Qoolchain: A QUBO Preprocessing Toolchain for Enhancing Quantum Optimization

Abstract

Solving combinatorial optimization problems is crucial in research and industry but still challenging since these problems are usually NP-hard or NP-complete. Classical solvers struggle with their non-polynomial complexity. Although heuristic algorithms are widely used, they often fall short in execution time and accuracy, increasing the interest in quantum computing alternatives using Quadratic Unconstrained Binary Optimization (QUBO) formulations. However, current Noisy Intermediate-Scale Quantum (NISQ) computers and future early fault-tolerant quantum devices face limitations in qubit availability and circuit depth, necessitating preprocessing to reduce problem complexity. This study introduces Qoolchain, a QUBO preprocessing toolchain designed to reduce problem size and enhance solver performance. Developed in Cython, Qoolchain is compatible with major quantum frameworks and optimized for the Grover Adaptive Search (GAS) algorithm. It includes steps like persistency identification, decomposition, and probing to estimate function bounds, all with polynomial complexity. Qoolchain also proposes using the Grover Search algorithm for problem segments whose optimal value is known a priori from graph theory and Shannon decomposition to reduce QUBO problem complexity further. Evaluated against the D-Wave preprocessing toolchain on various problems, Qoolchain demonstrates higher efficiency and accuracy. It represents a significant advancement in enabling practical quantum solvers, addressing hardware limitations, and solving complex industry-relevant problems.