Related papers: Quantum Mechanics for Closure of Dynamical Systems
A pedagogical introduction is given to the quantum mechanics of closed systems, most generally the universe as a whole. Quantum mechanics aims at predicting the probabilities of alternative coarse-grained time histories of a closed system.…
The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics using quantum computers. This problem arises frequently in applications such as quantum control and…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
This paper is concerned with a class of open quantum systems whose dynamic variables have an algebraic structure, similar to that of the Pauli matrices pertaining to finite-level systems. The system interacts with external bosonic fields,…
The resources needed to conventionally characterize a quantum system are overwhelmingly large for high- dimensional systems. This obstacle may be overcome by abandoning traditional cornerstones of quantum measurement, such as general…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…
In this work, we consider a state estimation problem for large-scale nonlinear processes in the absence of first-principles process models. By exploiting process operation data, both process modeling and state estimation design are…
The dynamics of finite dimension open quantum systems is studied with the help of the simplest possible form of projection operators, namely the ones which project only onto one dimensional subspaces. The simplicity of the action of the…
This paper uses data-driven operator theoretic approaches to explore the global phase space of a dynamical system. We defined conditions for discovering new invariant subspaces in the state space of a dynamical system starting from an…
Hybrid quantum-classical algorithms are among the most promising systems to implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ) technology. In this paper, at first, we investigate a quantum dynamics algorithm for…
In this paper we: 1) show how the smooth geometry of spaces of normal quantum states over W*-algebras (generalised spaces of density matrices) may be used to substantially enrich the description of quantum dynamics in the algebraic and path…
In this survey the possible approaches to the description of the evolution of states of quantum many-particle systems by means of the possible modifications of the density operator which kernel known as density matrix are considered. In…
In recent years, the success of the Koopman operator in dynamical systems analysis has also fueled the development of Koopman operator-based control frameworks. In order to preserve the relatively low data requirements for an approximation…
Autonomous driving technologies have received notable attention in the past decades. In autonomous driving systems, identifying a precise dynamical model for motion control is nontrivial due to the strong nonlinearity and uncertainty in…
A pedagogical derivation of statistical mechanics from quantum mechanics is provided, by means of open quantum systems. Besides, a new definition of Boltzmann entropy for a quantum closed system is also given to count microstates in a way…
We investigate quantum dynamical systems defined on a finite dimensional Hilbert space and subjected to an interaction with an environment. The rate of decoherence of initially pure states, measured by the increase of their von Neumann…
Capturing the dynamics of quantum many-body systems under time-dependent driving protocols is a central challenge for numerical simulations. Existing methods such as tensor networks and time-dependent neural quantum states, however, must be…
The analysis of symmetry in quantum systems is of utmost theoretical importance, useful in a variety of applications and experimental settings, and is difficult to accomplish in general. Symmetries imply conservation laws, which partition…
A data driven, kernel-based method for approximating the leading Koopman eigenvalues, eigenfunctions, and modes in problems with high dimensional state spaces is presented. This approach approximates the Koopman operator using a set of…