Quantum Annealing for the Set Splitting Problem

TL;DR

This paper introduces a quantum annealing approach for the Set Splitting Problem, formulating a QUBO model that converges to optimal solutions, with potential for faster problem-solving in various scientific fields.

Contribution

It presents a novel QUBO formulation with penalty functions for the Set Splitting Problem, demonstrating linear scaling and empirical convergence to optimal solutions.

Findings

High accuracy in solutions over trials

Linear scaling of logical qubits with problem size

Potential for faster solutions than classical methods

Abstract

I present a novel use of quantum annealing to solve the Set Splitting Problem using (QUBO) problem formulation. The contribution of the work is in formulating penalty functions that ensure the ground state of the QUBO Hamiltonian corresponds to valid solutions that split the input subsets. This approach scales linearly in terms of the number of logical qubits relative to problem size. Empirical tests of the proposed solution show convergence to globally optimal solutions, with high accuracy rates over repeated trials. Hardware limitations of current quantum annealers lead to an exponential rise in required physical qubits, versus the theoretical linear increase, although this can improve with future developments. Further work is needed to enhance formulation robustness, reduce qubit requirements for embedded problems, and to conduct more extensive bench-marking. Quantum solutions to the Set-Splitting problem lead to reduced time complexity versus classical solutions, and may accelerate research in biology, cybersecurity, and other domains.