An efficient online estimation algorithm with measurement noise for time-varying quantum states

Abstract Inspired by the online alternating direction multiplier method (OADM), we propose an efficient online quantum state estimation (QSE) algorithm (QSE-OADM) for recovering time-varying quantum states in this paper. Specifically, in QSE-OADM, the density matrix recovery subproblem and measurement noise minimization subproblem are divided and solved separately without running the algorithm iteratively, which makes the proposed method much more efficient than all previous works. In the numerical experiments, for a 4-qubit system, the proposed algorithm can achieve more than 97.57% (fidelity) estimation accuracy after 71 samples, and the average runtime of per estimation is ( 4.19 ± 0.41 ) × 10 − 4 seconds, which reveals its superior performance comparing with existing online processing algorithms.

[1]  Jonathan Bosse,et al.  Subspace Rejection for Matching Pursuit in the Presence of Unresolved Targets , 2018, IEEE Transactions on Signal Processing.

[2]  C. P. Malta,et al.  Critical assessment of the Schrödinger picture of quantum mechanics , 2002 .

[3]  A. N. Korotkov,et al.  Continuous weak measurement of quantum coherent oscillations , 2001 .

[4]  Shuang Cong,et al.  A reconstruction algorithm for compressive quantum tomography using various measurement sets , 2016, Scientific Reports.

[5]  Feng Ding,et al.  Decomposition based fast least squares algorithm for output error systems , 2013, Signal Process..

[6]  Shuang Cong,et al.  A Robust Compressive Quantum State Tomography Algorithm Using ADMM , 2014, ArXiv.

[7]  Arindam Banerjee,et al.  Online Alternating Direction Method , 2012, ICML.

[8]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[9]  Ivan H Deutsch,et al.  Quantum state reconstruction via continuous measurement. , 2005, Physical review letters.

[10]  Akram Youssry,et al.  Efficient online quantum state estimation using a matrix-exponentiated gradient method , 2018, New Journal of Physics.

[11]  Shuang Cong,et al.  An Efficient Online Estimation Algorithm for Evolving Quantum States , 2021, 2020 28th European Signal Processing Conference (EUSIPCO).

[12]  D. Gross,et al.  Efficient quantum state tomography. , 2010, Nature communications.

[13]  Shuang Cong,et al.  State Transfer via On-Line State Estimation and Lyapunov-Based Feedback Control for a N-Qubit System , 2019, Entropy.

[14]  Stephen Becker,et al.  Quantum state tomography via compressed sensing. , 2009, Physical review letters.

[15]  Itay Hen,et al.  Fidelity-optimized quantum state estimation , 2014, 1409.1952.

[16]  Jason F. Ralph,et al.  Frequency tracking and parameter estimation for robust quantum state estimation , 2009, 0907.5034.

[17]  Yonina C. Eldar.  Quantum signal processing , 2002, IEEE Signal Process. Mag..

[18]  Shuang Cong,et al.  Quantum State Filter With Disturbance and Noise , 2020, IEEE Transactions on Automatic Control.

[19]  Mazyar Mirrahimi,et al.  Back and forth nudging for quantum state estimation by continuous weak measurement , 2011, Proceedings of the 2011 American Control Conference.

[20]  Shuang Cong,et al.  Fast algorithm of high-dimensional quantum state estimation via low measurement rates , 2017, 2017 11th Asian Control Conference (ASCC).

[21]  Shuang Cong,et al.  On-line quantum state estimation using continuous weak measurement and compressed sensing , 2018, Science China Information Sciences.

[22]  A. Silberfarb,et al.  Efficient quantum-state estimation by continuous weak measurement and dynamical control. , 2006, Physical review letters.

[23]  Qing Ling,et al.  An Efficient and Fast Quantum State Estimator With Sparse Disturbance , 2019, IEEE Transactions on Cybernetics.

[24]  Sen Kuang,et al.  Real-time Quantum State Estimation Based on Continuous Weak Measurement and Compressed Sensing , 2022 .

[25]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[26]  Shuang Cong,et al.  Efficient reconstruction of density matrices for high dimensional quantum state tomography , 2017, Signal Process..

[27]  K. Jacobs,et al.  FEEDBACK CONTROL OF QUANTUM SYSTEMS USING CONTINUOUS STATE ESTIMATION , 1999 .