Integrating classical estimation and control theory with quantum systems holds potential for quantum measurement improvement. Here, we report a real-time linear quadratic regulator (LQR) optimal control for spin damping in electron-nuclear spin-coupling regime. The aim is a quicker response and enhanced noise suppression for precision quantum measurements. Using a Kalman quantum observer with electron spin data, we estimate the quantum state of nondirectly observable nuclear spin. LQR full-state feedback optimal control is applied to achieve faster spin-coupling damping. Demonstrated in an atomic spin gyroscope, our method significantly enhances dynamic response with a 4.3-fold improvement in rotational bandwidth. It also boosts long-term stability and measurement sensitivity by 62.9%, presenting a promising avenue to elevate spin-coupling ensemble performance in quantum measurements.
Integrating classical estimation and control theory with quantum systems holds potential for quantum measurement improvement. Here, we report a real-time linear quadratic regulator (LQR) optimal control for spin damping in electron-nuclear spin-coupling regime. The aim is a quicker response and enhanced noise suppression for precision quantum measurements. Using a Kalman quantum observer with electron spin data, we estimate the quantum state of nondirectly observable nuclear spin. LQR full-state feedback optimal control is applied to achieve faster spin-coupling damping. Demonstrated in an atomic spin gyroscope, our method significantly enhances dynamic response with a 4.3-fold improvement in rotational bandwidth. It also boosts long-term stability and measurement sensitivity by 62.9%, presenting a promising avenue to elevate spin-coupling ensemble performance in quantum measurements.
Quantum entanglement, in the form of spin squeezing, is known to improve the sensitivity of atomic sensors to static or slowly varying fields. Sensing transient events presents a distinct challenge, requires different analysis tools, and has not been shown to benefit from entanglement in practically important scenarios such as spin-precession magnetometry. To address this, we apply concepts from continuous quantum measurements and estimation theory to optical atomic magnetometers, aiming to accurately model these devices, interpret their measurement data, control their dynamics, and achieve optimal sensitivity. Quantifying this optimal performance requires determining a fundamental quantum limit on sensitivity. We derive this limit, imposed by noise, and show that it scales at best linearly with sensing time and atom number N, ruling out any super-classical scaling. This limit is independent of the initial state, measurement, estimator, and measurement-based feedback, and depends only on the decoherence model and the strength of field fluctuations. Thus, finding an estimator that attains this bound proves the sensing strategy optimal. To approach this limit, we develop a quantum dynamical model scalable with N, based on a co-moving Gaussian approximation of the stochastic master equation, which includes measurement backaction and decoherence. This enables a real-time estimation and control architecture integrating an extended Kalman filter with a linear quadratic regulator. Simulating the magnetometer with our model and EKF+LQR strategy shows that quantum-limited tracking of constant and fluctuating fields is within reach of current atomic magnetometers. Our sensing strategy can also track biologically relevant signals, such as heartbeat-like waveforms, and drive the atomic ensemble into an entangled state, even when the measurement record is used for feedback but later discarded.
Sensing a magnetic field with an atomic magnetometer operated in real time presents significant challenges, primarily due to sensor nonlinearity, the presence of noise, and the need for one-shot estimation. To address these challenges, we propose a comprehensive approach that integrates measurement, estimation, and control strategies. Specifically, this involves implementing a quantum nondemolition measurement based on continuous light probing of the atomic ensemble. The resulting photocurrent is then directed into an extended Kalman filter to produce instantaneous estimates of the system’s dynamical parameters. These estimates, in turn, are utilized by a linear quadratic regulator, whose output is applied back to the system through a feedback loop. This procedure automatically steers the atomic ensemble into a spin-squeezed state, yielding a quantum enhancement in precision. Furthermore, thanks to the feedback proposed, the atoms exhibit entanglement even when the measurement data are discarded. To prove that our approach constitutes the optimal strategy in realistic scenarios, we derive ultimate bounds on the estimation error applicable in the presence of both local and collective decoherence, and show that these are indeed attained. Additionally, we demonstrate that, for large ensembles, the extended Kalman filter not only reliably predicts its own estimation error in real time, but also accurately estimates spin squeezing at short timescales.
The atomic spin gyroscope (ASG), based on spin-exchange relaxation-free (SERF) co-magnetometers, is poised to become the next generation of high-precision inertial sensors. However, the long-term stability of the gyro can be limited by electron spin polarization. In this study, we investigate a novel real-time, in situ quantum feedback control technique for electron spin polarization in ASGs. By varying the pumping rates, we analyze the gyroscope’s response to the modulation magnetic field, finding that electron polarization dramatically affects the magnetic field response properties of ASGs. It’s demonstrated that the amplitude or phase of the electron spin resonance can be locked for in situ control of electron spin polarization in real-time. A K-Rb-21Ne co-magnetometer is established to implement the proposed method, where a transverse modulating magnetic field is applied to resonate with the electron spin. The lock-in amplification (LIA) technique is used to obtain the amplitude or phase of the electron spin resonance, and the electron spin polarization is closed-loop controlled by locking the second harmonic resonance amplitude or phase. The gyro signal is extracted from the first harmonic of the electron spin resonance. Our experimental results show that real-time in situ feedback control of electron spin significantly improves ASG’s long-term stability and suppresses low-frequency noise. This proposed method has broad application prospects, including optically pumped magnetometers (OPMs), nuclear magnetic resonance gyroscopes (NMRGs), and co-magnetometers.
The accuracy of quantum state estimation and dynamic signal tracking is crucial for the reliability and performance of quantum sensing instruments such as spin-exchange re-laxation-free (SERF) co-magnetometers and gyroscopes. To improve the performance of the SERF gyroscope for future quantum navigation application, an adaptive quantum estimation and closed-loop optimal control method based on fault detection and isolation (FDI) and adaptive Kalman filter is proposed. Firstly, the system model of the SERF gyroscope is established, and a real-time angular velocity measurement method is provided. Then, the stochastic model of the SERF gyroscope is analyzed based on an adaptive quantum Kalman observer to track and compensate for real-time angular velocity error with the assistance of FDI. Finally, the real-time LQI (Linear-Quadratic-Integral) control method is adopted to improve the dynamic response and accuracy of the overall system. Simulations and experiments are conducted based on the SERF gyroscope platform. The results show that the system can achieve optimal tracking accuracy for polarization estimation and effectively isolate fault information. The dynamic response time has been improved by 58.2% under environmental disturbance, which provide a foundation for subsequent navigation applications.
The accuracy of quantum state estimation and dynamic signal tracking is crucial for the reliability and performance of quantum sensing instruments such as spin-exchange relaxation-free (SERF) co-magnetometers and gyroscopes. To improve the performance of the SERF gyroscope for future quantum navigation applications, an adaptive quantum estimation and closed-loop optimal control method based on fault detection and isolation (FDI) and an adaptive Kalman filter is proposed. Firstly, the system model of the SERF gyroscope is established, and a real-time angular velocity measurement method is provided. Then, the stochastic model of the SERF gyroscope is analyzed based on an adaptive quantum Kalman observer to track and compensate for real-time angular velocity error with the assistance of FDI. Finally, the real-time LQI (Linear-Quadratic-Integral) control method is adopted to improve the dynamic response and accuracy of the overall system. Simulations and experiments are conducted based on the SERF gyroscope platform. The results show that the system can achieve optimal tracking accuracy for polarization estimation and effectively isolate fault information. The dynamic response time has been improved by 58.2% under environmental disturbance, which provides a foundation for subsequent navigation applications.
We develop quantum algorithms for optimal control over a prescribed finite time interval (finite horizon), focusing on continuous-time linear-quadratic regulation (LQR). This foundational control problem often requires solving a nonlinear matrix Riccati equation, which can be costly for large systems and long control durations on conventional classical solvers. We instead work directly with the state-costate optimality equations, reformulating the LQR problem as a multiple-shooting linear system. Importantly, we prove a condition-number bound for the system that is independent of the horizon, under stabilizability and detectability assumptions. By incorporating the initial and final conditions into a single linear system, we can solve the subsequent linear system more efficiently with a quantum linear systems subroutine. For a given initial state, our quantum algorithms return classical estimates of the optimal cost and the optimal control inputs at a selected time, without constructing a Riccati solution operator. Given sparse-matrix block-encodings, an initial-state preparation oracle and a fixed number of control inputs, the query and gate complexities scale polylogarithmically with system size and control duration, provided that sparsity, relevant norms, and stability parameters are bounded. The dependence on the target error is inverse-linear up to logarithmic factors. We establish the required bounds uniformly in system size and duration for a family of damped mass-spring chains with two endpoint controls. Numerical experiments support the analysis.