Efficient Quantum Mixed-State Tomography with Unsupervised Tensor Network Machine Learning

TL;DR

This paper introduces a tensor network and machine learning-based quantum state tomography method that efficiently reconstructs large-scale mixed states with fewer measurements, outperforming traditional techniques in fidelity and robustness.

Contribution

It presents a novel efficient and robust mixed-state tomography scheme using the locally purified state ansatz combined with machine learning, reducing measurement requirements significantly.

Findings

Achieves high fidelity with fewer POVM bases than conventional methods.

Successfully reconstructs GHZ states with high accuracy on superconducting circuits.

Demonstrates robustness to experimental noise in quantum state reconstruction.

Abstract

Quantum state tomography (QST) is plagued by the ``curse of dimensionality'' due to the exponentially-scaled complexity in measurement and data post-processing. Efficient QST schemes for large-scale mixed states are currently missing. In this work, we propose an efficient and robust mixed-state tomography scheme based on the locally purified state ansatz. We demonstrate the efficiency and robustness of our scheme on various randomly initiated states with different purities. High tomography fidelity is achieved with much smaller numbers of positive-operator-valued measurement (POVM) bases than the conventional least-square (LS) method. On the superconducting quantum experimental circuit [Phys. Rev. Lett. 119, 180511 (2017)], our scheme accurately reconstructs the Greenberger-Horne-Zeilinger (GHZ) state and exhibits robustness to experimental noises. Specifically, we achieve the fidelity $F \simeq 0.92$ for the 10-qubit GHZ state with just $N_m = 500$ POVM bases, which far outperforms the fidelity $F \simeq 0.85$ by the LS method using the full $N_m = 3^{10} = 59049$ bases. Our work reveals the prospects of applying tensor network state ansatz and the machine learning approaches for efficient QST of many-body states.