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.

翻译：二次无约束二进制优化（QUBO）是物流、供应链、金融、制药科学、化学、信息技术及能源等诸多行业与学术领域的核心问题。这类问题通常涉及优化大量二进制变量，使得精确求解的难度呈指数级增长。因此，大多数QUBO问题被归类为NP难问题。为应对这一挑战，我们开发了一种针对任意QUBO问题的强大前馈神经网络优化器。本研究表明，该FNN优化器能够为大规模问题（包括稠密80变量加权MaxCut及随机QUBO问题）提供高质量近似解，在8核CPU上以不足1.1秒的平均耗时实现超过99%的求解精度。此外，在200变量随机QUBO问题中，FNN优化器在100秒计算时限内以72%的优势超越Gurobi优化器，展现出在实时优化任务中的强大潜力。基于此模型，我们探索了将FNN与基于量子退火器的激活函数相结合的新方法，构建量子-经典编码解码器优化器，旨在进一步提升FNN在QUBO优化中的性能。