基于量子-经典对应理论的温度目标QAOA公平采样
Fair sampling with temperature-targeted QAOA based on quantum-classical correspondence theory
AI总结：
本文提出基于量子-经典对应理论的SBO-QAOA算法，通过温度依赖的哈密顿量实现退化态的公平采样，解决了标准QAOA在退化态采样中的偏差问题。
摘要：
在具有退化基态的组合优化问题中，公平采样退化解是至关重要的。然而，标准横场混合器的量子近似优化算法（QAOA）在电路深度增加时会导致退化态之间出现偏差。基于量子-经典对应理论，我们提出SBO-QAOA，其采用一个依赖温度的哈密顿量，该哈密顿量编码了一个吉布斯分布作为基态。数值模拟显示，与标准QAOA不同，SBO-QAOA在退化态之间产生均匀分布的基态概率，这些公平性和温度目标特性即使在仅使用四个变分参数和线性调度的情况下也得以保持。
英文摘要：
In combinatorial optimization problems with degenerate ground states, fair sampling of degenerate solutions is essential. However, the quantum approximate optimization algorithm (QAOA) with a standard transverse-field mixer induces biases among degenerate states as circuit depth increases. Based on quantum-classical correspondence theory, we propose SBO-QAOA, which employs a temperature-dependent Hamiltonian encoding a Gibbs distribution as its ground state. Numerical simulations show that, unlike standard QAOA, SBO-QAOA yields ground-state probabilities converging to finite-temperature values with uniform distribution among degenerate states. These fairness and temperature-targeting properties are preserved even with only four variational parameters under a linear schedule.
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