We present an optimal control-based strategy to enhance the estimation of impulse-like disturbances in continuously monitored linear classical and quantum systems by exploiting non-equilibrium states. Using optimal estimation techniques for linear Gaussian systems to collect information from the temporal vicinity of the disturbance, we cast the minimization of disturbance estimation uncertainty as a nonlinear optimal control problem over time-dependent system parameters. The resulting method dynamically shapes the estimation covariances through parametric modulation, maximizing information gain at a known impulse time. This differs fundamentally from conventional squeezing protocols using periodic modulation that effectively degrade inference of impulse-like disturbances. Applied to nanomechanical resonators and levitated nanoparticles, optimal parametric driving reduces estimation variance by up to a factor of two relative to steady-state operation
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Accepted for presentation at IFAC-Worldcongress 2026
We present an optimal control-based strategy to enhance the estimation of impulse-like disturbances in continuously monitored linear classical and quantum systems by exploiting non-equilibrium states. Using optimal estimation techniques for linear Gaussian systems to collect information from the temporal vicinity of the disturbance, we cast the minimization of disturbance estimation uncertainty as a nonlinear optimal control problem over time-dependent system parameters. The resulting method dynamically shapes the estimation covariances through parametric modulation, maximizing information gain at a known impulse time. This differs fundamentally from conventional squeezing protocols using periodic modulation that effectively degrade inference of impulse-like disturbances. Applied to nanomechanical resonators and levitated nanoparticles, optimal parametric driving reduces estimation variance by up to a factor of two relative to steady-state operation
Levitated high-mass quantum systems provide access to unprecedented regimes in both fundamental science and technological applications. However, deterministic generation and manipulation of quantum non-Gaussian states, which are central to many continuous-variable quantum advantages, remain elusive in such platforms. In this work, we propose a theoretical protocol for preparing a continuous-variable degree of freedom of a levitated massive object in a variety of quantum states, including Fock and Schrödinger cat states, without coupling to auxiliary two-level systems. Our approach enhances otherwise weak nonharmonic effects by transient wave-function delocalization and combines this with optimal control of the potential. Specifically, time-dependent modulation of the linear component of the potential, in the presence of a static cubic nonharmonicity, provides a route to universal control of the mode. We analyze quantum state preparation under such control and estimate the required nonharmonicity, motional delocalization, and maximum tolerable decoherence for generating target non-Gaussian states. The proposed optimal-control scheme can also be readily extended beyond single-particle state preparation, for example, to unitary transformations and nonlinear measurements. As a concrete example, we demonstrate mechanical Bell-state preparation for two interacting particles using only local modulation of weakly nonharmonic potentials, while the interparticle interaction remains effectively linear. We emphasize that the protocols presented here apply to different mechanical degrees of freedom, such as center-of-mass motion and libration, and can also be implemented in other weakly nonharmonic systems with a leading cubic nonharmonicity.
We propose an optimal control scheme for generating quantum entanglement between two optically-levitated nanoparticles in free space. Specifically, we consider that the mechanical motion frequencies of the two levitated particles are modulated by adjusting the amplitude of the trapping beam. The two particles are coupled through Coulomb interaction, and the particles' positions are continuously monitored via homodyne detection on the back-scattered light from both particles. By employing an optimal Bayesian feedback scheme, we achieve unconditional entanglement between the two particles in steady states. More precisely, a Kalman filter is used to estimate the states of the two particles and subsequently a linear quadratic regulator is applied to derive the optimal feedback forces exerted on the particles. Physically, periodic modulation enables significant quantum squeezing in both the common mode and the differential mode of the two particles. The Coulomb coupling between the particles introduces a difference in the squeezing of the two normal modes, thereby facilitating the entanglement of the two levitated particles. Our scheme allows for the realization of both conditional and unconditional entanglement at relatively low measurement efficiencies and with low requirements for Coulomb coupling strength, significantly enhancing the feasibility of implementation.
We address the problem of continuous-variable quantum phase estimation in the presence of linear disturbance at the Hamiltonian level by means of Gaussian probe states. In particular we discuss both unitary and random disturbance by considering the parameter which characterizes the unwanted linear term present in the Hamiltonian as fixed (unitary disturbance) or random with a given probability distribution (random disturbance). We derive the optimal input Gaussian states at fixed energy, maximizing the quantum Fisher information over the squeezing angle and the squeezing energy fraction, and we discuss the scaling of the quantum Fisher information in terms of the output number of photons, nout. We observe that, in the case of unitary disturbance, the optimal state is a squeezed vacuum state and the quadratic scaling is conserved. As regards the random disturbance, we observe that the optimal squeezing fraction may not be equal to one and, for any nonzero value of the noise parameter, the quantum Fisher information scales linearly with the average number of photons. Finally, we discuss the performance of homodyne measurement by comparing the achievable precision with the ultimate limit imposed by the quantum Cram\'er--Rao bound.
This thesis addresses the of developing a counter-part of the well established classical theory of control. We dwell on the fundamental fact that states are generally not perfectly distinguishable, and measurements typically introduce noise in the system being measured. Because of these, it is generally not clear whether the central concept of the classical control theory --- that of observing the system and then applying feedback --- is always useful in the setting. We center our investigations around the of transforming the state of a system into a given target state, when the system can be prepared in different ways, and the target state depends on the choice of preparation. We call this the quantum tracking problem and show how it can be formulated as an optimization that can be approached both numerically and analytically. This provides a simple route to the characterization of the trade-off between information gain and disturbance, and is seen to have several applications in information. In order to characterize the optimality of our tracking procedures, some figure-of-merit has to be specified. Naturally, distance measures for states are the ideal candidates for this purpose. We investigated several possibilities, and found that there is usually a compromise between physically motivated and mathematically tractable measures. We also introduce an alternative to the Uhlmann-Jozsa fidelity for mixed states, which besides reproducing a number of properties of the standard fidelity, is especially attractive because it is simpler to compute. We employ some ideas of convex analysis to construct optimal control schemes analytically. In particular, we obtain analytic forms of optimal controllers for stabilizing and tracking any pair of states of a single-qubit. In the case of stabilization, we find that feedback control is always useful, but because of the trade-off between information gain and disturbance, somewhat different from the type of feedback performed in classical systems. In the case of tracking, we find that feedback is not always useful, meaning that depending on the choice of states one wants to achieve, it may be better not to introduce any noise by the application of measurements. We also demonstrate that our optimal controllers are immediately applicable in several information applications such as state-dependent cloning, purification, stabilization, and discrimination. In all of these cases, we were able to recover and extend previously known optimal strategies and performances. Finally we show how optimal single-step control schemes can be concatenated to provide multi-step strategies that usually over-perform optimal control protocols based on a single interaction between the controller and the system.
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.
Abstract Squeezing is a crucial resource for quantum information processing and quantum sensing. In levitated nanomechanics, squeezed states of motion can be generated via temporal control of the trapping frequency of a massive particle. However, the amount of achievable squeezing typically suffers from detrimental environmental effects. We propose a scheme for the generation of significant levels of mechanical squeezing in the motional state of a levitated nanoparticle by leveraging on the careful temporal control of the trapping potential. We analyse the performance of such a scheme by fully accounting for the most relevant sources of noise, including measurement backaction. The feasibility of our proposal, which is close to experimental state-of-the-art, makes it a valuable tool for quantum state engineering.