小 Ising 模型的偏差退化基态采样与融合量子近似优化算法.
1Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Physical review. E
|June 19, 2025
概括
这项研究比较了量子近似优化算法 (QAOA) 混合器来解决优化问题. 格罗弗混合器QAOA提供比横场混合器更公平的解决方案采样,特别是复杂的问题.
科学领域:
- 量子计算是一种量子计算.
- 组合优化的优化.
- 量子算法中的量子算法
背景情况:
- 量子近似优化算法 (QAOA) 是用于组合优化的突出量子算法.
- QAOA通常使用横向场混合器,这可能导致退化基态的非均采样.
- 公平的抽样对于确保所有最佳解决方案都有同等机会被发现至关重要.
研究的目的:
- 数字检查和比较横场混合器QAOA和格罗弗混合器QAOA (GM-QAOA) 的公平采样特性.
- 为了量化公平采样使用Shannon的基态幅度.
- 为了在各种量子特征哈密尔顿式和自旋玻璃实例上研究这些特性.
主要方法:
- 使用JuliQAOA软件进行数值模拟.
- 横场混合器QAOA和GM-QAOA性能的比较.
- 通过香农的公平抽样量化.
- 分析QAOA角度和近似比,以增加参数p.
主要成果:
- GM-QAOA提供了理论上的保证,以公平地抽取退化最佳解决方案的样本.
- 横向场混合器QAOA展示了不均的采样,一些实例显示了退化的基本状态的指数抑制.
- 一些问题实例与横场混合器QAOA和香农在0 (最大偏差分布) 随着近似比接近1.
- 其他实例保持最大的香农 (均分布),无论p.
结论:
- 与横场混合器QAOA相比,GM-QAOA具有优越的公平采样特性.
- 混合器的选择对QAOA中退化的基态的采样分布产生重大影响.
- 了解公平抽样对于开发有效的量子优化算法至关重要.
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