ISSN 0253-2778

CN 34-1054/N

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Time-optimal control of open quantum ensembles based on sampling and learning

  • Department of Automation, University of Science and Technology of China, Hefei 230027, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2019.10.001
  • Received Date: 19 April 2018
  • Accepted Date: 13 October 2018
  • Rev Recd Date: 13 October 2018
  • Publish Date: 31 October 2019
    Abstract

  • Abstract

    For open quantum ensembles with Hamiltonian fluctuations composed of a large number of single quantum systems, a two-stage approximate time-optimal control algorithm is proposed in the framework of coherence vectors of density matrices and achieves a high-fidelity state transition of all member systems to a common target state within an approximate minimum control time. According to the parameter distribution rule that characterizes Hamiltonian fluctuations, this algorithm first samples the whole ensemble to obtain a sample system set. Then, based on the obtained sample system set and via the basic gradient method, the fidelity and the control time are optimized in the two stages respectively, and the resulting optimal control law is obtained. Numerical simulation experiments on a two-level open quantum ensemble verify the effectiveness of the proposed algorithm.

    Abstract

    For open quantum ensembles with Hamiltonian fluctuations composed of a large number of single quantum systems, a two-stage approximate time-optimal control algorithm is proposed in the framework of coherence vectors of density matrices and achieves a high-fidelity state transition of all member systems to a common target state within an approximate minimum control time. According to the parameter distribution rule that characterizes Hamiltonian fluctuations, this algorithm first samples the whole ensemble to obtain a sample system set. Then, based on the obtained sample system set and via the basic gradient method, the fidelity and the control time are optimized in the two stages respectively, and the resulting optimal control law is obtained. Numerical simulation experiments on a two-level open quantum ensemble verify the effectiveness of the proposed algorithm.
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    • References(27)
  • [1]
    BLOKHINTSEV D I. Foundations of quantum mechanics[A]// Quantum Mechanics, Springer, 1964: 31-59.
    [2]
    DUAN L M, LUKIN M D, CIRAC J I, et al. Long-distance quantum communication with atomic ensembles and linear optics[J]. Nature, 2001, 414: 413-418.
    [3]
    BENSKY G, PETROSYAN D, MAJER J, et al. Optimizing inhomogeneous spin ensembles for quantum memory[J]. Physical Review A, 2012: 86(1): 012310.
    [4]
    DONG D Y, PETERSEN I R. Quantum control theory and applications: A survey[J]. IET Control Theory & Applications, 2010: 4(12): 2651-2671.
    [5]
    KUANG S, CONG S. Lyapunov control methods of closed quantum systems[J]. Automatica, 2008: 44(1):98-108.
    [6]
    KUANG S, DONG D Y, PETERSEN IR. Rapid Lyapunov control of finite-dimensional quantum systems[J]. Automatica, 2017, 81: 164-175.
    [7]
    KALACHEV A, KRLL S. Coherent control of collective spontaneous emission in an extended atomic ensemble and quantum storage[J]. Physical Review A, 2006, 74(2): 023814.
    [8]
    MISCHUCK B E, MERKEL S T, DEUTSCH I H. Control of inhomogeneous atomic ensembles of hyperfine qudits[J]. Physical Review A, 2012, 85(2): 022302.
    [9]
    LI J S. Ensemble control of finite-dimensional time-varying linear systems[J]. IEEE Transactions on Automatic Control, 2011, 56(2): 345-357.
    [10]
    RUTHS J, LI J S. Optimal control of inhomogeneous ensembles[J]. IEEE Transactions on Automatic Control, 2012, 57(8): 2021-2032.
    [11]
    BEAUCHARD K, DA SILVA P S P, ROUCHON P. Stabilization for an ensemble of half spin systems[J]. Automatica, 2012, 48(1): 68-76.
    [12]
    CHEN C L, DONG D Y, LONG R X, et al. Sampling-based learning control of inhomogeneous quantum ensembles[J]. Physical Review A, 2014, 89(2): 023402.
    [13]
    CHEN C L, DONG D Y, QI B, et al. Quantum ensemble classification: A sampling-based learning control approach[J]. IEEE transactions on neural networks and learning systems, 2017, 28(6): 1345-1359.
    [14]
    VANDERSYPEN L MK, CHUANG I L. NMR techniques for quantum control and computation[J]. Reviews of Modern Physics, 2005, 76(4): 1037.
    [15]
    KOBZAR K, LUY B, KHANEJA N, et al. Pattern pulses: Design of arbitrary excitation profiles as a function of pulse amplitude and offset[J]. Journal of Magnetic Resonance, 2005, 173(2): 229-235.
    [16]
    PAULY J, ROUX P L, NISHIMURA D, et al. Parameter relations for the shinnarle roux selective excitation pulse design algorithm (NMR imaging)[J]. IEEE Transactions on Medical Imaging, 1991, 10(1): 53-65.
    [17]
    MEYER C H, PAULY J M, MACOVSKIAND A, et al. Simultaneous spatial and spectral selective excitation[J]. Magnetic Resonance in Medicine, 1990, 15(2): 287-304.
    [18]
    ZHANG T M, WU R B, ZHANG F H, et al. Minimum-time selective control of homonuclear spins[J]. IEEE Transactions on Control Systems Technology, 2015, 23(5): 2018-2025.
    [19]
    KHANEJA N, BROCKETT R, GLASER SJ. Time optimal control in spin systems[J]. Physical Review A, 2001, 63(3): 032308.
    [20]
    WERSCHNIK J, GROSS E K U. Quantum optimal control theory[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 2007, 40(18): R175.
    [21]
    BOOZER A D. Time-optimal synthesis of su (2) transformations for a spin-1/2 system[J]. Physical Review A, 2012, 85(1): 012317.
    [22]
    BOSCAIN U, CHITOURN Y. Time-optimal synthesis for left-invariant control systems on so (3)[J]. SIAM Journal on Control and Optimization, 2005, 44(1): 111-139.
    [23]
    BOSCAIN U, MASON P. Time minimal trajectories for a spin 1/2 particle in a magnetic field[J]. Journal of Mathematical Physics, 2006, 47(6): 062101.
    [24]
    CARLINI A, HOSOYA A, KOIKE T, et al. Time-optimal unitary operations[J]. Physical Review A, 2007, 75(4): 042308.
    [25]
    KHANEJA N, REISS T, KEHLET C, et al. Optimal control of coupled spin dynamics: Design of NMR pulse sequences by gradient ascent algorithms. Journal of Magnetic Resonance, 2005, 172(2): 296-305.
    [26]
    CHEN Q M, WU R B, ZHANG T M, et al. Near-time-optimal control for quantum systems[J]. Physical Review A, 2015, 92(6): 063415.
    [27]
    YANG F, CONG S, LONG R X, et al. Exploring the transition-probability-control landscape of open quantum systems: Application to a two-level case[J]. Physical Review A, 2013, 88(3): 033420.
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    [1]
    BLOKHINTSEV D I. Foundations of quantum mechanics[A]// Quantum Mechanics, Springer, 1964: 31-59.
    [2]
    DUAN L M, LUKIN M D, CIRAC J I, et al. Long-distance quantum communication with atomic ensembles and linear optics[J]. Nature, 2001, 414: 413-418.
    [3]
    BENSKY G, PETROSYAN D, MAJER J, et al. Optimizing inhomogeneous spin ensembles for quantum memory[J]. Physical Review A, 2012: 86(1): 012310.
    [4]
    DONG D Y, PETERSEN I R. Quantum control theory and applications: A survey[J]. IET Control Theory & Applications, 2010: 4(12): 2651-2671.
    [5]
    KUANG S, CONG S. Lyapunov control methods of closed quantum systems[J]. Automatica, 2008: 44(1):98-108.
    [6]
    KUANG S, DONG D Y, PETERSEN IR. Rapid Lyapunov control of finite-dimensional quantum systems[J]. Automatica, 2017, 81: 164-175.
    [7]
    KALACHEV A, KRLL S. Coherent control of collective spontaneous emission in an extended atomic ensemble and quantum storage[J]. Physical Review A, 2006, 74(2): 023814.
    [8]
    MISCHUCK B E, MERKEL S T, DEUTSCH I H. Control of inhomogeneous atomic ensembles of hyperfine qudits[J]. Physical Review A, 2012, 85(2): 022302.
    [9]
    LI J S. Ensemble control of finite-dimensional time-varying linear systems[J]. IEEE Transactions on Automatic Control, 2011, 56(2): 345-357.
    [10]
    RUTHS J, LI J S. Optimal control of inhomogeneous ensembles[J]. IEEE Transactions on Automatic Control, 2012, 57(8): 2021-2032.
    [11]
    BEAUCHARD K, DA SILVA P S P, ROUCHON P. Stabilization for an ensemble of half spin systems[J]. Automatica, 2012, 48(1): 68-76.
    [12]
    CHEN C L, DONG D Y, LONG R X, et al. Sampling-based learning control of inhomogeneous quantum ensembles[J]. Physical Review A, 2014, 89(2): 023402.
    [13]
    CHEN C L, DONG D Y, QI B, et al. Quantum ensemble classification: A sampling-based learning control approach[J]. IEEE transactions on neural networks and learning systems, 2017, 28(6): 1345-1359.
    [14]
    VANDERSYPEN L MK, CHUANG I L. NMR techniques for quantum control and computation[J]. Reviews of Modern Physics, 2005, 76(4): 1037.
    [15]
    KOBZAR K, LUY B, KHANEJA N, et al. Pattern pulses: Design of arbitrary excitation profiles as a function of pulse amplitude and offset[J]. Journal of Magnetic Resonance, 2005, 173(2): 229-235.
    [16]
    PAULY J, ROUX P L, NISHIMURA D, et al. Parameter relations for the shinnarle roux selective excitation pulse design algorithm (NMR imaging)[J]. IEEE Transactions on Medical Imaging, 1991, 10(1): 53-65.
    [17]
    MEYER C H, PAULY J M, MACOVSKIAND A, et al. Simultaneous spatial and spectral selective excitation[J]. Magnetic Resonance in Medicine, 1990, 15(2): 287-304.
    [18]
    ZHANG T M, WU R B, ZHANG F H, et al. Minimum-time selective control of homonuclear spins[J]. IEEE Transactions on Control Systems Technology, 2015, 23(5): 2018-2025.
    [19]
    KHANEJA N, BROCKETT R, GLASER SJ. Time optimal control in spin systems[J]. Physical Review A, 2001, 63(3): 032308.
    [20]
    WERSCHNIK J, GROSS E K U. Quantum optimal control theory[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 2007, 40(18): R175.
    [21]
    BOOZER A D. Time-optimal synthesis of su (2) transformations for a spin-1/2 system[J]. Physical Review A, 2012, 85(1): 012317.
    [22]
    BOSCAIN U, CHITOURN Y. Time-optimal synthesis for left-invariant control systems on so (3)[J]. SIAM Journal on Control and Optimization, 2005, 44(1): 111-139.
    [23]
    BOSCAIN U, MASON P. Time minimal trajectories for a spin 1/2 particle in a magnetic field[J]. Journal of Mathematical Physics, 2006, 47(6): 062101.
    [24]
    CARLINI A, HOSOYA A, KOIKE T, et al. Time-optimal unitary operations[J]. Physical Review A, 2007, 75(4): 042308.
    [25]
    KHANEJA N, REISS T, KEHLET C, et al. Optimal control of coupled spin dynamics: Design of NMR pulse sequences by gradient ascent algorithms. Journal of Magnetic Resonance, 2005, 172(2): 296-305.
    [26]
    CHEN Q M, WU R B, ZHANG T M, et al. Near-time-optimal control for quantum systems[J]. Physical Review A, 2015, 92(6): 063415.
    [27]
    YANG F, CONG S, LONG R X, et al. Exploring the transition-probability-control landscape of open quantum systems: Application to a two-level case[J]. Physical Review A, 2013, 88(3): 033420.
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