Clustering-Based Sub-QUBO Extraction for Hybrid QUBO Solvers

TL;DR

This paper introduces a clustering-based method to decompose large QUBO problems into smaller sub-problems, enabling the use of NISQ quantum devices for larger instances with improved solution quality.

Contribution

It proposes a novel sub-QUBO extraction protocol using correlation-based clustering, enhancing problem decomposition for quantum optimization.

Findings

Outperforms previous methods in objective function quality

Maintains similar quantum resource usage

Applicable to various QUBO problem classes

Abstract

Quantum Approximate Optimization Algorithm (QAOA) can be used to solve quadratic unconstrained binary optimization (QUBO) problems. However, the size of the solvable problem is limited by the number of qubits. To leverage noisy intermediate-scale quantum (NISQ) devices to solve large-scale QUBO problems, one possible way is to decompose the full problem into multiple sub-problems, which we refer to as the Sub-QUBO Formalism. In this work, we enhance this formalism by proposing a sub-QUBO extraction protocol. To do so, we define a measure to quantify correlations between variables and use it to build a correlation matrix. This matrix serves as the input for clustering algorithms to group variables. Variables belonging to the same group form sub-QUBOs and are subsequently solved using QAOA. Our numerical analysis on several classes of randomly generated QUBO problems demonstrates that this grouping method outperforms previous approaches in terms of objective function values, while maintaining a comparable number of quantum subroutine calls. This method offers wide applicability for solving QUBO problems on NISQ devices.