Density matrix reconstruction using non-negative matrix product states

TL;DR

This paper introduces an efficient quantum state tomography algorithm using non-negative matrix product states, enabling accurate density matrix reconstruction with manageable measurement data, demonstrated on spin chain models.

Contribution

The work presents a novel tensor train-based tomography method that improves density matrix reconstruction efficiency over neural network approaches.

Findings

Successfully reconstructs ground states of XXZ spin chains

Operates effectively under depolarizing noise conditions

Uses measurement data that does not grow exponentially with system size

Abstract

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.