Fast adiabatic evolution by oscillating initial Hamiltonians

TL;DR

This paper introduces a method to accelerate adiabatic quantum evolution by embedding oscillations into the initial Hamiltonian, effectively approximating counterdiabatic driving without extra control components.

Contribution

It presents a novel approach to achieve fast adiabatic-like evolution using oscillating initial Hamiltonians, avoiding additional Hamiltonian terms and strong controls.

Findings

Effective speedup of adiabatic processes demonstrated in quantum state transfer.

Method successfully approximates counterdiabatic driving with oscillating controls.

Applicable to entanglement creation and avoided-crossing problems.

Abstract

We propose a method to produce fast transitionless dynamics for finite-dimensional quantum systems without requiring additional Hamiltonian components not included in the initial control setup, remaining close to the true adiabatic path at all times. The strategy is based on the introduction of an effective counterdiabatic scheme: a correcting Hamiltonian is constructed which approximatively cancels nonadiabatic effects, inducing an evolution tracking the adiabatic states closely. This can be absorbed into the initial Hamiltonian by adding a fast oscillation in the control parameters. We show that a consistent speedup can be achieved without requiring strong control Hamiltonians, using it both as a stand-alone shortcut-to-adiabaticity and as a weak correcting field. A number of examples are treated, dealing with quantum state transfer in avoided-crossing problems and entanglement creation.