A Fidelity Susceptibility Approach to Quantum Annealing of NP-hard problems

TL;DR

This paper investigates the physical origins of the exponential energy gap closing in quantum annealing for NP-hard problems, identifying a phase transition via fidelity susceptibility divergence as the cause of QA failure.

Contribution

It introduces a fidelity susceptibility approach to detect phase transitions linked to QA failure in NP-hard problems using quantum Monte Carlo simulations.

Findings

Identified a phase transition associated with QA failure.

Found that gapless points are located in the phase transition region.

Suggested the physical reason behind the exponential gap closing.

Abstract

The computational complexity conjecture of NP $\nsubseteq$ BQP implies that there should be an exponentially small energy gap for Quantum Annealing (QA) of NP-hard problems. We aim to verify how this computation originated gapless point could be understood based on physics, using the quantum Monte Carlo method. As a result, we found a phase transition detectable only by the divergence of fidelity susceptibility. The exponentially small gapless points of each instance are all located in the phase found in this study, which suggests that this phase transition is the physical cause of the failure of QA for NP-hard problems.