Related papers: Numerical approaches to time evolution of complex …
In this paper is described the general aspect of a numerical method for piecewise determin-istic Markov processes with boundary. Under very natural hypotheses, a crucial result about uniqueness of solution of a generalized Kolmogorov…
We present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in $\sqrt{N \beta/{\cal Z}}$ and polynomial in…
World-wide efforts aim at the realization of advanced quantum simulators and processors. However, despite the development of intricate hardware and pulse control systems, it may still not be generally known which effective quantum dynamics,…
Krylov subspace methods in quantum dynamics identify the minimal subspace in which a process unfolds. To date, their use is restricted to time evolutions governed by time-independent generators. We introduce a generalization valid for…
Quantum chemistry has been viewed as one of the potential early applications of quantum computing. Two techniques have been proposed for electronic structure calculations: (i) the variational quantum eigensolver and (ii) the…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…
We propose and develop a general method of numerical calculation of the wave function time evolution in a quantum system which is described by Hamiltonian of an arbitrary dimensionality and with arbitrary interactions. For this, we obtain a…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
The elucidation of many physical problems in science and engineering is subject to the accurate numerical modelling of complex wave propagation phenomena. Over the last decades, high-order numerical approximation for partial differential…
Using the projection evolution (PEv) approach, time can be included in the quantum mechanics as an observable. Having the time operator, it is possible to explore the temporal structure of various quantum events. In the present paper we…
Often, when we consider the time evolution of a system, we resort to approximation: Instead of calculating the exact orbit, we divide the time interval in question into uniform segments. Chernoff's results in this direction provide us with…
Nonlinear equations are challenging to solve due to their inherently nonlinear nature. As analytical solutions typically do not exist, numerical methods have been developed to tackle their solutions. In this article, we give a quantum…
We numerically analyze the complexity of unitary time-evolution and precursor operators in one- and two-qubit systems using the framework of Nielsen complexity geometry. We find that, as expected, the complexities of unitary time evolution…
In this study linear and nonlinear higher order singularly perturbed problems are examined by a numerical approach, the differential quadrature method. Here, the main idea is using Chebyshev polynomials to acquire the weighting coefficient…
For open quantum systems,a short-time evolution is usually well described by the effective non-Hermitian Hamiltonians,while long-time dynamics requires the Lindblad master equation,in which the Liouvillian superoperators characterize the…
This paper proposes a numerical method for solving time-dependent Schrodinger equations with finite spectral bandwidth, which applies to both periodic and non-periodic cases. We introduce the concept of Pulse Width Modulation (PWM), which…
We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…
In the second part of this paper in micro canonical ensemble the new numerical approach for consideration of quantum dynamics and calculations of the average values of quantum operators and time correlation functions in the Wigner…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
Characterizing the interactions and dynamics of quantum mechanical systems is an essential task in the development of quantum technologies. We propose an efficient protocol based on the estimation of the time derivatives of few qubit…