Non-Hermitian Quantum Annealing in the Ferromagnetic Ising Model

TL;DR

This paper introduces a non-Hermitian quantum annealing method that efficiently finds the ground state of large ferromagnetic Ising models, significantly reducing annealing time and promising for solving NP-complete problems.

Contribution

The paper presents a novel non-Hermitian quantum annealing algorithm with analytical and numerical validation, achieving logarithmic scaling of annealing time with system size.

Findings

Annealing time scales as ln N with system size N.

Method successfully applied to models with up to 1024 spins.

Potential for faster solutions to NP-complete problems.

Abstract

We developed a non-Hermitian quantum optimization algorithm to find the ground state of the ferromagnetic Ising model with up to 1024 spins (qubits). Our approach leads to significant reduction of the annealing time. Analytical and numerical results demonstrate that the total annealing time is proportional to ln N, where N is the number of spins. This encouraging result is important in using classical computers in combination with quantum algorithms for the fast solutions of NP-complete problems. Additional research is proposed for extending our dissipative algorithm to more complicated problems.