Coherent control in quantum open systems: An approach for accelerating dissipation-based quantum state generation

Abstract

In this paper, we propose an approach to accelerate the dissipation dynamics for quantum state generation with Lyapunov control. The strategy is to add target-state-related coherent control fields into the dissipation process to intuitively improve the evolution speed. By applying the current approach, without losing the advantages of dissipation dynamics, the target stationary states can be generated in a much shorter time as compared to that via traditional dissipation dynamics. As a result, the current approach containing the advantages of coherent unitary dynamics and dissipation dynamics allows for significant improvement in quantum state generation. where the overdot stands for a time derivative and L k are the so-called Lindblad operators. By using dissipation, one can generate high-fidelity quantum states without accurately controlling the initial state or the operation time (usually, the longer the operation time is, the higher is the fidelity). Besides, dissipation dynamics is shown to be robust against parameter (instantaneous) fluctuations [1]. Due to these advantages, many schemes [9-21] have been proposed for dissipation-based quantum state generation in recent years based on different physical systems. Generally speaking, to generate quantum states by quantum dissipation, the key point is to find (or design) a unique stationary state (marked as |S ) which can not be transferred to other states while other states can be transferred to it. That is, the reduced system should satisfywhere |M (M = S) are the orthogonal partners of the state |S in a reduced system satisfying M |S = 0 and M |M M | + |S S| = 1, andL k are the effective Lindblad operators. Hence, if the system is in |M , it will always be transferred to other states because H 0 |M = 0 andL † k |S = 0, while if the system is in |S , it remains invariant. Therefore, the process of pumping and decaying continues until the system is finally stabilized into the stationary state |S . * E-mail: xia-208@163.comTo show such a dissipation process in more detail, we introduce a functionV to describe the system evolution speed, where V = Tr(ρρ s ) is known as the Lyapunov function [22] and ρ s is the density matrix of the target state |S . Lyapunov control is a form of local optimal control with numerous variants [22][23][24][25], which has the advantage of being sufficiently simple to be amenable to rigorous analysis and has been used to manipulate open quantum systems [25][26][27]. For example, Yi et al. proposed a scheme in 2009 to drive a finite-dimensional quantum system into the decoherence-free subspaces by Lyapunov control [25].When the system evolves into a target state at a final time t f , i.e., ρ| t=t f → ρ s , V approaches a maximum value V = 1. Based on Eqs. (1) and (2), we finḋin which we have assumedL k = √ Γ k |S E k |, with Γ k being the effective dissipation rates and |E k being the effective excited states. Obviously, the evolution speed strongly dependents on the effective dissipation rates and the total population of effective ex...

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