Variational Quantum Algorithms for Combinatorial Optimization

TL;DR

This paper reviews the current state of Variational Quantum Algorithms, especially QAOA, for solving combinatorial optimization problems like MaxCut on NISQ devices, demonstrating practical implementation and challenges.

Contribution

It provides an overview of VQAs for combinatorial optimization, implements QAOA for MaxCut on small graphs, and discusses practical challenges and potential of NISQ-era quantum algorithms.

Findings

QAOA shows promise for combinatorial optimization on NISQ devices.

Implementation on small graphs demonstrates potential and current limitations.

Open-source code and data facilitate further research.

Abstract

The promise of quantum computing to address complex problems requiring high computational resources has long been hindered by the intrinsic and demanding requirements of quantum hardware development. Nonetheless, the current state of quantum computing, denominated Noisy Intermediate-Scale Quantum (NISQ) era, has introduced algorithms and methods that are able to harness the computational power of current quantum computers with advantages over classical computers (referred to as quantum advantage). Achieving quantum advantage is of particular relevance for the combinatorial optimization domain, since it often implies solving an NP-Hard optimization problem. Moreover, combinatorial problems are highly relevant for practical application areas, such as operations research, or resource allocation problems. Among quantum computing methods, Variational Quantum Algorithms (VQA) have emerged as one of the strongest candidates towards reaching practical applicability of NISQ systems. This paper explores the current state and recent developments of VQAs, emphasizing their applicability to combinatorial optimization. We identify the Quantum Approximate Optimization Algorithm (QAOA) as the leading candidate for these problems. Furthermore, we implement QAOA circuits with varying depths to solve the MaxCut problem on graphs with 10 and 20 nodes, demonstrating the potential and challenges of using VQAs in practical optimization tasks. We release our code, dataset and optimized circuit parameters under https://github.com/DanielFPerez/VQA-for-MaxCut.