Related papers: Quantum Stochastic Gradient Descent in its continu…
The stochastic dissipative Schrodinger equation is derived for an open quantum system consisting of a sub-system able to exchange energy with a thermal reservoir. The resultant evolution of the wave function also gives the evolution of the…
With rapid advancements in machine learning, first-order algorithms have emerged as the backbone of modern optimization techniques, owing to their computational efficiency and low memory requirements. Recently, the connection between…
We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…
The master equation for a linear open quantum system in a general environment is derived using a stochastic approach. This is an alternative derivation to that of Hu, Paz and Zhang, which was based on the direct computation of path…
An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one dimensional chaotic dynamical systems. Environmental fluctuations -- characteristic of all realistic dynamical systems -- suppress…
This paper describes an algorithm for selecting a consistent set within the consistent histories approach to quantum mechanics and investigates its properties. The algorithm select from among the consistent sets formed by projections…
We present a Wigner function-based approach for the particle density evolution in fermionic and bosonic open quantum many-body systems, including the effects of dephasing. In particular, we focus on chains of non-interacting particles…
In this paper for the first time, we construct quantum analogs starting from classical stochastic processes, by replacing random which path decisions with superpositions of all paths. This procedure typically leads to non-unitary quantum…
The use of the Wigner function for the study of quantum transport in open systems present severe criticisms. Some of the problems arise from the assumption of infinite coherence length of the electron dynamics outside the system of…
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical…
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…
We consider the general Wigner function for a particle confined to a finite interval and subject to Dirichlet boundary conditions. We derive the boundary corrections to the "star-genvalue" equation and to the time evolution equation. These…
We extend the Wigner current vector field (Wigner current) construct to single bosonic mode quantum systems interacting with an environment. In terms of the Wigner function quasiprobability density and associated Wigner current, the open…
Quantum counterparts of Schrodinger's classical bridge problem have been around for the better part of half a century. During that time, several quantum approaches to this multifaceted classical problem have been introduced. In the present…
Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation.…
The semiclassically scaled time-dependent multi-particle Schr\"odinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This…
Within the context of hybrid quantum-classical optimization, gradient descent based optimizers typically require the evaluation of expectation values with respect to the outcome of parameterized quantum circuits. In this work, we explore…
The optimal control problem for open quantum systems can be formulated as a time-dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…