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arXiv:1004.4301

Optimal control of population transfer in Markovian open quantum systems

Wei Cui, Zairong Xi, Yu Pan

Published Apr 24, 2010• 0 citations
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Abstract

There has long been interest to control the transfer of population between specified quantum states. Recent work has optimized the control law for closed system population transfer by using a gradient ascent pulse engineer- ing algorithm [1]. Here, a spin-boson model consisting of two-level atoms which interact with the dissipative environment, is investigated. With opti- mal control, the quantum system can invert the populations of the quantum logic states. The temperature plays an important role in controlling popula- tion transfer. At low temperatures the control has active performance, while at high temperatures it has less erect. We also analyze the decoherence be- havior of open quantum systems with optimal population transfer control, and we find that these controls can prolong the coherence time. We hope that active optimal control can help quantum solid-state-based engineering.

DOI
10.48550/arxiv.1004.4301

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We consider an optimal control problem for the quantum population transfer in open quantum systems. Quantum optimal control using the Pontryagin maximum principle is specifically derived. The influences of surrounding environment are analytically and numerically studied. In particular, we demonstrate that the quantum optimal control ability remarkablely dependents on temperatures. Only at low temperatures, the derived control laws have active performance and the quantum decoherence time can be extended.
A central challenge for implementing quantum computing in the solid state is decoupling the qubits from the intrinsic noise of the material. We investigate the implementation of quantum gates for a paradigmatic, non-Markovian model: a single-qubit coupled to a two-level system that is exposed to a heat bath. We systematically search for optimal pulses using a generalization of the novel open systems gradient ascent pulse engineering algorithm. Next to the known optimal bias point of this model, there are optimal pulses which lead to high-fidelity quantum operations for a wide range of decoherence parameters.
We investigate the optimal control problem in non-Markovian open, dissipative quantum system. Optimal control using Pontryagin maximum principle of this problem has been specifically derived. The influences of Ohmic reservoir with Lorentz-Drude regularization are numerically studied in a two-level system under the following three conditions w0Lt wc, w0ap wcor w0Gt wcrespectively. The optimal control process shows its remarkable influences to the decoherence dynamics. The temperature is a key factor in the decoherence dynamics. We analysis the optimal decoherence control in high temperature, intermediate temperature, and low temperature reservoirs respectively. It implies that designing some engineered reservoirs with the controlled coupling and state of the environment can slow down the decoherence rate and delay the decoherence time. Moreover, we compared the non-Markovian optimal decoherence control with the Markovian one, we find that with non-Markovian the engineered artificial reservoirs are better than with the Markovian approximate in controlling the open, dissipative quantum systempsilas decoherence.
We propose a control approach to transfer the population between selected quantum states in the non-Markovian open quantum system. This transfers, assisted by single qubit phase shift operations can generate universal logic gates for quantum computing. We find that the occupation probability behaves differently for different environmental conditions, such as the temperature and the ratio between the frequency of the quantum system of interest, and the cut-off frequency of Ohmic reservoir. We provide an active control over non-Markovian open quantum system for the quantum state engineering.
We investigate the optimal control problem for a non-Markovian open, dissipative quantum system. Optimal control using the Pontryagin maximum principle is specifically derived. The influences of ohmic reservoir with Lorentz-Drude regularization are numerically studied in a two-level system under the following three conditions: ${\ensuremath{\omega}}_{0}⪡{\ensuremath{\omega}}_{c}$, ${\ensuremath{\omega}}_{0}\ensuremath{\approx}{\ensuremath{\omega}}_{c}$, or ${\ensuremath{\omega}}_{0}⪢{\ensuremath{\omega}}_{c}$, where ${\ensuremath{\omega}}_{0}$ is the characteristic frequency of the quantum system of interest, and ${\ensuremath{\omega}}_{c}$ the cutoff frequency of the ohmic reservoir. The optimal control process shows its remarkable influences on the decoherence dynamics. The temperature is a key factor in the decoherence dynamics. We analyze the optimal decoherence control in high temperature, intermediate temperature, and low temperature reservoirs, respectively. It implies that designing some engineered reservoirs with the controlled coupling and state of the environment can slow down the decoherence rate and delay the decoherence time. Moreover, we compare the non-Markovian optimal decoherence control with the Markovian one and find that with non-Markovian the engineered artificial reservoirs are better than with the Markovian approximation in controlling the open, dissipative quantum system's decoherence.
Quantum control, an interdisciplinary field combining quantum mechanics and control theory, provides essential tools for manipulating quantum systems in applications such as quantum information, computing, and communication. This paper proposes a novel control strategy for population transfer in quantum systems based on the Fully Actuated Systems (FAS) approach. The study focuses on finite-level open quantum systems, which exhibit intricate behaviors such as dissipation, decoherence, and non-Markovian dynamics due to interactions with their environments. Utilizing the Lindblad equation to describe the time evolution of the system's density matrix, we derive effective control laws for population transfer. Simulation experiments demonstrate the efficacy of the FAS method in achieving desired population transfers in both two-level and threelevel quantum systems, highlighting its potential for advancing quantum control strategies and enabling more precise manipulation of quantum states.