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Although the study of ultracold quantum gases trapped by light is a prominent direction of modern research, the quantum properties of light were widely neglected in this field. Quantum optics with quantum gases closes this gap and addresses…
We investigate in detail the stimulated photon emission in pulse-shaped Laguerre-Gauss beams of arbitrary mode decomposition within the framework of Euler-Heisenberg effective theory. We elaborate on the analytic structure of the photon…
The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schr\"odinger equation and account for relativistic and QED effects by perturbation…
The stress-energy tensor of the quantum vacuum is studied for the particular case of quantum electrodynamics (QED), that is a fictituous universe where only the electromagnetic and the electron-positron fields exist. The integrals involved…
The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are…
We present substantially generalized and improved quantum algorithms over prior work for inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we show how the norm of the matrix exponential characterizes…
Nonlinear stochastic differential equations (NSDEs) are a pillar of mathematical modeling for scientific and engineering applications. Accurate and efficient simulation of large-scale NSDEs is prohibitive on classical computers due to the…
The two-dimensional cubic nonlinear Schr\"{o}dinger equation is used to describe the propagation of an intense laser beam through a medium with Kerr nonlinearity. The coupled two-dimensional cubic nonlinear Schr\"{o}dinger equations are…
In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
We outline mechanical effects of light-matter interaction inside hollow-core optical fibers. Starting with quantized electromagnetic radiation, we demonstrate how dispersion, mode functions and losses define an open quantum system and how…
High-fidelity general-purpose numerical methods are increasingly needed to improve superconducting circuit quantum information processor performance. One challenge in developing such numerical methods is the lack of reference data to…
We present a model for quantum computation using n steady 3-level atoms or 3-level quantum dots, kept inside a quantum electro-dynamics (QED) cavity. Our model allows one-qubit operations and the two-qubit controlled-NOT gate as required…
Quantum adiabatic algorithm is of vital importance in quantum computation field. It offers us an alternative approach to manipulate the system instead of quantum gate model. Recently, an interesting work arXiv:1805.10549 indicated that we…
This work develops a class of probabilistic algorithms for the numerical solution of nonlinear, time-dependent partial differential equations (PDEs). Current state-of-the-art PDE solvers treat the space- and time-dimensions separately,…
We analyze some crucial questions regarding the practical feasibility of quantum simulation for lattice gauge models. Our analysis focuses on two models suitable for the quantum simulation of the Schwinger Hamiltonian, or QED in 1+1…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum…
Nonlinear optical signals from an assembly of N noninteracting particles consist of an incoherent and a coherent component, whose magnitudes scale \sim N and \sim N(N-1), respectively. A unified microscopic description of both types of…
In this paper we consider the spatial semi-discretization of conservative PDEs. Such finite dimensional approximations of infinite dimensional dynamical systems can be described as flows in suitable matrix spaces, which in turn leads to the…