Numerically Optimized Control of Analogue Physical Systems

Abstract

We study numerically optimized control of analog behavior in physical systems for the design of large scale interferometers in gravitational-wave observatories and the development of coherent quantum technology. Remarkable milestones have been achieved over the course of the development of these technologies, reaching high precision operational regimes that enable the detection of gravitational waves or the coherent control of quantum systems. These achievements advance various scientific fields and have sparked numerous endeavors toward industry-ready quantum technology.

In the first part of this thesis, we design machine learning-assisted strategies for the purpose of seismic noise mitigation in gravitational-wave observatories based on large-scale michelson interferometers. In a collaboration with the experimental group of Roman Schnabel, we study pendulum suspension systems in a proof-of-principle experiment consisting of a pendulum with a high quality factor (high-Q) and a triaxial force-feedback seismometer. In publication [1], we demonstrate the capabilities of machine learning-assisted multivariate time-series-forecasting to predict the motion of the high-Q pendulum subject to witnessed seismic noise. Our system provides a flexible architecture to include seismic sensing networks in a model-free approach. We achieve a reduction in the displacement power spectral density for a wide range of frequencies including mechanical resonances. Additionally, we find a reduction of non-linear instrumentation artifacts rendering advantages of non-linear artificial neural networks over conventional approaches, such as Wiener filtering. Our results support the idea of machine learning-assisted corrective forward stabilization in next-generation gravitational-wave detectors utilizing seismic sensing networks.

In the second part of this thesis, we study the optimization of coherent control in quantum computers for the purpose of the design of high-fidelity qubit gates under experimentally motivated losses and constraints. In a collaboration with the experimental group of Klaus Sengstock, we implement a numerical platform for the design of optimized quantum gates for Rydberg-atom based quantum computers in publication [2]. For this, we implement a hybrid quantum-classical loop that allows to train the underlying parameterization on a classical device, based on gradients of the loss landscape that are obtained via feedback from our platform. Specifically, we use gradient ascent pulse engineering (GRAPE) to approximate gradients via finite differences in the parameter space. For fixed gate durations, we identify high-fidelity implementations for a wide range of interatomic distances, ranging from the Blockade regime to the weak-coupling limit. We demonstrate the robustness of optimized implementations of quantum gates to spatial fluctuations of the trapped atoms for the considered range of interatomic distances. Furthermore, we present a quantum optimal control method that utilizes linear response theory to estimate gradients in publication [3]. With our method, we offer an extension to gradient-based optimal control methods such as GRAPE. We estimate gradients in terms of finite differences in the space spanned by the control operators via the linear response of the system to time-local perturbations of the control fields. This allows for a multi-parameter update in a hyperparameter-free manner, capitalizing on from the multi-mode overlap of the perturbation and the underlying parameterization of the control fields. We show clear improvements in convergence and optimal fidelity of the generated protocols, for the example of a quantum gate on two qubits, in comparison to standard GRAPE. We demonstrate our method in the presence of experimentally motivated constraints and decoherence, showing that the resulting fidelities converge close to estimated values.