Related papers: Open quantum systems integrable by partial commuta…
The wide-spread opinion is that original quantum mechanics is a reversible theory, but this statement is only true for undecomposed systems, that are those systems which sub-systems are out of consideration. Taking sub-systems into account,…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a…
These notes are a short introduction to the mathematical theory of open quantum systems. They are meant to serve as an entry point into a broad research area which has applications across the quantum sciences dealing with systems subjected…
Correlations between different regions of a quantum many-body system can be quantified through measures based on entropies of (reduced) subsystem states. For closed systems, several analytical and numerical tools, e.g., hydrodynamic…
This thesis is split into two parts, which are united in the sense that they involve applying ideas from quantum information to fundamental physics. The first part is focused on examining discrete-time models in quantum computation…
Open quantum systems exhibit dynamics ranging from unitary evolution to irreversible dissipation. While the Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) equation uniquely characterizes Markovian CPTP evolution, many physical platforms…
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…
Open quantum systems provide a conceptually simple setting for the exploration of collective behavior stemming from the competition between quantum effects, many-body interactions, and dissipative processes. They may display dynamics…
The promising performance increase offered by quantum computing has led to the idea of applying it to neural networks. Studies in this regard can be divided into two main categories: simulating quantum neural networks with the standard…
How to introduce thermodynamics to quantum mechanics ? Among from numerous possibilities of solving this task, the simple choice is here: The conventional von Neumann equation deals with a density operator whose probability weights are time…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Open quantum systems are governed by both unitary and non-unitary dynamics, with dissipation arising from the latter. Traditional quantum divergence measures, such as quantum relative entropy, fail to account for the non-unitary oriented…
The finite-difference time-domain (FDTD) algorithm is a popular numerical method for solving electromagnetic problems. FDTD simulations can suffer from instability due to the explicit nature of the method. Stability enforcement can be…
The effects of dissipation on the thermodynamic properties of nonlinear quantum systems are approached by the path-integral method in order to construct approximate classical-like formulas for evaluating thermal averages of thermodynamic…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
This paper establishes the applicability of density functional theory methods to quantum computing systems. We show that ground-state and time-dependent density functional theory can be applied to quantum computing systems by proving the…
The accurate description of the interaction of a quantum system with a its environment is a challenging problem ubiquitous across all areas of physics, and lies at the foundation of quantum mechanics theory. Here we pioneer a new strategy…
This paper establishes a far-reaching connection between the Finite-Difference Time-Domain method (FDTD) and the theory of dissipative systems. The FDTD equations for a rectangular region are written as a dynamical system having the…
Using equations of motion with the anisotropic dissipative term for quantum particle and quantum-mechanical commutation rules, the general Maxwell-type differential equations are derived. The direct modifications of the well-known Maxwell…