Related papers: Structure-preserving quantum algorithms for linear…
We consider the numerical simulation of Hamiltonian systems of ordinary differential equations. Two features of Hamiltonian systems are that energy is conserved along trajectories and phase space volume is preserved by the flow. We want to…
As is well known, energy is generally deemed as one of the most important physical invariants in many conservative problems and hence it is of remarkable interest to consider numerical methods which are able to preserve it. In this paper,…
We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit, K-symplectic in the extended phase space with long time energy conservation properties. They are based on extending the original…
It is well-known that a numerical method which is at the same time geometric structure-preserving and physical property-preserving cannot exist in general for Hamiltonian partial differential equations. In this paper, we present a novel…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
Solving quaternion kinematical differential equations is one of the most significant problems in the automation, navigation, aerospace and aeronautics literatures. Most existing approaches for this problem neither preserve the norm of…
On this paper, we have proposed an approach to observe the time-centered difference scheme for dissipative mechanical systems from a Hamiltonian perspective and to introduce the idea of symplectic algorithm to dissipative systems. The…
As is known that various dynamical systems including all Hamiltonian systems preserve volume in phase space. This qualitative geometrical property of the analytical solution should be respected in the sense of Geometric Integration. This…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
Symplectic integrators that preserve the geometric structure of Hamiltonian flows and do not exhibit secular growth in energy errors are suitable for the long-term integration of N-body Hamiltonian systems in the solar system. However, the…
Quantum mechanics features a variety of distinct properties such as coherence and entanglement, which could be explored to showcase potential advantages over classical counterparts in information processing. In general, legitimate quantum…
Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient…
We derive variational integrators for stochastic Hamiltonian systems on Lie groups using a discrete version of the stochastic Hamiltonian phase space principle. The structure-preserving properties of the resulting scheme, such as…
For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each…
Symplectic integrators for Hamiltonian systems have been quite successful for studying few-body dynamical systems. These integrators are frequently derived using a formalism built on symplectic maps. There have been recent efforts to extend…
There is a growing interest in the conservation of invariants when numerically solving a system of ordinary differential equations. Methods that exactly preserve these quantities in time are known as geometric integrators. In this paper we…
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…
Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…
For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians…
Unitarity is a cornerstone of quantum theory, ensuring the conservation of probability and information. Although non-Hermitian Hamiltonians are typically associated with open or dissipative systems, pseudo-Hermitian quantum mechanics shows…