This paper gives a unified approach to feedback control theory of quantum mechanical systems of bosonic modes described by noncommutative operators. A quantum optical closed-loop, including a plant and controller, is developed and its fundamental structural properties are analyzed extensively from a purely quantum mechanical point of view, in order to facilitate the use of control theory in microscopic world described by quantum theory. In particular, an input-output description of quantum mechanical systems which is essential in describing the behavior of the feedback systems is fully formulated and developed. This would then provide a powerful tool for quantum control and pave an avenue that connects control theory to quantum dynamics. This paper is divided into two parts. The first part is devoted to the basic formulation of quantum feedback control via quantum communication and local operations on an optical device, cavity, that can be regarded as a unit of quantum dynamics of bosonic modes. The formulation introduced in this paper presents the feature intrinsic in quantum feedback systems based on quantum stochastic differential equations. The input-output description provides a basis for developing quantum feedback control through the transfer function representation of quantum feedback systems. In the follow-up paper, the quantum mechanical representation of feedback is further elaborated to yield the control theoretical representation of fundamental notions of quantum theory, uncertainty principle, e.g., and some applications are presented.
This paper investigates the dynamic suppression of quantum noise within the framework of quantum control theory. The core challenge in implementing precise quantum operations lies in the significant influence of environmental noise, which introduces uncertainties and degrades control fidelity. We propose a novel approach utilizing real-time feedback control, leveraging quantum sensors to monitor the noise levels within a quantum system. Based on this continuous assessment, control parameters are dynamically adjusted to mitigate the impact of noise. The effectiveness of this method is demonstrated through theoretical analysis and mathematical modeling. We aim to enhance the accuracy and stability of quantum control processes, ultimately contributing to the reliable execution of complex quantum operations. The system is described by the following Hamiltonian:
H=H0+HI, where
H0 is the system Hamiltonian and
HI represents the interaction Hamiltonian. The time evolution of the system is governed by the equation:
dtd∣ψ(t)>=ℏi[H,∣ψ(t)]. Noise is modeled as a stochastic term, adding to the Hamiltonian:
H=H0+HI+HN, where
HN represents the noise Hamiltonian. The control pulse can be described as:
U(t)=∑i=1Nαie−iωit, where
αi are the amplitudes and
ωi are the carrier frequencies. The fidelity of the quantum operation is evaluated using the overlap between the initial and final states:
Fidelity=∣∣2. The control parameters are optimized to maximize the fidelity. The quantum state evolution is described by the equation:
∣ψ(t+δt)>=U(t)∣ψ(t)>, where U(t) is the control pulse. The time-dependent Schrodinger equation is: i/ħ ∂/∂t |ψ(t)> = H|ψ(t)>. The noise introduces uncertainties which can be represented as:
σ2=−2, where N is the noise operator.
No quantum measurement can give full information on the state of a quantum system; hence any quantum feedback control problem is necessarily one with partial observations and can generally be converted into a completely observed control problem for an appropriate quantum filter as in classical stochastic control theory. Here we study the properties of controlled quantum filtering equations as classical stochastic differential equations. We then develop methods, using a combination of geometric control and classical probabilistic techniques, for global feedback stabilization of a class of quantum filters around a particular eigenstate of the measurement operator.
Abstract. No quantum measurement can give full information on the state of a quantum system; hence any quantum feedback control problem is necessarily one with partial observations and can generally be converted into a completely observed control problem for an appropriate quantum filter as in classical stochastic control theory. Here we study the properties of controlled quantum filtering equations as classical stochastic differential equations. We then develop methods, using a combination of geometric control and classical probabilistic techniques, for global feedback stabilization of a class of quantum filters around a particular eigenstate of the measurement operator.
In this paper, we investigate the state preparation problem of quantum noiselsss subsystems for the quantum Markovian systems via quantum feedback control. The controlled dynamics we consider are given by the so-called stochastic master equation including the coupling terms with the environment. We formulate the problem as a stochastic stabilization problem of an invariant set. This formulation allows us to utilize the stochastic Lyapunov technique and derive a globally stabilizing controller. The effectiveness of this method is evaluated by applying it to the 3-qubit systems subject to the collective noise.
In this paper, we investigate the state preparation problem of quantum noiselsss subsystems for the quantum Markovian systems via quantum feedback control. The controlled dynamics we consider are given by the so-called stochastic master equation including the coupling terms with the environment. We formulate the problem as a stochastic stabilization problem of an invariant set. This formulation allows us to utilize the stochastic Lyapunov technique and derive a globally stabilizing controller. The effectiveness of this method is evaluated by applying it to the 3-qubit systems subject to the collective noise.