基于压缩感知的高效率量子态层析技术

项目名称： 基于压缩感知的高效率量子态层析技术

项目编号： No.61201332

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 电子学与信息系统

项目作者： 刘吉英

作者单位： 中国人民解放军国防科学技术大学

项目金额： 25万元

中文摘要： 量子态层析是量子信息学的重要研究内容之一。测量算子优化和状态重构是量子态层析的两个关键组成部分。现有的测量算子优化研究虽给出了理论上的充分必要条件，但在数值计算方面仍不完善：仅通过构造对偶问题解决了纯态情形下的算子凸优化。本项目将在压缩感知中的新型可重构条件研究和投影矩阵设计的基础上，结合密度矩阵的低秩特点，实现非纯态下的测量算子优化。另一方面，现有的量子态重构方法以极大似然方法为主，需耗费大量时间和资源获取较多的测量数据才能完成重构。本项目将通过矩阵核范数或量子态的其它物理属性，构造稀疏重构模型，在此基础上通过对阈值奇异值分解方法进行改进，开发相应的稀疏重构算法，从而显著降低高精度量子态重构所需的测量数据。最后，利用线性光学系统搭建平台，开展量子态层析物理实验。本项目的成果可降低量子态层析的实现难度，推进量子信息学的实用化进程。

中文关键词： 压缩感知；量子成像；稀疏重构；重构条件；大尺度

英文摘要： Quantum state tomography is a central task in quantum information science. The optimization of measurement operator and reconstruction of quantum state are two key points in the process of tomography. The existing researches for the optimization have given the theoretical conditions for pure states, but the numerical computations are not satisfied: only have solved the convex optimization for pure sate by deriving a dual problem. In this project, according to the row-rank characteristic, we will realize the optimization for non-pure stat based on new recovery conditions and design of projective matrix from compressed sensing. Besides, the classical approaches for the reconstruction of quantum state, take Maximum-Likelihood as example, require huge time and resource to get sufficient measurement. In this project, in order to significantly reduce the amount of required measurements, we will establish mathematical models for sparse recovery according to nuclear norm or other physical attributes of quantum state and develop new sparse recovery algorithm based on the modification of Singular Value Thresholding. Finally, we will carry out the experiment of quantum state tomography by the platform based on linear optical systems. The results of this project can reduce the difficulty of realization of quantum state tomo

英文关键词： compressive sensing；quantum imaging；sparse recovery；recovery condition；large scale