Investigating Quantum Approximate Optimization Algorithms under Bang-bang Protocols

TL;DR

This paper studies the performance of quantum approximate optimization algorithms (QAOA) under bang-bang protocols, revealing phase transitions and the impact of initialization strategies on optimization outcomes.

Contribution

It introduces a detailed analysis of bang-bang QAOA, highlighting phase transitions, performance jumps, and the benefits of adiabatic initialization in a randomized setting.

Findings

Phase transitions occur with respect to total time.

Performance exhibits jumps and plateaus as total time increases.

Adiabatic initialization improves local optima finding.

Abstract

The quantum approximate optimization algorithm (QAOA) is widely seen as a possible usage of noisy intermediate-scale quantum (NISQ) devices. We analyze the algorithm as a bang-bang protocol with fixed total time and a randomized greedy optimization scheme. We investigate the performance of bang-bang QAOA on MAX-2-SAT, finding the appearance of phase transitions with respect to the total time. As the total time increases, the optimal bang-bang protocol experiences a number of jumps and plateaus in performance, which match up with an increasing number of switches in the standard QAOA formulation. At large times, it becomes more difficult to find a globally optimal bang-bang protocol and performances suffer. We also investigate the effects of changing the initial conditions of the randomized optimization algorithm and see that better local optima can be found by using an adiabatic initialization.