Efficient factored gradient descent algorithm for quantum state tomography

TL;DR

This paper introduces an efficient quantum state tomography method combining factored gradient descent with eigenvalue mapping and momentum acceleration, significantly improving accuracy and speed for high-dimensional quantum systems.

Contribution

The authors develop a novel factored gradient descent algorithm with eigenvalue mapping and momentum acceleration for quantum tomography, addressing rank deficiency and enhancing efficiency.

Findings

Achieves orders of magnitude better accuracy and convergence speed.

Successfully performs full-state tomography of 11-qubit states within one minute.

Effectively mitigates the rank-deficient problem in quantum state reconstruction.

Abstract

Reconstructing the state of quantum many-body systems is of fundamental importance in quantum information tasks, but extremely challenging due to the curse of dimensionality. In this work, we present an efficient quantum tomography protocol that combines the state-factored with eigenvalue mapping to address the rank-deficient issue and incorporates a momentum-accelerated gradient descent algorithm to speed up the optimization process. We implement extensive numerical experiments to demonstrate that our factored gradient descent algorithm efficiently mitigates the rank-deficient problem and admits orders of magnitude better tomography accuracy and faster convergence. We also find that our method can accomplish the full-state tomography of random 11-qubit mixed states within one minute.