A Novel Solver for QUBO Problems: Performance Analysis and Comparative Study with State-of-the-Art Algorithms

TL;DR

This paper introduces QIS3, a quantum-inspired solver for QUBO problems that combines multiple optimization techniques and outperforms existing algorithms in solution quality and speed across various problem classes.

Contribution

The paper presents QIS3, a novel adaptive quantum-inspired solver that integrates branch-and-bound, gradient descent, and heuristics, demonstrating superior performance over state-of-the-art methods.

Findings

QIS3 achieves the best solutions on nearly all tested instances.

QIS3 attains 94% optimality in max-cut problems.

QIS3 outperforms eight leading solvers in speed and accuracy.

Abstract

Quadratic Unconstrained Binary Optimization (QUBO) provides a versatile framework for representing NP-hard combinatorial problems, yet existing solvers often face trade-offs among speed, accuracy, and scalability. In this work, we introduce a quantum-inspired solver (QIS) that unites branch-and-bound pruning, continuous gradient-descent refinement, and quantum-inspired heuristics within a fully adaptive control architecture. We benchmark QIS3 against eight state-of-the-art solvers, including genetic algorithms, coherent Ising machines, simulated bifurcation, parallel tempering, simulated annealing, our prior QIS2 version, D-Wave's simulated-annealing (Neal), and Gurobi on three canonical QUBO problem classes: Max-Cut, NAE-3SAT, and Sherrington-Kirkpatrick spin glass problems. Under a uniform runtime budget, QIS3 attains the best solution on nearly all instances, achieving optimality in 94% of max-cut instances. These results establish QIS3 as a robust, high-performance solver that bridges classical exact strategies and quantum-inspired heuristics for scalable QUBO optimization.