Related papers: Pathwise Solution of a Class of Stochastic Master …
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
The Primitive Equations are a basic model in the study of large scale Oceanic and Atmospheric dynamics. These systems form the analytical core of the most advanced General Circulation Models. For this reason and due to their challenging…
We study strictly parabolic stochastic partial differential equations on $\R^d$, $d\ge 1$, driven by a Gaussian noise white in time and coloured in space. Assuming that the coefficients of the differential operator are random, we give…
We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by…
Using ideas from paracontrolled calculus, we prove local well-posedness of a renormalized version of the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity forced by an additive space-time white noise on a…
This article proposes for stochastic partial differential equations (SPDEs) driven by additive noise, a novel approach for the approximate parameterizations of the ``small'' scales by the ``large'' ones, along with the derivaton of the…
This study systematically benchmarks classical optimization strategies for the Quantum Approximate Optimization Algorithm when applied to Generalized Mean-Variance Problems under near-term Noisy Intermediate-Scale Quantum conditions. We…
In this work we investigate the phenomenon of pathwise non-uniqueness for the stochastic incompressible Euler equations with a passive tracer on the whole Euclidean space. The stochastic perturbations are interpreted as a transport noise…
We investigate the evolution of the quantum state for a free particle placed into a random external potential of white-noise type. The master equation for the density matrix is derived by means of path integral method. We propose an…
Abstract. We take a pathwise approach to classical McKean-Vlasov stochastic differential equations with additive noise, as e.g. exposed in Sznitmann [38]. Our study was prompted by some concrete problems in battery modelling [23], and also…
From K\"ummerer's investigations on stationary Markov processes has emerged an operator algebraic definition of white noises which captures many examples from classical as well as from non-commutative probability. Within non-commutative…
Path integral-based simulation methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical…
This work develops a stochastic model predictive controller~(SMPC) for uncertain linear systems with additive Gaussian noise subject to state and control constraints. The proposed approach is based on the recently developed finite-horizon…
Stochastic perturbation of two-level atoms strongly driven by a coherent light field is analyzed by the quantum trajectory method. A new method is developed for calculating the resonance fluorescence spectra from numerical simulations. It…
Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the…
Parameter estimation is of fundamental importance in areas from atomic spectroscopy and atomic clocks to gravitational wave detection. Entangled probes provide a significant precision gain over classical strategies in the absence of noise.…
Focusing on two-level atoms, we apply the positive $P$ representation to a full-wave mixed bosonic and fermionic system of Jaynes-Cummings type and identify an advantageous degree of freedom in the choice of the involved nonorthogonal…
Implicit inverse problems, in which noisy observations of a physical quantity are used to infer a nonlinear functional applied to an associated function, are inherently ill posed and often exhibit non uniqueness of solutions. Such problems…
Quantum reservoir computing is strongly emerging for sequential and time series data prediction in quantum machine learning. We make advancements to the quantum noise-induced reservoir, in which reservoir noise is used as a resource to…
Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…