Quantum Adiabatic Evolution Algorithms versus Simulated Annealing

TL;DR

This paper compares quantum adiabatic evolution algorithms and simulated annealing, showing they perform similarly in symmetric cases but diverge in efficiency on certain asymmetric problems.

Contribution

It provides a detailed analysis of when quantum adiabatic algorithms outperform simulated annealing, highlighting specific problem structures that influence their relative success.

Findings

Quantum algorithms and simulated annealing are similar for symmetric cost functions.

Quantum adiabatic algorithms can solve certain problems in polynomial time.

Simulated annealing requires exponential time for some related problems.

Abstract

We explain why quantum adiabatic evolution and simulated annealing perform similarly in certain examples of searching for the minimum of a cost function of n bits. In these examples each bit is treated symmetrically so the cost function depends only on the Hamming weight of the n bits. We also give two examples, closely related to these, where the similarity breaks down in that the quantum adiabatic algorithm succeeds in polynomial time whereas simulated annealing requires exponential time.