论文标题
使用非负基质产品状态的密度矩阵重建
Density matrix reconstruction using non-negative matrix product states
论文作者
论文摘要
量子状态断层扫描是用于量子信息处理的关键技术，但由于其与系统大小的复杂性的指数增长，这是具有挑战性的。在这项工作中，我们提出了一种算法，该算法迭代地发现了基于一组测量结果的最佳非负矩阵乘积状态近似，这些测量结果不一定会成倍增长。与基于神经网络状态的断层扫描方法相比，我们的方案采用了所谓的张量列表表示，可以直接恢复矩阵乘积状态形式的未知密度矩阵。作为应用，在数值上证明了我们的算法的有效性，以重建去极化噪声下XXZ自旋链的基态。
Quantum state tomography is a key technique for quantum information processing, but is challenging due to the exponential growth of its complexity with the system size. In this work, we propose an algorithm which iteratively finds the best non-negative matrix product state approximation based on a set of measurement outcomes whose size does not necessarily grow exponentially. Compared to the tomography method based on neural network states, our scheme utilizes a so-called tensor train representation that allows straightforward recovery of the unknown density matrix in the matrix product state form. As applications, the effectiveness of our algorithm is numerically demonstrated to reconstruct the ground state of the XXZ spin chain under depolarizing noise.
