Non-Adiabatic Quantum Optimization for Crossing Quantum Phase Transitions

TL;DR

This paper introduces Non-Adiabatic Quantum Optimization (NAQO), a new framework that outperforms existing adiabatic schedules in crossing quantum phase transitions by leveraging Landau-Zener physics and higher excited states.

Contribution

The authors propose NAQO, a novel approach that surpasses local adiabatic schedules in speed and efficiency for quantum state transitions, applicable to complex models beyond exactly solvable cases.

Findings

NAQO outperforms local adiabatic schedules in models tested.

Schedules based on local adiabaticity do not significantly speed up transitions.

NAQO is effective even in disordered non-integrable models.

Abstract

We consider the optimal driving of the ground state of a many-body quantum system across a quantum phase transition in finite time. In this context, excitations caused by the breakdown of adiabaticity can be minimized by adjusting the schedule of the control parameter that drives the transition. Drawing inspiration from the Kibble-Zurek mechanism, we characterize the timescale of onset of adiabaticity for several optimal control procedures. Our analysis reveals that schedules relying on local adiabaticity, such as Roland-Cerf's local adiabatic driving and the quantum adiabatic brachistochrone, fail to provide a significant speedup over the adiabatic evolution in the transverse-field Ising and long-range Kitaev models. As an alternative, we introduce a novel framework, Non-Adiabatic Quantum Optimization (NAQO), that, by exploiting the Landau-Zener formula and taking into account the role of higher-excited states, outperforms schedules obtained via both local adiabaticity and state-of-the-art numerical optimization. NAQO is not restricted to exactly solvable models, and we further confirm its superior performance in a disordered non-integrable model.