Recursive Quantum Relaxation for Combinatorial Optimization Problems

TL;DR

This paper introduces RQRAO, a recursive quantum relaxation method for MAX-CUT, unifying quantum optimization techniques and leveraging QRACs, achieving superior results on large benchmark graphs in classical simulations.

Contribution

It proposes a novel recursive quantum relaxation approach called RQRAO that unifies existing quantum optimization methods and improves solution quality for MAX-CUT problems.

Findings

RQRAO outperforms Goemans-Williamson and recursive QAOA methods.

RQRAO is comparable to state-of-the-art classical solvers.

Experiments conducted on large benchmark graphs demonstrate effectiveness.

Abstract

Quantum optimization methods use a continuous degree-of-freedom of quantum states to heuristically solve combinatorial problems, such as the MAX-CUT problem, which can be attributed to various NP-hard combinatorial problems. This paper shows that some existing quantum optimization methods can be unified into a solver to find the binary solution which is most likely measured from the optimal quantum state. Combining this finding with the concept of quantum random access codes (QRACs) for encoding bits into quantum states on fewer qubits, we propose an efficient recursive quantum relaxation method called recursive quantum random access optimization (RQRAO) for MAX-CUT. Experiments on standard benchmark graphs with several hundred nodes in the MAX-CUT problem, conducted in a fully classical manner using a tensor network technique, show that RQRAO not only outperforms the Goemans-Williamson and recursive QAOA methods, but also is comparable to state-of-the-art classical solvers. The code is available at \url{https://github.com/ToyotaCRDL/rqrao}.