameter. While conventional counterdiabatic protocols are designed to eliminate excitations, they often require complex many-body terms that are difficult to realize experimentally. In contrast, our approach employs a local, time-dependent modulation of an existing coupling term in the Hamiltonian. Within the framework of quantum optimal control, we find that under a linear ramp of the transverse field, the optimal evolution of the second parameter follows a non-monotonic trajectory. For the TFIM, this protocol yields higher fidelity and improved robustness against noise compared to several orders of approximate counterdiabatic driving. Furthermore, we provide an analytical demonstration of anti-Kibble-Zurek scaling in the presence of noise acting on either the transverse field or the longitudinal coupling. These results highlight the potential of this approach for developing simple, noise-resilient protocols for finite-time quantum state preparation.