Related papers: High-order geometric integrators for the local cub…
We present a quantum algorithm for simulating rovibrational Hamiltonians on fault-tolerant quantum computers. The method integrates exact curvilinear kinetic energy operators and general-form potential energy surfaces expressed in a hybrid…
Gaussian building blocks are essential for photonic quantum information processing, and universality can be practically achieved by equipping Gaussian circuits with adaptive measurement and feedforward. The number of adaptive steps then…
We design a novel, exactly energy-conserving implicit non-symplectic integration method for an eight-dimensional Hamiltonian system with four degrees of freedom. In our algorithm, each partial derivative of the Hamiltonian with respect to…
Variational quantum eigensolvers (VQE) are among the most promising approaches for solving electronic structure problems on near-term quantum computers. A critical challenge for VQE in practice is that one needs to strike a balance between…
In this work, we develop energy-preserving iterative schemes for the (non-)linear systems arising in the Gauss integration of Poisson systems with quadratic Hamiltonian. Exploiting the relation between Gauss collocation integrators and…
The efficient simulation of quantum dynamics and ground states is a central challenge in physics and a key frontier for quantum advantage. While short-time evolution in one-dimensional systems can often be simulated classically, extending…
Variable-order time-fractional wave equations provide a flexible model for wave phenomena with evolving memory effects and anomalous temporal dynamics. Their numerical approximation is challenging because the variable-order fractional…
The recent literature on near-term applications for quantum computers contains several examples of the applications of hybrid quantum/classical variational approaches. This methodology can be applied to a variety of optimization problems,…
In this paper we describe a numerical algorithm for integrating the multicomponent, reacting, compressible Navier-Stokes equations, targeted for direct numerical simulation of combustion phenomena. The algorithm addresses two shortcomings…
The generator coordinate method (GCM) casts the wavefunction as an integral over a weighted set of non-orthogonal single determinantal states. In principle this representation can be used like the configuration interaction (CI) or shell…
This article presents a new and efficient alternative to well established algorithms for molecular geometry optimization. The new approach exploits the approximate decoupling of molecular energetics in a curvilinear internal coordinate…
By use of the recently derived $universal$ discrete imaginary-time propagator of the harmonic oscillator, both thermodynamic and Hamiltonian energies can be given analytically, and evaluated numerically at each imaginary time step, for…
Discretizing variational principles, as opposed to discretizing differential equations, leads to discrete-time analogues of mechanics, and, systematically, to geometric numerical integrators. The phase space of such variational…
A fixed time-step variational integrator cannot preserve momentum, energy, and symplectic form simultaneously for nonintegrable systems. This barrier can be overcome by treating time as a discrete dynamic variable and deriving adaptive…
We present a variational integrator based on the Lobatto quadrature for the time integration of dynamical systems issued from the least action principle. This numerical method uses a cubic interpolation of the states and the action is…
The paper is devoted to the efficient computation of high-order cubature formulas for volume potentials obtained within the framework of approximate approximations. We combine this approach with modern methods of structured tensor product…
A variational formulation for non-equilibrium thermodynamics was developed by Gay-Balmaz and Yoshimura. In a recent article, the first two authors of the present paper introduced partially cosymplectic structures as a geometric framework…
We derive a formalism, the separation method, for the efficient and accurate calculation of two-body matrix elements for a Gaussian potential in the cylindrical harmonic-oscillator basis. This formalism is of critical importance for…
Modular variables serve as a striking example of quantum nonlocality, particularly in superpositions of wave packets that are spatially well separated, where the relative phase between components cannot be accessed through conventional…
This paper deals with the numerical integration of Hamiltonian systems in which a stiff anharmonic potential causes highly oscillatory solution behavior with solution-dependent frequencies. The impulse method, which uses micro- and…