AI 中文总结
研究约束组合优化问题，开发光谱理论统一量子优化算法，揭示计算速度减慢由纠缠重组驱动，指出约束代数性质引发重组，约束感知动力学可减少减慢，解释了约束感知量子方法优势并连接多方面内容。
AI 中文摘要
约束组合优化是许多工业和技术决策问题的基础。我们开发了一种光谱理论，统一了许多量子优化算法。我们表明，计算速度减慢是由纠缠重组驱动的：系统演化过程中纠缠的产生、重新分布和破坏。减慢的严重程度取决于必须改变的纠缠量。我们表明，约束的代数性质会引发这种重组，而约束感知动力学通过避免不必要的重组来减少相关的减慢。该框架解释了为什么约束感知量子方法可以优于基于通用惩罚的方法。该理论连接了约束优化、计算复杂性、纠缠动力学和哈密顿光谱结构，跨越连续时间和基于电路的量子优化范式。
英文摘要
Constrained combinatorial optimization underlies many industrial and technological decision problems. We develop a spectral theory that unifies many quantum optimization algorithms. We show that computational slowdown is driven by entanglement restructuring: the creation, redistribution, and destruction of entanglement during system evolution. The severity of the slowdown depends on how much entanglement must be changed. We show that algebraic properties of constraints induce such restructuring, and that constraint-aware dynamics reduce the associated slowdown by avoiding unnecessary restructuring. This framework explains why constraint-aware quantum methods can outperform generic penalty-based approaches. The theory connects constrained optimization, computational complexity, entanglement dynamics, and Hamiltonian spectral structure across continuous-time and circuit-based quantum optimization paradigms.
