Performance of the Quantum Approximate Optimization Algorithm on the Maximum Cut Problem

TL;DR

This paper evaluates the Quantum Approximate Optimization Algorithm (QAOA) on the MaxCut problem, demonstrating its potential to outperform classical algorithms with modest quantum resources and efficient implementation strategies.

Contribution

It provides empirical evidence that QAOA can surpass classical algorithms on MaxCut with limited circuit depth and scalable problem size, using classical simulation and optimization techniques.

Findings

QAOA can outperform the Goemans-Williamson classical algorithm.

Performance is insensitive to problem size at fixed circuit depth.

Efficient implementation on limited connectivity quantum hardware is feasible.

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) is a promising approach for programming a near-term gate-based hybrid quantum computer to find good approximate solutions of hard combinatorial problems. However, little is currently know about the capabilities of QAOA, or of the difficulty of the requisite parameters optimization. Here, we study the performance of QAOA on the MaxCut combinatorial optimization problem, optimizing the quantum circuits on a classical computer using automatic differentiation and stochastic gradient descent, using QuantumFlow, a quantum circuit simulator implemented with TensorFlow. We find that we can amortize the training cost by optimizing on batches of problems instances; that QAOA can exceed the performance of the classical polynomial time Goemans-Williamson algorithm with modest circuit depth, and that performance with fixed circuit depth is insensitive to problem size. Moreover, MaxCut QAOA can be efficiently implemented on a gate-based quantum computer with limited qubit connectivity, using a qubit swap network. These observations support the prospects that QAOA will be an effective method for solving interesting problems on near-term quantum computers.