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IEEE International Conference on Information and Automation (ICIA)

Tracking of quantum state in Markovian systems by model reference adaptive control

Qiang Ke, Yinghua Ji, Juju Hu

Published Jul 1, 2017• 0 citations
Publisher

Abstract

In quantum state transfer and tracking, control of quantum states are effective against decoherence caused by external environment and information processing. In this paper, utilizing model reference adaptive control theory and Lyapunov stability theorem, we derive the adaptive law for the model reference adaptive system. Then we design the Lyapunov control law by double control functions and we investigate the orbit tracking of quantum state for Markovian quantum system. Meanwhile, through counteracting the shift term by simplization, the control law avoids oscillating state trajectory in a two-level Markovian quantum system. Finally, numerical simulations for a two-level open quantum system validate the effectiveness of the method.

DOI
10.1109/icinfa.2017.8078967

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One main problem of quantum control in quantum systems is the manipulation of states including state transfer and state tracking. We design control fields to realize arbitrary state transfer for open quantum system by Lyapunov stability theory, and investigate the state transfer for non-Markovian system with phase relaxation and energy dissipative relaxation. The numerical simulations illustrate that arbitrary state (eigenstate, superposition state or mixed state) transfer and maintenance for non-Markovian system can be realized under Lyapunov control function by an external steady control field of proper amplitude, with a success rate of more than 98%. When the right control field and function are implemented, not only the decoherence is compensated completely but also the purity of quantum states is maintained in the process of state transfer.
A Lyapunov-based approach of trajectory tracking in Liouville equation for quantum systems is proposed. By selecting density matrix of controlled system as the system state, and defining the error between controlled state and target one as an error state, the paper regards this error as a new controlled state of system. In such a way the quantum state trajectory tracking problem is changed into the state regulation problem by driving the error state to zero. The control law is designed according to the Lyapunov stability theorem, which can be applied to track different kinds of quantum states including pure state, superposition state and mixed-state. Finally, numerical simulation experiments and results analysis are given.