Solving Larger Maximum Clique Problems Using Parallel Quantum Annealing

TL;DR

This paper presents a hybrid method combining parallel quantum annealing and graph decomposition to solve larger maximum clique problems on current quantum hardware.

Contribution

It introduces a novel hybrid approach that enables solving larger NP-hard problems by leveraging parallel quantum annealing and graph decomposition techniques.

Findings

Successfully solved maximum clique problems on graphs with up to 120 nodes.

Demonstrated the effectiveness of hybrid quantum-classical methods for larger problem sizes.

Showed that parallel quantum annealing can be combined with graph decomposition for improved performance.

Abstract

Quantum annealing has the potential to find low energy solutions of NP-hard problems that can be expressed as quadratic unconstrained binary optimization problems. However, the hardware of the quantum annealer manufactured by D-Wave Systems, which we consider in this work, is sparsely connected and moderately sized (on the order of thousands of qubits), thus necessitating a minor-embedding of a logical problem onto the physical qubit hardware. The combination of relatively small hardware sizes and the necessity of a minor-embedding can mean that solving large optimization problems is not possible on current quantum annealers. In this research, we show that a hybrid approach combining parallel quantum annealing with graph decomposition allows one to solve larger optimization problem accurately. We apply the approach on the Maximum Clique problem on graphs with up to 120 nodes and 6395 edges.