Algorithmic approach to adiabatic quantum optimization

TL;DR

This paper introduces an adiabatic quantum algorithm that adaptively modifies the initial Hamiltonian to eliminate small energy gaps caused by anticrossings, significantly improving the efficiency of solving complex optimization problems.

Contribution

The authors propose a novel iterative algorithm that uses local minima information to penalize problematic pathways, enhancing adiabatic quantum optimization performance.

Findings

Successfully solved 64-qubit maximum independent set instances

Algorithm converges in approximately 10 iterations

Effective in handling highly-degenerate local minima

Abstract

It is believed that the presence of anticrossings with exponentially small gaps between the lowest two energy levels of the system Hamiltonian, can render adiabatic quantum optimization inefficient. Here, we present a simple adiabatic quantum algorithm designed to eliminate exponentially small gaps caused by anticrossings between eigenstates that correspond with the local and global minima of the problem Hamiltonian. In each iteration of the algorithm, information is gathered about the local minima that are reached after passing the anticrossing non-adiabatically. This information is then used to penalize pathways to the corresponding local minima, by adjusting the initial Hamiltonian. This is repeated for multiple clusters of local minima as needed. We generate 64-qubit random instances of the maximum independent set problem, skewed to be extremely hard, with between 10^5 and 10^6 highly-degenerate local minima. Using quantum Monte Carlo simulations, it is found that the algorithm can trivially solve all the instances in ~10 iterations.