Density matrix reconstruction using non-negative matrix product states

Quantum state tomography is a key technique for quantum information processing but challenging due to the exponential growth of its complexity with system size. In this work we propose an algorithm which iteratively finds best non-negative matrix product approximation based on set measurement outcomes whose size does not necessarily grow exponentially. Compared method neural network states, our scheme utilizes so-called tensor train representation that allows straightforward recovery unknown density in operator form. As applications, effectiveness numerically demonstrated reconstruct ground XXZ spin chain under depolarizing noise.