An adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer

TL;DR

This paper introduces an adaptive, problem-specific version of the quantum approximate optimization algorithm (QAOA) that converges faster and is more hardware-efficient for solving combinatorial problems like Max-Cut.

Contribution

The authors develop an iterative, adaptive QAOA that outperforms the standard version in convergence speed and resource efficiency, tailored to specific problems and hardware constraints.

Findings

Faster convergence of the adaptive QAOA compared to standard QAOA.

Reduced number of CNOT gates and optimization parameters.

Evidence linking speedup to shortcuts to adiabaticity.

Abstract

The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the standard QAOA ansatz is not optimal, there is no systematic approach for finding better ans\"atze. We address this problem by developing an iterative version of QAOA that is problem-tailored, and which can also be adapted to specific hardware constraints. We simulate the algorithm on a class of Max-Cut graph problems and show that it converges much faster than the standard QAOA, while simultaneously reducing the required number of CNOT gates and optimization parameters. We provide evidence that this speedup is connected to the concept of shortcuts to adiabaticity.