基于传感压缩的量子层析成像技术的研究

Research on Technology of Quantum Tomography Based on Compressed Sensing

建立基于传感压缩的量子态层析成像方法。该方法是专门为那些相当纯的量子态设计的,对于大型的量子系统在性能方面有显著的提高,特别是相对于需要设置d2的标准方法而言,可以利用O(rdlog2d)度量设置,重建d维、秩为r的未知密度矩阵。该方法具有一些特征,使得它们便于实验的实施,这些特征是:仅仅需要简单的泡利测量,使用快速凸面优化,对噪声稳定性,可以应用于低秩近似的量子态。实验得到的数据可以用于证明量子态实际上是近似状态,因此不需要任何先验假设。最后给出理论界限和数值模拟的结果。

This paper establishes the methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In particular, they are able to reconstruct an unknown density matrix of dimension d and rank r using O（rdlog2d） measurement settings, compared to standard methods that require d^2 settings. The methods have several features that make them amenable to experimental implementation： they require only simple Pauli measurements, use fast convex optimization, are stable against noise, and can be applied to states that are only approximately low rank. The acquired data can be used to certify that the state is indeed close to pure, so no a priori assumptions are needed.