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IEEE International Conference on Quantum Control, Computing and Learning (qCCL)

Feedback Stabilization of Perturbed Quantum Systems via Reduced Filters

Weichao Liang

Published Jun 25, 2025• 0 citations
Publisher

Abstract

In practical scenarios, quantum systems often encounter significant uncertainties-such as unknown initial states, imprecise physical parameters, and unmodeled noise that challenge robust quantum control. We propose a feedback approach leveraging a reduced quantum filter capable of handling both Hamiltonian perturbations and additional unmodeled dissipative dynamics, without requiring prior knowledge of initial states or precise system parameters. Notably, the reduced filter tracks only$\mathcal{O}(N)$real parameters instead of$\mathcal{O}\left(N^{2}\right)$, where$N$is the Hilbert space dimension. By substantially lowering the dimensionality of the filter, this method significantly simplifies real-time implementation and offers a scalable path to robust quantum control in uncertain environments.

DOI
10.1109/qccl65142.2025.11158313

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In practical scenarios, quantum systems often encounter significant uncertainties-such as unknown initial states, imprecise physical parameters, and unmodeled noise that challenge robust quantum control. We propose a feedback approach leveraging a reduced quantum filter capable of handling both Hamiltonian perturbations and additional unmodeled dissipative dynamics, without requiring prior knowledge of initial states or precise system parameters. Notably, the reduced filter tracks onlyO(N)\mathcal{O}(N)O(N)real parameters instead ofO(N2)\mathcal{O}\left(N^{2}\right)O(N2), whereNNNis the Hilbert space dimension. By substantially lowering the dimensionality of the filter, this method significantly simplifies real-time implementation and offers a scalable path to robust quantum control in uncertain environments.
In practical applications, quantum systems are inevitably subject to significant uncertainties, including unknown initial states, imprecise physical parameters, and unmodeled environmental noise, all of which pose major challenges to robust quantum feedback control. This paper proposes a feedback stabilization strategy based on a reduced quantum filter that achieves robustness against time-varying Hamiltonian perturbations and additional dissipative effects, without requiring prior knowledge of the initial state or exact system parameters. The proposed filter estimates only O(N) real variables corresponding to the diagonal elements of the system density matrix in a quantum non-demolition basis in contrast to the O(N^2) variables required by a full stochastic master equation, where N is the Hilbert space dimension. This dimensionality reduction substantially simplifies real-time computation and feedback implementation while preserving both convergence and robustness guarantees. Rigorous analysis further establishes global exponential stability of the target subspace. The results provide a scalable framework for robust and efficient measurement-based feedback control applicable to high-dimensional perturbed open quantum systems.
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+HIH = H_0 + H_IH=H0​+HI​, where H0H_0H0​ is the system Hamiltonian and HIH_IHI​ represents the interaction Hamiltonian. The time evolution of the system is governed by the equation: d∣ψ(t)>dt=iℏ[H,∣ψ(t)]\frac{d|ψ(t)>}{dt} = \frac{i}{\hbar} [H, |ψ(t)]dtd∣ψ(t)>​=ℏi​[H,∣ψ(t)]. Noise is modeled as a stochastic term, adding to the Hamiltonian: H=H0+HI+HNH = H_0 + H_I + H_NH=H0​+HI​+HN​, where HNH_NHN​ represents the noise Hamiltonian. The control pulse can be described as: U(t)=∑i=1Nαi e−iωitU(t) = \sum_{i=1}^N \alpha_i \, e^{-i\omega_i t}U(t)=∑i=1N​αi​e−iωi​t, where αi\alpha_iαi​ are the amplitudes and ωi\omega_iωi​ are the carrier frequencies. The fidelity of the quantum operation is evaluated using the overlap between the initial and final states: Fidelity=∣∣2Fidelity = ||^2Fidelity=∣∣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)>|ψ(t+\delta t)> = U(t) |ψ(t)>∣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\sigma^2 = - ^2σ2=−2, where N is the noise operator.
Obtaining reliable state preparation protocols is a key step toward practical implementation of many quantum technologies, and one of the main tasks in quantum control. In this work, different reinforcement learning approaches are used to derive a feedback law for state preparation of a desired state in a target system. In particular, we focus on the robustness of the obtained strategies with respect to different types and amount of noise. Comparing the results indicates that the learned controls are more robust to unmodeled perturbations with respect to simple feedback strategy based on optimized population transfer, and that training on a simulated nominal model retains the same advantages displayed by controllers trained on real data. The possibility of effective off-line training of robust controllers promises significant advantages toward practical implementation.
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This paper proposes and analyzes an adaptive quantum feedback control system designed to optimize the performance of quantum devices. The core of the system lies in a real-time monitoring and adjustment mechanism utilizing a quantum sensor to measure the state of the quantum system. This measurement data is then fed back into a control algorithm, which dynamically adjusts the system parameters to achieve precise control. Unlike traditional control systems that are sensitive to parameter uncertainties, this adaptive approach leverages the inherent properties of quantum systems to enhance stability and performance. The theoretical framework presented here establishes a foundation for future research and development in adaptive quantum control, addressing key challenges in quantum device operation and manipulation. The system aims to provide a robust and flexible solution for controlling quantum systems with varying characteristics. The primary focus is on the control loop design and the feedback algorithm implementation, with an emphasis on achieving optimal performance under conditions of parameter uncertainty. This work contributes to the growing field of quantum control by introducing a novel adaptive strategy that can significantly improve the operational capabilities of quantum devices.
This paper presents a novel approach to dynamic quantum control utilizing feedback learning algorithms. The core idea is to develop a system capable of real-time adjustment of control parameters based on feedback information obtained from the quantum system itself. This approach addresses the inherent challenges in precisely controlling quantum systems, which are often highly sensitive to environmental noise and difficult to model accurately. The proposed framework leverages the principles of quantum control and feedback learning to achieve optimal control performance. The system architecture incorporates a closed-loop control mechanism where the system's output is continuously monitored, and the control parameters are adjusted accordingly. Mathematical formulations detailing the control process, feedback mechanisms, and optimization strategies are provided. This work contributes to advancements in quantum control by offering a robust and adaptable method for manipulating quantum states, with potential applications in quantum computing, quantum sensing, and quantum communication. The algorithm is designed to minimize the influence of external disturbances and maximize the accuracy of state preparation and manipulation. The presented approach provides a pathway towards more reliable and efficient quantum control strategies.