NISQ-compatible approximate quantum algorithm for unconstrained and constrained discrete optimization

TL;DR

This paper introduces a gradient-based quantum algorithm compatible with NISQ devices for solving large-scale unconstrained and constrained discrete optimization problems, demonstrating its effectiveness through simulations and real quantum hardware.

Contribution

It presents a novel approximate quantum algorithm that efficiently incorporates simple constraints directly into the circuit, enhancing scalability and performance for large optimization problems.

Findings

Hybrid quantum-classical approach outperforms classical solver CPLEX on large MaxCut problems.

Algorithm successfully tested on a superconducting quantum processor.

Demonstrates potential of hybrid quantum algorithms for practical large-scale optimization.

Abstract

Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum algorithms training, the shape of their cost landscape, the accuracy of their output, and their ability to scale to large-size problems. Here, we present an approximate gradient-based quantum algorithm for hardware-efficient circuits with amplitude encoding. We show how simple linear constraints can be directly incorporated into the circuit without additional modification of the objective function with penalty terms. We employ numerical simulations to test it on MaxCut problems with complete weighted graphs with thousands of nodes and run the algorithm on a superconducting quantum processor. We find that for unconstrained MaxCut problems with more than 1000 nodes, the hybrid approach combining our algorithm with a classical solver called CPLEX can find a better solution than CPLEX alone. This demonstrates that hybrid optimization is one of the leading use cases for modern quantum devices.