Benchmarking adiabatic transformation by alternating unitaries

TL;DR

This paper evaluates an alternating unitary approach for adiabatic transformation, comparing its performance to traditional adiabatic driving, and finds it can effectively sample low-energy states in nonadiabatic regimes, useful for quantum annealing.

Contribution

It provides a numerical benchmark of the alternating unitary method against adiabatic driving, highlighting its ability to sample low-energy eigenstates in small-gap Hamiltonians.

Findings

Broader energy eigenstate distribution than adiabatic driving.

Effective sampling of low-energy states in small-gap scenarios.

Potential applicability to quantum annealing for hard problems.

Abstract

Adiabatic transformation can be approximated as alternating unitary operators of a Hamiltonian and its parameter derivative as proposed in a gate-based approach to counterdiabatic driving (van Vreumingen, arXiv:2406.08064). In this paper, we conduct numerical benchmarking of this alternating unitary method in a finite-parameter range against adiabatic driving in nonadiabatic timescale. We find that the alternating unitary method results in broader distribution on energy eigenstates than that obtained by adiabatic driving, but it has ability to sample low-energy eigenstates when an energy gap of a given Hamiltonian is small. It indicates that the alternating unitary method may be able to find good approximate solutions in quantum annealing applied to hard instances.