Anti-crossings and spectral gap during quantum adiabatic evolution

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.

References in corpus (2)

• Quantum annealing: the fastest route to quantum computation?
• The Effects of the Problem Hamiltonian Parameters on the Minimum Spectral Gap in Adiabatic Quantum Optimization