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Canadian Journal of Physics

State control strategy of open quantum systems by reverse engineering: via homodyne-based feedback control

Shan Xiao, Qiang Ke, Yinghua Ji

Published Jun 15, 2022• 2 citations
Publisher

Abstract

Quantum state transition is the core content of quantum control. This paper presents a control scheme of the state evolution path based on feedback control and reverse engineering design. To achieve high-precision state transition, we first adopt a homodyne-based feedback control strategy to form a closed-loop system. Then, based on the idea of reverse engineering design, the state evolution path of the system is planned and designed by considering the influence of environment decoherence on the state evolution. Numerical simulation results show that the control pulse based on planning design can drive the system from any initial state to the desired target state, and the coherence of the system is effectively protected during state transition.

DOI
10.1139/cjp-2021-0403

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Quantum state transition is the core content of quantum control. This paper presents a control scheme of the state evolution path based on feedback control and reverse engineering design. To achieve high-precision state transition, we first adopt a homodyne-based feedback control strategy to form a closed-loop system. Then, based on the idea of reverse engineering design, the state evolution path of the system is planned and designed by considering the influence of environment decoherence on the state evolution. Numerical simulation results show that the control pulse based on planning design can drive the system from any initial state to the desired target state, and the coherence of the system is effectively protected during state transition.
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In this paper, based on the idea of reverse engineering, we propose a scheme to find analytical expressions of a laser pulse that allows for controlling the evolution of two-level systems as desired, regardless of the time-dependent phase of the system. The pulse relates to particular functions that predefine the evolution of a system. For illustration, we present concrete examples of driving the system from an arbitrary initial state to a final state along the user-prescribed particular way in both closed and open quantum systems. Simulation results indicate that the desired evolutionary path is accurately obtained when the rotating wave approximation (RWA) is satisfied. Most importantly, the scheme allows us to maintain system coherence and populations even in the presence of certain dephasing and thermal noises. Thus it may naturally find applications in quantum computing and quantum memories.
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In this Letter, we propose a scheme to control the evolution of a two-level quantum system in the strong-coupling regime, based on the idea of reverse engineering. A coherent control field is designed to drive the system along a user-predefined evolution trajectory without utilizing the rotating-wave approximation. As concrete examples, we show that complete population inversion, an equally weighted coherent superposition, and even oscillation-like dynamics can be achieved. Since there are no limitations on the coupling strength between the control field and matter, the scheme is attractive for applications such as accelerating desired system dynamics and fast quantum information processing.
We propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum driving (TQD), the present scheme is focus on only one or parts of moving states in a D-dimension (D ≥ 3) system. The numerical simulation shows that the present scheme not only contains the results of TQD, but also has more free parameters, which make this scheme more flexible. An example is given by using this scheme to realize the population transfer for a Rydberg atom. The influences of various decoherence processes are discussed by numerical simulation and the result shows that the scheme is fast and robust against the decoherence and operational imperfection. Therefore, this scheme may be used to construct a Hamiltonian which can be realized in experiments.
This paper investigates the reconstruction and control of quantum decoherence through a novel approach of inverse back-erasure. Traditional decoherence control strategies primarily focus on mitigating the effects of environmental noise, often employing passive shielding or error correction techniques. This work proposes a proactive method utilizing feedback control to actively reverse the decoherence process, thereby enhancing the coherence of quantum states. The core concept involves precisely measuring the quantum system's interaction with its environment and applying corrective actions to counteract the detrimental effects of decoherence. We explore theoretical frameworks based on Hamiltonian engineering and feedback control theory, formulating a mathematical model for the system and outlining the control strategy. The central equation governing the process is: Δψ(t+Δt) = α(t) Δψ(t) + β(t) (H - η(t) ⋅ H') Δψ(t) where Δψ(t+Δt) is the quantum state at time t+Δt, α(t) is the decoherence factor, β(t) is the control factor, H is the Hamiltonian of the system, H' is the environmental Hamiltonian, and η(t) is the feedback control term. The goal is to manipulate β(t) and η(t) to minimize the effect of decoherence. The effectiveness of this approach is discussed in terms of coherence time extension and entanglement preservation. The research contributes a new paradigm for quantum control, offering potential advancements in quantum computing, quantum communication, and quantum sensing. ---