Quantum State Tomography with Locally Purified Density Operators and Local Measurements

TL;DR

This paper introduces a tensor network-based approach for quantum state tomography using locally purified density operators and local measurements, demonstrating efficiency and robustness through simulations and experiments.

Contribution

It presents a novel method combining tensor networks and local measurements for efficient quantum state tomography, especially for two-dimensional systems.

Findings

Effective tomography of 1D and 2D quantum states demonstrated

Method shows high accuracy and robustness in simulations

Experimental validation on IBM and Quafu platforms

Abstract

Understanding quantum systems is of significant importance for assessing the performance of quantum hardware and software, as well as exploring quantum control and quantum sensing. An efficient representation of quantum states enables realizing quantum state tomography with minimal measurements. In this study, we propose an alternative approach to state tomography that uses tensor network representations of mixed states through locally purified density operators and employs a classical data postprocessing algorithm requiring only local measurements. Through numerical simulations of one-dimensional pure and mixed states and two-dimensional pure states up to size $8\times 8$, we demonstrate the efficiency, accuracy, and robustness of our proposed methods. Experiments on the IBM and Quafu Quantum platforms complement these numerical simulations. Our study opens avenues in quantum state tomography for two-dimensional systems using tensor network formalism.