Related papers: Robust Stability Analysis of an Optical Parametric…
Errors occurring on noisy hardware pose a key challenge to reliable quantum computing. Existing techniques such as error correction, mitigation, or suppression typically separate the error handling from the algorithm analysis and design. In…
This paper is concerned with robust instability analysis for linear multi-agent dynamical systems with cyclic structure. This relates to interesting and important periodic oscillation phenomena in biology and neuronal science, since the…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
This work studies the symmetries, the associated momentum map, and relative equilibria of a mechanical system consisting of a small axisymmetric magnetic body-dipole in an also axisymmetric external magnetic field that additionally exhibits…
Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be…
We study linear time-invariant dissipative Hamiltonian differential-algebraic systems. We characterize when the systems are robustly asymptotically stable and derive exact conditions and bounds when this property is lost under…
We consider a generic optomechanical system, consisting of a driven optical cavity and a movable mirror attached to a cantilever. Systems of this kind (and analogues) have been realized in many recent experiments. It is well known that…
An observer-based Hamiltonian identification algorithm for quantum systems is proposed. For the 2-level case an exponential convergence result based on averaging arguments and some relevant transformations is provided. The convergence for…
In this paper, we are concerned with the stabilization of linear port-Hamiltonian systems of arbitrary order $N \in \mathbb{N}$ on a bounded $1$-dimensional spatial domain $(a,b)$. In order to achieve stabilization, we couple the system to…
Learning stable dynamics from observed time-series data is an essential problem in robotics, physical modeling, and systems biology. Many of these dynamics are represented as an inputs-output system to communicate with the external…
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…
Optomechanical systems provide a unique platform for observing quantum behavior of macroscopic objects. However, efforts towards realizing nonlinear behavior at the single photon level have been inhibited by the small size of the radiation…
This note studies the robust output feedback stabilization problem of a class of multi-input multi-output invertible nonlinear systems, for which an "ideal" state feedback based on feedback linearization can be designed under certain mild…
A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results, obtained for cold Cesium atoms when driven…
We demonstrate that quantum fluctuations can cause, under certain conditions, the dynamical instability of pure states that can result in their evolution into mixed states. It is shown that the degree and type of such an instability are…
The generation of large-amplitude coherent states of a massive mechanical resonator, and their quantum-limited detection represent useful tools for quantum sensing and for testing fundamental physics theories. In fact, any weak perturbation…
Constrained Hamiltonian dynamics of a quantum system of nonlinear oscillators is used to provide the mathematical formulation of a coarse-grained description of the quantum system. It is seen that the evolution of the coarse-grained system…
With an increasing coupling between light and mechanics, nonlinearities begin to play an important role in optomechanics. We solve the quantum dynamics of an optomechanical system in the multi-photon strong coupling regime retaining…
The synthesis of robust invariant sets for nonlinear systems has traditionally been hindered by the inherent non convexity and a strict reliance on exact analytical models. This paper presents a purely data-driven framework to compute…
Differential sensitivity techniques originally developed to study the robustness of energy landscape controllers are generalized to the important case of closed quantum systems subject to continuously varying controls. Vanishing sensitivity…