Does Adiabatic Quantum Optimization Truly Fail for NP-complete problems?

TL;DR

This paper challenges the notion that adiabatic quantum optimization necessarily fails for NP-complete problems by showing that certain paths avoid problematic energy gaps, questioning previous assumptions about its limitations.

Contribution

It demonstrates analytically that for the maximum independent set problem, there exist adiabatic paths without small gaps, suggesting the failure of previous no-go arguments.

Findings

Existence of adiabatic paths without small gaps for maximum independent set

Previous claims of failure rely on the assumption of unavoidable small gaps

Proving failure for all NP-complete problems requires showing no such paths exist

Abstract

It has been recently argued that adiabatic quantum optimization would fail in solving NP-complete problems because of the occurrence of exponentially small gaps due to crossing of local minima of the final Hamiltonian with its global minimum near the end of the adiabatic evolution. Using perturbation expansion, we analytically show that for the NP-hard problem of maximum independent set there always exist adiabatic paths along which no such crossings occur. Therefore, in order to prove that adiabatic quantum optimization fails for any NP-complete problem, one must prove that it is impossible to find any such path in polynomial time.