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Acta Physica Sinica

Quantum constraint dynamics and tracking control of a thermal dissipative qubit

Jing-Min Zhu, Shun-Jin Wang, (1)四川大学物理系,成都 610064; (2)四川大学物理系,成都 610064;兰州重离子加速器国家实验室核理论中心,兰州 730000

Published Jan 1, 2006• 4 citations
Publisher

Abstract

Quantum constraint dynamics and tracking control strategy to stabilize the coherence of a decoherent system is applied to a dissipative qubit system at a finite temperature. By using a control field dependent on the dynamical state of the qubit through the constraint equations, we show that the quantum state of the qubit can be preserved within a finite time duration by the feedback effect of the qubit system. It is also shown that the temperature plays a negative role in the control strategy.

DOI
10.7498/aps.55.5018

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Quantum constraint dynamics and tracking control strategy to stabilize the coherence of a decoherent system is applied to a dissipative qubit system at a finite temperature. By using a control field dependent on the dynamical state of the qubit through the constraint equations, we show that the quantum state of the qubit can be preserved within a finite time duration by the feedback effect of the qubit system. It is also shown that the temperature plays a negative role in the control strategy.
When a quantum system interacts with its environment, the so-called decoherence effect will normally destroy the coherence in the quantum state and the entanglement between its subsystems. We propose a feedback control strategy based on quantum weak measurements to protect coherence and entanglement of the quantum state against environmental disturbance. For a one-qubit quantum system under amplitude damping and dephasing decoherence channels, our strategy can preserve the coherence based on the measured information about the population difference between its two levels. For a two-qubit quantum system disentangled by independent amplitude damping and dephasing decoherence channels, the designed feedback control can preserve coherence between the ground state and the highest excited states by tuning the coupling strength between the two qubits, and at the same time minimize the loss of entanglement between the two qubits. As a consequence of dynamic symmetry, the generalization of these results derives the concept of control-induced decoherence-free observable subspace, for which several criteria are provided.
Quantum decoherence represents a significant obstacle to the advancement of quantum computing. This paper presents a novel approach to modeling and suppressing quantum decoherence, leveraging quantum control techniques. We establish a comprehensive mathematical model for quantum state decoherence, incorporating factors such as dephasing and dissipation. Subsequently, we develop a feedback control strategy based on real-time measurement of the quantum state, enabling precise suppression of decoherence. The core of our method relies on dynamically adjusting control pulses to counteract the detrimental effects of environmental interactions. Through theoretical analysis and mathematical formulation, we demonstrate the potential of this approach to significantly enhance the precision and stability of quantum computations. Our model incorporates key parameters including the initial state vector (ψ), the decoherence rate (γ), the dephasing rate (δ), the dissipation rate (κ), and the control pulse amplitude (F). The effectiveness of the control strategy is evaluated through simulations, showcasing a notable reduction in decoherence and improved fidelity of quantum operations. The proposed method offers a viable pathway towards building robust and scalable quantum computers.
The problem of optimal control of non-Markovian open quantum system via weak measurement is presented. Based on the non-Markovian master equation, we evaluate exactly the non-Markovian effect on the dynamics of the system of interest interacting with a dissipative reservoir. We find that the non-Markovian reservoir has dual effects on the system: dissipation and backaction. The dissipation exhausts the coherence of the quantum system, whereas the backaction revives it. Moreover, we design the control Hamiltonian with the control laws attained by the stochastic optimal control and the corresponding optimal principle. At last, we considered the exact decoherence dynamics of a qubit in a dissipative reservoir composed of harmonic oscillators, and demonstrated the effectiveness of our optimal control strategy. Simulation results showed that the coherence will completely lost in the absence of control neither in non-Markovian nor Markovian system. However, the optimal feedback control steers it to a stationary stochastic process which fluctuates around the target. In this case the decoherence can be controlled effectively, which indicates that the engineered artificial reservoirs with optimal feedback control may be designed to protect the quantum coherence in quantum information and quantum computation.