Quantum search using non-Hermitian adiabatic evolution

TL;DR

This paper introduces a non-Hermitian quantum annealing method that leverages relaxation parameters to efficiently solve optimization problems like Grover's search, reducing search time by avoiding exponentially small energy gaps.

Contribution

The paper presents a novel non-Hermitian quantum annealing approach that improves search efficiency by controlling energy gaps through dissipation, unlike traditional Hermitian methods.

Findings

Energy gap depends on relaxation parameters

Search time can be significantly reduced

Quantum survival probability is analyzed in dissipative environments

Abstract

We propose a non-Hermitian quantum annealing algorithm which can be useful for solving complex optimization problems. We demonstrate our approach on Grover's problem of finding a marked item inside of unsorted database. We show that the energy gap between the ground and excited states depends on the relaxation parameters, and is not exponentially small. This allows a significant reduction of the searching time. We discuss the relations between the probabilities of finding the ground state and the survival of a quantum computer in a dissipative environment.