Related papers: Structures and Transformations for Model Reduction…
While the preparation of a general quantum state is challenging, realistic problem instances, such as those encountered in quantum chemistry and quantum machine learning-typically exhibit hierarchical amplitude structures, consisting of a…
We derive equations for the strongly coupled system of light and dense atomic ensembles. The formalism includes an arbitrary internal level structure for the atoms and is not restricted to weak excitation of atoms by light. In the low light…
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
Data-driven reduced-order models often fail to make accurate forecasts of high-dimensional nonlinear dynamical systems that are sensitive along coordinates with low-variance because such coordinates are often truncated, e.g., by proper…
In this paper, several numerical examples to illustrate limitations of Quasi Steady-State (QSS) model in long-term voltage stability analysis are presented. In those cases, the QSS model provided incorrect stability assessment. Causes of…
Topological properties of quantum systems are one of the most intriguing emerging phenomena in condensed matter physics. A crucial property of topological systems is the symmetry-protected robustness towards local noise. Experiments have…
Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…
In this paper, we propose a new model reduction technique for linear stochastic systems that builds upon knowledge filtering and utilizes optimal Kalman filtering techniques. This new technique will reduce the dimension of the noise…
This work aims to address the bottleneck issues of hardware resource limitation and decoherence error in the Hamiltonian simulation of quantum fluids, which are caused by the standard quantum Fourier transform and the evolution of momentum…
Quantum computers can efficiently simulate highly entangled quantum systems, offering a solution to challenges facing classical simulation of Quantum Field Theories (QFTs). This paper presents an alternative to traditional methods for…
In the analysis of Markov chains and processes, it is sometimes convenient to replace an unbounded state space with a "truncated" bounded state space. When such a replacement is made, one often wants to know whether the equilibrium behavior…
In this paper, a theoretical foundation for the Quasi Steady-State (QSS) model in power system long-term stability analysis is developed. Sufficient conditions under which the QSS model gives accurate approximations of the long-term…
Quantum state tomography is a fundamental task in quantum information science, enabling detailed characterization of correlations, entanglement, and electronic structure in quantum systems. However, its exponential measurement and…
In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition…
The purpose of this paper is to present a theoretic and numerical study of utilizing squeezing and phase shift in coherent feedback control of linear quantum optical systems. A quadrature representation with built-in phase shifters is…
Coupled quantum harmonic oscillators, studied by many authors using many different techniques over the decades, are frequently used toy-models to study open quantum systems. In this manuscript, we explicitly study the simplest oscillator…
In this paper, the problem of full state approximation by model reduction is studied for stochastic and bilinear systems. Our proposed approach relies on identifying the dominant subspaces based on the reachability Gramian of a system. Once…
An important class of physical systems that are of interest in practice are input-output open quantum systems that can be described by quantum stochastic differential equations and defined on an infinite-dimensional underlying Hilbert…
In this paper, we present a generalization of the certainty equivalence principle of stochastic control. One interpretation of the classical certainty equivalence principle for linear systems with output feedback and quadratic costs is as…
We analyze a structure-preserving model order reduction technique for delay and stochastic delay equations based on the balanced truncation method and provide a system theoretic interpretation. Transferring error bounds based on Hankel…