用前馈神经网络快速求解各类量子优化问题，精度超99%。
Towards Arbitrary QUBO Optimization: Analysis of Classical and Quantum-Activated Feedforward Neural Networks
- 设计前馈神经网络直接优化任意QUBO问题
- 80变量最大割问题精度超99%，8核CPU<1.1秒完成
- 融合量子退火激活函数，适合实时优化场景
二次无约束二值优化（QUBO）广泛存在于物流、供应链、金融、制药、化学、IT和能源等领域。这类问题通常涉及大量二值变量，求解精确解呈指数级困难，多数属于NP难问题。为此，我们开发了一种强大的前馈神经网络（FNN）优化器，可高效求解任意QUBO问题。实验表明，该优化器在80变量密集加权最大割问题及随机QUBO上均能提供高质量近似解，平均精度超过99%，且在8核CPU上耗时不足1.1秒。在200变量随机QUBO问题上，其性能优于Gurobi优化器72%（100秒时限内），展现出显著的实时优化潜力。在此基础上，我们进一步探索将FNN与基于量子退火的激活函数结合，构建量子-经典编码器-解码器（QCED）优化器，以进一步提升性能。
原文摘要 · Abstract (English)
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.
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