Benchmarking quantum tomography completeness and fidelity with machine learning

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We train convolutional neural networks to predict whether or not a set of measurements is informationally complete to uniquely reconstruct any given quantum state with no prior information. In addition, we perform fidelity benchmarking based on this measurement set without explicitly carrying out state tomography. The networks are trained to recognize the fidelity and a reliable measure for informational completeness. By gradually accumulating measurements and data, these trained convolutional networks can efficiently establish a compressive quantum-state characterization scheme by accelerating runtime computation and greatly reducing systematic drifts in experiments. We confirm the potential of this machine-learning approach by presenting experimental results for both spatial-mode and multiphoton systems of large dimensions. These predictions are further shown to improve when the networks are trained with additional bootstrapped training sets from real experimental data. Using a realistic beam-profile displacement error model for Hermite-Gaussian sources, we further demonstrate numerically that the orders-of-magnitude reduction in certification time with trained networks greatly increases the computation yield of a large-scale quantum processor using these sources, before state fidelity deteriorates significantly.
© 2021 The Author(s). YST, SS and HJ acknowledge support by the National Research Foundation of Korea (Grant Nos. 2019R1A6A1A10073437, 2019M3E4A1080074, 2020R1A2C1008609, and 2020K2A9A1A06102946) via the Institute of Applied Physics at Seoul National University, and by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (Grant Nos. 2020-0-01606 and 2021-0-01059). GL acknowledges support by the Center of Excellence ⟪Center of Photonics⟫ funded by the Ministry of Science and Higher Education of the Russian Federation, Contract No. 075-15-2020-906. YK and Y-HK acknowledge support by the National Research Foundation of Korea (Grant No. 2019R1A2C3004812) and the ITRC support program (IITP-2020-0-01606). LLSS acknowledges support from European Union's Horizon 2020 research and innovation program (ApresSF and STORMYTUNE) and the Ministerio de Ciencia e Innovación (PGC2018-099183-B-I00). The MSU team acknowledges support from the Russian Foundation for Basic Research (RFBR Project No. 19-32-80043 and RFBR Project No. 19-52-80034) and support under the Russian National Technological Initiative via MSU Quantum Technology Centre. SSS and SPK acknowledge support by the Development Program of the Interdisciplinary Scientific and Educational School of Lomonosov Moscow State University 'Photonic and quantum technologies: Digital medicine.