Quantum State Tomography with Conditional Generative Adversarial Networks

Abstract

Quantum state tomography (QST) is a challenging task in intermediate-scale quantum devices. Here, we apply conditional generative adversarial networks (CGANs) to QST. In the CGAN framework, two duelling neural networks, a generator and a discriminator, learn multi-modal models from data. We augment a CGAN with custom neural-network layers that enable conversion of output from any standard neural network into a physical density matrix. To reconstruct the density matrix, the generator and discriminator networks train each other on data using standard gradient-based methods. We demonstrate that our QST-CGAN reconstructs optical quantum states with high fidelity orders of magnitude faster, and from less data, than a standard maximum-likelihood method. We also show that the QST-CGAN can reconstruct a quantum state in a single evaluation of the generator network if it has been pre-trained on similar quantum states.

5 pages, 5 figures, code will be available at https://github.com/quantshah/qst-cgan; v2: minor updates; see also the companion paper arXiv:2012.02185

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• On the experimental feasibility of quantum state reconstruction via machine learning
• Neural networks in quantum many-body physics: a hands-on tutorial
• All-optical neural network quantum state tomography
• Maximum-Likelihood Quantum State Tomography by Cover's Method with Non-Asymptotic Analysis