Related papers: Predicting quantum ground-state energy by data-dri…
Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…
In this paper, data-driven algorithms based on Koopman Operator Theory are applied to identify and predict the nonlinear dynamics of a vapor compression system and cabin temperature in a light-duty electric vehicle. By leveraging a…
We propose a new quantum computational way of obtaining a ground-state energy and expectation values of observables of interacting Hamiltonians. It is based on the combination of the adiabatic quantum evolution to project a ground state of…
Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular dynamics, climate science, engineering, and biology. Applications include detecting metastable or coherent sets,…
Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…
A new approach to data-driven discovery of Koopman eigenfunctions without a pre-defined set of basis functions is proposed. The approach is based on a reference trajectory, for which the Koopman mode amplitudes are first identified, and the…
We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian…
We propose a variational quantum algorithm to study the real time dynamics of quantum systems as a ground-state problem. The method is based on the original proposal of Feynman and Kitaev to encode time into a register of auxiliary qubits.…
A new variational technique for investigation of the ground state and correlation functions in 1D quantum magnets is proposed. A spin Hamiltonian is reduced to a fermionic representation by the Jordan-Wigner transformation. The ground state…
This paper presents an interpretable machine learning approach that characterizes load dynamics within an operator-theoretic framework for electricity load forecasting in power grids. We represent the dynamics of load data using the Koopman…
Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman…
Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…
This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using…
Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and…
Externally driven dense packings of particles can exhibit nonlinear wave phenomena that are not described by effective medium theory or linearized approximate models. Such nontrivial wave responses can be exploited to design…
Accurately determining ground-state properties of quantum many-body systems remains one of the major challenges of quantum simulation. In this work, we present a protocol for estimating the ground-state energy using only global time…
Koopman spectral theory has provided a new perspective in the field of dynamical systems in recent years. Modern dynamical systems are becoming increasingly non-linear and complex, and there is a need for a framework to model these systems…
The Koopman operator enables the analysis of nonlinear dynamical systems through a linear perspective by describing time evolution in the infinite-dimensional space of observables. Here this formalism is applied to shear flows, specifically…
In this paper, we propose linear operator theoretic framework involving Koopman operator for the data-driven identification of power system dynamics. We explicitly account for noise in the time series measurement data and propose robust…
Estimating the ground-state energy of Hamiltonians is a fundamental task for which it is believed that quantum computers can be helpful. Several approaches have been proposed toward this goal, including algorithms based on quantum phase…