基于压缩传感的量子状态估计算法的性能对比分析
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摘要
在已完成5个量子位的密度矩阵估计基础上,采用基于压缩传感的交替方向乘子算法(ADMM),对6个量子位的量子态密度矩阵进行估计研究.并进一步分别针对无外部干扰及存在干扰情况下,与最小二乘法、Dantzig优化算法进行性能对比研究,在Matlab环境下设计量子估计的优化方案,实现快速的量子纯态的估计.实验表明ADMM在抵抗外部扰动及估计精度上的优越性.
The alternating direction method of multipliers( ADMM) is used to estimate quantum density matrix with 6 qubits based on the completed research on 5 qubits estimation. In addition,the comparison with least squares and Dantzig optimization method is studied under the situations with and without external interference. The optimization schemes are implemented in Matlab environment to realize the fast estimation of quantum pure state. The experimental results show that ADMM is superior to two other algorithms in estimation accuracy and resistance to external disturbances.
The alternating direction method of multipliers( ADMM) is used to estimate quantum density matrix with 6 qubits based on the completed research on 5 qubits estimation. In addition,the comparison with least squares and Dantzig optimization method is studied under the situations with and without external interference. The optimization schemes are implemented in Matlab environment to realize the fast estimation of quantum pure state. The experimental results show that ADMM is superior to two other algorithms in estimation accuracy and resistance to external disturbances.
引文
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[6]BANASZEK K,CRAMER M,GROSS D.Focus on Quantum Tomography.New Journal of Physics,2013,15(12).DOI:10.1088/1367-2630/15/12/125020.
[7]JELONEK J,KRAWIEC K,SLOWIN'SKI R.Rough Set Reduction of Attributes and Their Domains for Neural Networks.Computational Intelligence,1995,11(2):339-347.
[8]丛爽,匡森.量子系统中状态估计方法的综述.控制与决策,2008,23(2):121-126,132.(CONG S,KUANG S.Review of State Estimation Methods in Quantum Systems.Control and Decision,2008,23(2):121-126,132.)
[9]丛爽.基于李雅普诺夫量子系统控制方法的状态调控.控制理论与应用,2012,29(3):273-281.(CONG S.State Manipulation in Lyapunov-Based Quantum System Control Methods.Control Theory&Applications,2012,29(3):273-281.)
[10]FLAMMIA S T,GROSS D,LIU Y K,et al.Quantum Tomography via Compressed Sensing:Error Bounds,Sample Complexity,and Efficient Estimators.New Journal of Physics,2012,14(9).DOI:10.1088/1367-2630/14/9/095022.
[11]MIOSSO C J,VON BORRIES R,ARGAEZ M,et al.Compressive Sensing Reconstruction with Prior Information by Iteratively Reweighted Least-Squares.IEEE Trans on Signal Processing,2009,57(6):2424-2431.
[12]CANDS E J.The Restricted Isometry Property and Its Implications for Compressed Sensing.Comptes Rendus Mathematique,2008,346(9/10):589-592.
[13]DANTZIG G B,INFANGER G.Multi-stage Stochastic Linear Programs for Portfolio Optimization.Annals of Operations Research,1993,45(1):59-76.
[14]BOYD S,VANDENBERGHE L.Convex Optimization.Cambridge,UK:Cambridge University Press,2004.
[15]SMITH A,RIOFRIO C A,ANDERSON B E,et al.Quantum State Tomography by Continuous Measurement and Compressed Sensing.Physical Review A,2013,87(3).DOI:10.1103/PhysRev A.87.030102.
[16]LIU Y K.Universal Low-Rank Matrix Recovery from Pauli Measurements//SHAWE-TAYLOR J,ZEMEL R S,BARTLETT P L,et al.,eds.Advances in Neural Information Processing Systems24.Cambridge,USA:MIT Press,2011:1638-1646.
[17]BOYD S,PARIKH N,CHU E,et al.Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers.Foundations and Trends in Machine Learning,2011,3(1):1-122.
[18]CANDES E J,PLAN Y.Tight Oracle Inequalities for Low-Rank Matrix Recovery from a Minimal Number of Noisy Random Measurements.IEEE Trans on Information Theory,2011,57(4):2342-2359.
[19]LI K,CONG S.A Robust Compressive Quantum State Tomography Algorithm Using ADMM//Proc of the 19th World Congress of the International Federation of Automation Control.Cape Town,South Africa,2014:6878-6883.