Related papers: Quantum Lattice Representation of Nonlinear Classi…
The dynamics of a quantum nonlinear oscillator is studied in terms of its quasi-flow, a dynamical mapping of the classical phase plane that represents the time-evolution of the quantum observables. Explicit expressions are derived for the…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
In previous works, it was shown that the Lagrangians and Hamiltonians of cosmological linear scalar, vector and tensor perturbations of homogeneous and isotropic space-times with flat spatial sections containing a perfect fluid can be put…
We advocate lattice methods as the tool of choice to constructively define a background-independent theory of Lorentzian quantum gravity and explore its physical properties in the Planckian regime. The formulation that arguably has most…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…
We study a soliton in an optical lattice holding bosonic atoms quantum mechanically using both an exact numerical solution and quantum Monte Carlo simulations. The computation of the state is combined with an explicit account of the…
Presented are several example quantum computing representations of quantum systems with a relativistic energy relation. Basic unitary representations of free Dirac particles and BCS superconductivity are given. Then, these are combined into…
Presented is a quantum computing representation of Dirac particle dynamics. The approach employs an operator splitting method that is an analytically closed-form product decomposition of the unitary evolution operator. This allows the Dirac…
It is shown that the Lattice Boltzmann equation for hydrodynamics can be extended in such a way as to describe non-relativistic quantum mechanics.
An interpretation of non-relativistic quantum mechanics is presented in the spirit of Erwin Madelung's hydrodynamic formulation of QM and Louis de Broglie's and David Bohm's pilot wave models. The aims of the approach are as follows: 1) to…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
A new model of nonlinear charged quantum relativistic fluids is presented. This model can be discretized into Discrete Time Quantum Walks (DTQWs), and a new hybrid (quantum-classical) algorithm for implementing these walks on NISQ devices…
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…
A general lattice Boltzmann method for simulation of fluids with tailored transport coefficients is presented. It is based on the recently introduced quasi-equilibrium kinetic models, and a general lattice Boltzmann implementation is…
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…
We define a natural coarse-graining procedure which can be applied to any closed equilibrium quantum system described by a density matrix ensemble and we show how the coarse-graining leads to the Gaussian and canonical ensembles. After this…
We show that non-relativistic Quantum Mechanics can be faithfully represented in terms of a classical diffusion process endowed with a gauge symmetry of group Z_4. The representation is based on a quantization condition for the realized…
Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small…
Using a new state-dependent, $\lambda$-deformable, linear functional operator, ${\cal Q}_{\psi}^{\lambda}$, which presents a natural $C^{\infty}$ deformation of quantization, we obtain a uniquely selected non--linear, integro--differential…