Non-Hermitian Quantum Annealing in the Antiferromagnetic Ising Chain

TL;DR

This paper introduces a non-Hermitian quantum annealing method that significantly speeds up finding ground states in antiferromagnetic Ising chains, potentially improving solutions for complex NP-complete problems.

Contribution

The paper presents a novel non-Hermitian quantum annealing algorithm that reduces annealing time from quadratic to logarithmic scale in system size, demonstrating both analytical and numerical results.

Findings

Annealing time scales as ln N for the non-Hermitian approach

Significant reduction in annealing time compared to Hermitian algorithms

Potential application to classical-quantum hybrid solutions for NP-complete problems

Abstract

A non-Hermitian quantum optimization algorithm is created and used to find the ground state of an antiferromagnetic Ising chain. We demonstrate analytically and numerically (for up to N=1024 spins) that our approach leads to a significant reduction of the annealing time that is proportional to $\ln N$, which is much less than the time (proportional to $N^2$) required for the quantum annealing based on the corresponding Hermitian algorithm. We propose to use this approach to achieve similar speed-up for NP-complete problems by using classical computers in combination with quantum algorithms.