Quantum state tomography with tensor train cross approximation

TL;DR

This paper introduces a scalable quantum state tomography method using tensor train cross approximation, which efficiently reconstructs states with fewer measurements and can be enhanced with machine learning.

Contribution

It presents a novel tomography approach leveraging tensor train cross approximation that reduces measurement complexity for certain quantum states.

Findings

Requires exponentially fewer state copies than previous methods

Works with local measurements routinely performed in experiments

Fidelity can be improved with supervised machine learning

Abstract

It has been recently shown that a state generated by a one-dimensional noisy quantum computer is well approximated by a matrix product operator with a finite bond dimension independent of the number of qubits. We show that full quantum state tomography can be performed for such a state with a minimal number of measurement settings using a method known as tensor train cross approximation. The method works for reconstructing full rank density matrices and only requires measuring local operators, which are routinely performed in state-of-art experimental quantum platforms. Our method requires exponentially fewer state copies than the best known tomography method for unstructured states and local measurements. The fidelity of our reconstructed state can be further improved via supervised machine learning, without demanding more experimental data. Scalable tomography is achieved if the full state can be reconstructed from local reductions.