Neural networks for quantum inverse problems

• Published in: New journal of physics Vol. 24; no. 6; pp. 63002 - 63015
• Main Authors: Cao, Ningping, Xie, Jie, Zhang, Aonan, Hou, Shi-Yao, Zhang, Lijian, Zeng, Bei
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01-06-2022
• Subjects: Deep learning; Efficiency; Inverse problems; Maximum entropy; Neural networks; Physics; Probability distribution; quantum information; quantum inverse problem; quantum machine learning; Quantum theory; Robustness (mathematics); State estimation; Tomography
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/ac706c

Abstract
Quantum inverse problem (QIP) is the problem of estimating an unknown quantum system from a set of measurements, whereas the classical counterpart is the inverse problem of estimating a distribution from a set of observations. In this paper, we present a neural-network-based method for QIPs, which has been widely explored for its classical counterpart. The proposed method utilizes the quantumness of the QIPs and takes advantage of the computational power of neural networks to achieve remarkable efficiency for the quantum state estimation. We test the method on the problem of maximum entropy estimation of an unknown state
ρ
from partial information both numerically and experimentally. Our method yields high fidelity, efficiency and robustness for both numerical experiments and quantum optical experiments.