Improved gap dependence in adiabatic state preparation by adaptive schedule

TL;DR

This paper introduces an adaptive scheduling strategy for adiabatic quantum computing that significantly reduces the dependence of evolution time on the spectral gap, improving efficiency for a broad class of systems.

Contribution

The authors propose a nonlinear adaptive schedule that improves gap dependence from quadratic to linear, and demonstrate its optimality and superiority over linear schedules.

Findings

Quadratic gap dependence is reduced to linear for many systems.

The proposed schedule is shown to be optimal for linear gap systems.

Linear schedules are proven to be sub-optimal.

Abstract

Adiabatic quantum computing is a powerful framework for state preparation, while its evolution time often scales quadratically in the inverse Hamiltonian spectral gap, leading to sub-optimal computational complexity. In this work, we introduce a nonlinear adaptive strategy for finding the time scheduling function, and show that the gap dependence can be quadratically improved to be inverse linear for a wide range of systems under a mild gap measure condition. Through variational analysis, we further demonstrate the optimality of our schedule for systems with linear gap and the partial optimality for general systems, while we also rigorously show that the commonly used linear schedule is never optimal.