Related papers: Predicting quantum ground-state energy by data-dri…
We propose a machine-learning approach to model long-term out-of-sample dynamics of brain activity from task-dependent fMRI data. Our approach is a three stage one. First, we exploit Diffusion maps (DMs) to discover a set of variables that…
Conventional quantum chemical solvation theories are based on the mean-field embedding approximation. That is, the electronic wavefunction is calculated in the presence of the mean field of the environment. In this paper a direct quantum…
In this thesis, we focus on the energetic analysis within autonomous quantum systems. To this aim, we propose a novel and general formalism for a dynamic description of the energy exchanges between interacting subsystems. From the Schmidt…
We consider the quantum dynamics of a test particle in noncommutative space under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. A prescription for quantizing the classical Hamiltonian for…
Recently, variational quantum metrology was proposed for Hamiltonians with multiplicative parameters, wherein the estimation precision can be optimized via variational circuits. However, systems with generic Hamiltonians still lack these…
Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and prediction of these systems remains a challenge. Koopman operator theory circumvents some of these issues by considering the dynamics in the space of…
In this paper we propose a new Koopman operator approach to the decomposition of nonlinear dynamical systems using Koopman Gramians. We introduce the notion of an input-Koopman operator, and show how input-Koopman operators can be used to…
The internal state of a dynamical system, a set of variables that defines its evolving configuration, is often hidden and cannot be fully measured, posing a central challenge for real-time monitoring and control. While observers are…
This paper introduces an input-output bilinear Koopman realization with an optimization algorithm of lifting functions. For nonlinear systems with inputs, Koopman-based modeling is effective because the Koopman operator enables a…
Data-driven model predictive control based on Willems' fundamental lemma has proven effective for linear systems, but extending stability guarantees to nonlinear systems remains an open challenge. In this paper, we establish conditions…
This paper presents a distributed Koopman operator learning framework for modeling unknown nonlinear dynamics using sequential observations from multiple agents. Each agent estimates a local Koopman approximation based on lifted data and…
Inference, prediction and control of complex dynamical systems from time series is important in many areas, including financial markets, power grid management, climate and weather modeling, or molecular dynamics. The analysis of such highly…
Imaginary time evolution is a powerful tool for studying quantum systems. While it is possible to simulate with a classical computer, the time and memory requirements generally scale exponentially with the system size. Conversely, quantum…
Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps nonlinear systems into equivalent linear systems in embedding space, ready for real-time linear control…
Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
Transfer and Koopman operator methods offer a framework for representing complex, nonlinear dynamical systems via linear transformations, enabling a deeper understanding of the underlying dynamics. The spectra of these operators provide…
This paper presents a methodology to achieve lower-dimensional Koopman quasi-linear representations of nonlinear system dynamics using Koopman generalized eigenfunctions. The proposed approach considers the analytically derived Koopman…
We present a novel method for improving the quantum simulation of the ground state energy of molecules. We perform a pre-processing step classically, which reduces the dimensionality of the problem by generating a custom mapping which…
Traditional economic growth theories, grounded in deterministic and often linear frameworks, fail to adequately capture the inherent uncertainty, non-commutativity, and complex interdependencies of modern economies. This paper proposes a…