Related papers: Corrections to Wigner type phase space methods
We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…
Using the remarkable mathematical construct of Eugene Wigner to visualize quantum trajectories in phase space, quantum processes can be described in terms of a quasi-probability distribution analogous to the phase space probability…
Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical…
The integral Wigner - Liouwille equation describing time evolution of the semi-relativistic quantum 1D harmonic oscillator have been exactly solved by combination of the Monte-Carlo procedure and molecular dynamics methods. The strong…
Phase-space representations based on coherent states (P, Q, Wigner) have been successful in the creation of stochastic differential equations (SDEs) for the efficient stochastic simulation of high dimensional quantum systems. However many…
In this paper we generalize the concept of Wigner function in the case of quantum mechanics with a minimum length scale arising due to the application of a generalized uncertainty principle (GUP). We present the phase space formulation of…
This paper constructs a predictor-corrector technique with orthogonal spline collocation finite element method for simulating a FitzHugh-Nagumo system subject to suitable initial and boundary conditions. The developed computational…
A systematic numerical study on weak Galerkin (WG) finite element method for second order linear parabolic problems is presented by allowing polynomial approximations with various degrees for each local element. Convergence of both…
We compare recently proposed methods to compute the electronic state energies of the water molecule on a quantum computer. The methods include the phase estimation algorithm based on Trotter decomposition, the phase estimation algorithm…
We introduce a family of fourth order two-step methods that preserve the energy function of canonical polynomial Hamiltonian systems. Each method in the family may be viewed as a correction of a linear two-step method, where the correction…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
The Krylov subspace method is a standard approach to approximate quantum evolution, allowing to treat systems with large Hilbert spaces. Although its application is general, and suitable for many-body systems, estimation of the committed…
We study the wave function of a tensor model in the canonical formalism by Hamiltonian Monte Carlo method for Lie group symmetric or nearby values for the argument of the wave function, and show that there emerge Lie-group symmetric…
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian…
Variational inequalities represent a broad class of problems, including minimization and min-max problems, commonly found in machine learning. Existing second-order and high-order methods for variational inequalities require precise…
Extending the phase-space description of the Weyl-Wigner quantum mechanics to a subset of non-linear Hamiltonians in position and momentum, gaussian functions are identified as the quantum ground state. Once a Hamiltonian, $H^{W}(q,\,p)$,…
Incorporating second order curvature information in gradient based methods have shown to improve convergence drastically despite its computational intensity. In this paper, we propose a stochastic (online) quasi-Newton method with…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
Semiclassical approximations for various representations of a quantum state are constructed on a single (Lagrangian) surface in phase space, but it is not available for chaotic systems. An analogous evolution surface underlies semiclassical…
The Wigner function is known to evolve classically under the exclusive action of a quadratic hamiltonian. If the system does interact with the environment through Lindblad operators that are linear functions of position and momentum, we…