量子通道学习的方法
Mikhail Gennadievich Belov1, Victor Victorovich Dubov2, Alexey Vladimirovich Filimonov2
1Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, GSP-1, Moscow, Vorob'evy Gory 119991, Russia.
Physical review. E
|February 20, 2025
概括
本研究开发了一种代算法,用于密度矩阵之间的最佳量子通道映射,超越纯态单元学习. 该方法允许区分状态混合和叠加,适用于量子断层学和算法.
科学领域:
- 量子信息理论 量子信息理论
- 量子计算是一种量子计算.
- 数学物理 数学物理
背景情况:
- 目前的量子状态映射通常集中在纯状态和单元转换上.
- 将量子状态表示为密度矩阵,并将其绘制为量子通道,提供了一个更一般的框架.
- 区分叠加和量子状态的概率混合对于先进的量子信息处理至关重要.
研究的目的:
- 用密度矩阵来制定和解决输入 (IN) 和输出 (OUT) 希尔伯特空间之间的最佳映射问题.
- 开发一个代算法来学习基于忠实度最大化的量子通道.
- 将单元学习泛化为混合单元量子通道和密度矩阵映射.
主要方法:
- 将映射制定为一个优化问题,最大限度地提高总忠实度,但受概率保存约束.
- 开发一个代算法来最大化忠诚度,当忠诚度是二次形式时.
- 代表量子通道作为混合单元映射的层次结构.
主要成果:
- 一个代算法学习量子通道作为混合单元通道表示.
- 区分状态的概率混合与它们的叠加的能力.
- 在密度矩阵映射和量子通道的单元学习中证明了应用.
结论:
- 开发的方法将单元学习扩展到密度矩阵和量子通道.
- 该方法为分析和学习量子过程提供了一个强大的工具.
- 潜在的应用包括量子反向问题,变量量子算法和量子断层学.
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