Fast quantum state reconstruction via accelerated non-convex programming
Rice University（莱斯大学）；IBM T.J. Watson Research Center（IBM托马斯·J·沃森研究中心）；University of Southern California（南加州大学）；Information Sciences Institute（信息科学研究所）
Junhyung Lyle Kim, George Kollias, Amir Kalev, Ken X. Wei, Anastasios Kyrillidis
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} close to the true density matrix at an accelerated 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.
Accelerated stochastic first-order method for convex optimization under heavy-tailed noise
Department of Mathematics, Linköping University, Sweden（林雪平大学数学系）；Department of Industrial and Systems Engineering, University of Minnesota, USA（明尼苏达大学工业与系统工程系）
Univeristy of California, Berkeley（加州大学伯克利分校）；Georgia Institute of Technology（佐治亚理工学院）；Zuse Institute Berlin（柏林祖斯研究所）；Technische Universität Berlin（柏林工业大学）
