# OPTIMAL CONTROL OF MIXED-STATE QUANTUM SYSTEMS BASED ON LYAPUNOV METHOD

### Yuanyuan Zhang, Shuang Cong, Kezhi Li

#### Abstract

An optimal control strategy of mixed state steering in finite-dimensional closed quantum systems is proposed in this paper. Two different situations are considered: one is the target state is in statistical incoherent mixtures of energy eigenstates in which the target states are diagonal. Another is not all of the off-diagonal elements in the target states are zeros. We change the trajectory tracking problem into the state steering one by introducing the unitary transformation with all energy eigenstates in the inner Hamiltonian of system controlled. Based on Lyapunov stability theorem the stable parameters of controller designed is selected and the optimality of the control law proposed is proven. Moreover, two numerical system control simulations are performed on the diatomic molecule described by the Morse oscillator model under the control law proposed. The system control simulation experimental results demonstrate that the control strategies proposed are efficient even when the controlled system is not completely controllable.

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#### Paper Citation

#### in Harvard Style

Zhang Y., Cong S. and Li K. (2011). **OPTIMAL CONTROL OF MIXED-STATE QUANTUM SYSTEMS BASED ON LYAPUNOV METHOD** . In *Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2011)* ISBN 978-989-8425-35-5, pages 22-30. DOI: 10.5220/0003126000220030

#### in Bibtex Style

@conference{biosignals11,

author={Yuanyuan Zhang and Shuang Cong and Kezhi Li},

title={OPTIMAL CONTROL OF MIXED-STATE QUANTUM SYSTEMS BASED ON LYAPUNOV METHOD},

booktitle={Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2011)},

year={2011},

pages={22-30},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003126000220030},

isbn={978-989-8425-35-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2011)

TI - OPTIMAL CONTROL OF MIXED-STATE QUANTUM SYSTEMS BASED ON LYAPUNOV METHOD

SN - 978-989-8425-35-5

AU - Zhang Y.

AU - Cong S.

AU - Li K.

PY - 2011

SP - 22

EP - 30

DO - 10.5220/0003126000220030