Control of stochastic quantum dynamics by differentiable programming

Control of the stochastic dynamics of a quantum system is indispensable in fields such as quantum information processing and metrology. However, there is no general ready-made approach to the design of efficient control strategies. Here, we propose a framework for the automated design of control schemes based on differentiable programming. We apply this approach to the state preparation and stabilization of a qubit subjected to homodyne detection. To this end, we formulate the control task as an optimization problem where the loss function quantifies the distance from the target state, and we employ neural networks (NNs) as controllers. The system's time evolution is governed by a stochastic differential equation (SDE). To implement efficient training, we backpropagate the gradient information from the loss function through the SDE solver using adjoint sensitivity methods. As a first example, we feed the quantum state to the controller and focus on different methods of obtaining gradients. As a second example, we directly feed the homodyne detection signal to the controller. The instantaneous value of the homodyne current contains only very limited information on the actual state of the system, masked by unavoidable photon-number fluctuations. Despite the resulting poor signal-to-noise ratio, we can train our controller to prepare and stabilize the qubit to a target state with a mean fidelity of around 85%. We also compare the solutions found by the NN to a hand-crafted control strategy

Spatio-Temporal Optimization for Control of Infinite Dimensional Systems in Robotics, Fluid Mechanics, and Quantum Mechanics

The majority of systems in nature have a spatio-temporal dependence and can be described by Partial Differential Equations (PDEs). They are ubiquitous in science and engineering, and are of rising interest among the control, robotics, and machine learning communities. Related methods usually treat these infinite dimensional problems in finite dimensions with reduced order models. This leads to committing to specific approximation schemes and the subsequent control laws cannot generalize outside of the approximation schemes. Additionally, related work does not consider spatio-temporal descriptions of noise that realistically represent the stochastic nature of physical systems. This thesis develops a variety of approaches for control optimization and co-design optimization for PDE and stochastic PDE (SPDE) systems from a unified perspective that can be applied to macroscopic systems in robotics and fluid dynamics, as well as microscopic systems in quantum mechanics. These approaches are each developed completely in the infinite dimensional Hilbert spaces where the systems are mathematically described, enabling the frameworks to be agnostic to the discretization scheme used to implement them. The first three developed approaches are applied in simulation to classical systems in fluid dynamics such as the Heat and Burgers equation. The fourth approach is developed for second-order SPDEs that arise in robotic systems, and is applied in simulation to systems in soft-robotics such as the Euler-Bernoulli equation and a biological model of a soft-robotic limb. Finally, several approaches are developed in the context of quantum feedback control of open quantum systems with non-demolition measurement, and one such approach is applied in simulation to perform explicit feedback control of the two qubit open quantum system.Ph.D

Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics

Continuously measured quantum systems are characterized by an output current, in the form of a stochastic and correlated time series which conveys crucial information about the underlying quantum system. The many tools used to describe current fluctuations are scattered across different communities: quantum opticians often use stochastic master equations, while a prevalent approach in condensed matter physics is provided by full counting statistics. These, however, are simply different sides of the same coin. Our goal with this tutorial is to provide a unified toolbox for describing current fluctuations. This not only provides novel insights, by bringing together different fields in physics, but also yields various analytical and numerical tools for computing quantities of interest. We illustrate our results with various pedagogical examples, and connect them with topical fields of research, such as waiting-time statistics, quantum metrology, thermodynamic uncertainty relations, quantum point contacts and Maxwell's demons.Comment: This is a tutorial paper, submitted to PRX Quantu

Novel approaches to optomechanical transduction

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Quantum correlations in information theory

The project concerned the study of quantum correlations (QC) in compound systems, i.e. statistical correlations more general than entanglement which are predicted by quantum mechanics but not described in any classical scenario. I aimed to understand the technical and operational properties of the measures of QC, their interplay with entanglement quantifiers and the experimental accessibility. In the first part of my research path, after having acquired the conceptual and technical rudiments of the project, I provided solutions for some computational issues: I developed analytical and numerical algorithms for calculating bipartite QC in finite dimensional systems. Then, I tackled the problem of the experimental detection of QC. There is no Hermitian operator associated with entanglement measures, nor with QC ones. However, the information encoded in a density matrix is redundant to quantify them, thus the full knowledge of the state is not required to accomplish the task. I reported the first protocol to measure the QC of an unknown state by means of a limited number of measurements, without performing the tomography of the state. My proposal has been implemented experimentally in a NMR (Nuclear Magnetic Resonance) setting. In the final stage of the project, I explored the foundational and operational merits of QC. I showed that the QC shared by two subsystems yield a genuinely quantum kind of uncertainty on single local observables. The result is a promising evidence of the potential exploitability of separable (unentangled) states for quantum metrology in noisy conditions