Motzkin-Straus优化在熵计算平台上的应用
Motzkin-Straus Optimization on an Entropy-Computing Platform
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中文总结 AI 辅助
本文提出利用Motzkin-Straus定理将组合优化转化为连续二次规划，在Dirac-3S熵计算机上求解，并在DIMACS基准上超越多数经典求解器，展示了熵计算在非凸优化中的潜力。
中文摘要 AI 辅助
我们提出了一种组合优化框架，该框架使用和约束连续二次规划，可由QCi的Dirac-3S光子熵计算机求解。这得益于Motzkin-Straus定理，该定理在离散团问题和概率单纯形上的优化之间提供了强有力的桥梁。我们通过解决约束满足问题来展示该框架的通用性，并在DIMACS基准套件上提供了广泛的基准测试。Dirac-3S平台在超过五分之四的基准实例上匹配或直接领先于两个独立实现的经典基线，在几乎所有结构化图族上达到已知最优解，甚至在几个测试的最大实例上优于两个经典求解器。另一方面，调整良好的经典连续优化器仅在最具挑战性的植入团实例上保持优势。这项工作为使用原生模拟非常规计算平台解决组合优化问题建立了一条可行路径，同时将熵计算定位为导航非凸景观的竞争性方法，并为新兴计算范式提供了严格的基线。
英文摘要
We introduce a framework for combinatorial optimization using sum-constrained continuous quadratic programs solvable by QCi's Dirac-3S photonic entropy computer. This is enabled by the Motzkin-Straus theorem which provides a powerful bridge between discrete clique problems and optimization over the probability simplex. We demonstrate this framework's versatility by solving constraint satisfaction problems, providing extensive benchmarks on the DIMACS suite. The Dirac-3S platform matches or outright leads two independently implemented classical baselines on more than four-fifths of the benchmark instances, reaching the best known solution on nearly all structured graph families, even outperforming both classical solvers on several of the largest instances tested. On the other hand, well-tuned classical continuous optimizers retain an edge only on the hardest planted-clique instances. This work establishes a viable pathway for solving combinatorial optimization problems using natively analog unconventional computing platforms, while positioning entropy computing as a competitive approach for navigating non-convex landscapes and providing rigorous baselines for an emerging computational paradigm.
发表机构
- Quantum Computing Inc (QCi)（量子计算公司）
- University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
机构由 AI 辅助整理，请以论文原文为准。
