Fast quantum state reconstruction via accelerated non-convex programming

• URL: http://arxiv.org/abs/2104.07006v1
• Date: Wed, 14 Apr 2021 17:38:40 GMT
• Title: Fast quantum state reconstruction via accelerated non-convex programming
• Authors: Junhyung Lyle Kim, George Kollias, Amir Kalev, Ken X. Wei, Anastasios Kyrillidis
• Abstract summary: We propose a new quantum state method that combines ideas from compressed sensing, non- state noise optimization, and better acceleration methods. We find that the proposed code performs better in both synthetic and real experiments.
• Score: 8.19144665585397
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a new quantum state reconstruction method that combines ideas from compressed sensing, non-convex optimization, and acceleration methods. The algorithm, called Momentum-Inspired Factored Gradient Descent (\texttt{MiFGD}), extends the applicability of quantum tomography for larger systems. Despite being a non-convex method, \texttt{MiFGD} converges \emph{provably} to the true density matrix at a linear rate, in the absence of experimental and statistical noise, and under common assumptions. With this manuscript, we present the method, prove its convergence property and provide Frobenius norm bound guarantees with respect to the true density matrix. From a practical point of view, we benchmark the algorithm performance with respect to other existing methods, in both synthetic and real experiments performed on an IBM's quantum processing unit. We find that the proposed algorithm performs orders of magnitude faster than state of the art approaches, with the same or better accuracy. In both synthetic and real experiments, we observed accurate and robust reconstruction, despite experimental and statistical noise in the tomographic data. Finally, we provide a ready-to-use code for state tomography of multi-qubit systems.

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