Towards Arbitrary QUBO Optimization: Analysis of Classical and Quantum-Activated Feedforward Neural Networks

TL;DR

This paper introduces a neural network-based optimizer for QUBO problems that achieves high accuracy rapidly and outperforms traditional solvers, with a novel quantum-classical hybrid approach to further improve performance.

Contribution

The paper presents a new feedforward neural network optimizer for arbitrary QUBO problems and introduces a quantum-classical hybrid model to enhance optimization performance.

Findings

Achieves over 99% accuracy on large QUBO problems in under 1.1 seconds.

Outperforms Gurobi optimizer by 72% on 200-variable QUBO problems within 100 seconds.

Demonstrates the potential of neural network and quantum hybrid methods for real-time QUBO optimization.

Abstract

Quadratic Unconstrained Binary Optimization (QUBO) sits at the heart of many industries and academic fields such as logistics, supply chain, finance, pharmaceutical science, chemistry, IT, and energy sectors, among others. These problems typically involve optimizing a large number of binary variables, which makes finding exact solutions exponentially more difficult. Consequently, most QUBO problems are classified as NP-hard. To address this challenge, we developed a powerful feedforward neural network (FNN) optimizer for arbitrary QUBO problems. In this work, we demonstrate that the FNN optimizer can provide high-quality approximate solutions for large problems, including dense 80-variable weighted MaxCut and random QUBOs, achieving an average accuracy of over 99% in less than 1.1 seconds on an 8-core CPU. Additionally, the FNN optimizer outperformed the Gurobi optimizer by 72% on 200-variable random QUBO problems within a 100-second computation time limit, exhibiting strong potential for real-time optimization tasks. Building on this model, we explored the novel approach of integrating FNNs with a quantum annealer-based activation function to create a quantum-classical encoder-decoder (QCED) optimizer, aiming to further enhance the performance of FNNs in QUBO optimization.