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Quantum computing has the potential to reduce the computational cost required for quantum dynamics simulations. However, existing quantum algorithms for coupled electron-nuclear dynamics simulation either require fault-tolerant devices, or…
This study investigates computationally efficient algorithms for solving discrete-time infinite-horizon single-agent/multi-agent dynamic models with continuous actions. It shows that we can easily reduce the computational costs by slightly…
Dynamic properties of fermionic systems, like contollability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. Observing the parity superselection rule, we treat the fully…
We propose a numerical method to solve general hyperbolic systems in any space dimension using forward Euler time stepping and continuous finite elements on non-uniform grids. The properties of the method are based on the introduction of an…
We show that for a natural polynomial Hamiltonian system the existence of a single Darboux polynomial (a partial polynomial first integral) is equivalent to the existence of an additional first integral functionally independent with the…
A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
Discussed is a model of collective and internal degrees of freedom with kinematics based on affine group and its subgroups. The main novelty in comparison with the previous attempts of this kind is that it is not only kinematics but also…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
This paper provides an algorithmic pipeline for studying the intrinsic structure of a finite discrete dynamical system (DDS) modelling an evolving phenomenon. Here, by intrinsic structure we mean, regarding the dynamics of the DDS under…
We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…
A modification of the standard Boris algorithm, called filtered Boris algorithm, is proposed for the numerical integration of the equations of motion of charged particles in a strong non-uniform magnetic field in the asymptotic scaling…
In the density functional (DF) theory of Kohn and Sham, the kinetic energy of the ground state of a system of noninteracting electrons in a general external field is calculated using a set of orbitals. Orbital free methods attempt to…
First-order optimization algorithms can be considered as a discretization of ordinary differential equations (ODEs) \cite{su2014differential}. In this perspective, studying the properties of the corresponding trajectories may lead to…
We construct an efficient autonomous quantum-circuit design algorithm for creating efficient quantum circuits to simulate Hamiltonian many-body quantum dynamics for arbitrary input states. The resultant quantum circuits have optimal space…
Alternative computing paradigms open the door to exploiting recent innovations in computational hardware to probe the fundamental thermodynamic limits of information processing. One such paradigm employs superconducting quantum interference…
If $N \subset \R$ is a separable II$_1$-factor, the space $\Hom(N,\R)$ of unitary equivalence classes of unital *-homomorphisms $N \to \R$ is shown to have a surprisingly rich structure. If $N$ is not hyperfinite, $\Hom(N,\R)$ is an…
Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural…
Local integrals of motion (LIOMs) play a key role in understanding the long-time properties of closed macroscopic systems. They were found for selected integrable systems via complex analytical calculations. The existence of LIOMs and their…
The N-dimensional Hamiltonian H formed by a curved kinetic term (depending on a function f), a central potential (depending on a function U), a Dirac monopole term, and N centrifugal terms is shown to be quasi-maximally superintegrable for…