Anti-crossings and spectral gap during quantum adiabatic evolution

TL;DR

This paper investigates anti-crossings and spectral gaps in quantum adiabatic evolution, focusing on weighted max k-clique problems, revealing how anti-crossings affect the ground state and proposing a more general parametrization.

Contribution

It provides a detailed analysis of anti-crossings in quantum adiabatic computation and introduces a relaxed parametrization for better characterization.

Findings

Anti-crossings cause rapid changes in the ground state.

The spectral gap $elta_{min}$ influences adiabatic evolution.

A more general parametrization improves understanding of anti-crossings.

Abstract

We aim to give more insights on adiabatic evolution concerning the occurrence of anti-crossings and their link to the spectral minimum gap $\Delta_{min}$. We study in detail adiabatic quantum computation applied to a specific combinatorial problem called weighted max $k$-clique. A clear intuition of the parametrization introduced by V. Choi is given which explains why the characterization isn't general enough. We show that the instantaneous vectors involved in the anti-crossing vary brutally through it making the instantaneous ground-state hard to follow during the evolution. This result leads to a relaxation of the parametrization to be more general.