Related papers: Enhanced HBVMs for the numerical solution of Hamil…
Estimating the eigenvalue or energy gap of a Hamiltonian H is vital for studying quantum many-body systems. Particularly, many of the problems in quantum chemistry, condensed matter physics, and nuclear physics investigate the energy gap…
In this article, we provide a numerical method based on fitted finite volume method to approximate the Hamilton-Jacobi-Bellman (HJB) equation coming from stochastic optimal control problems. The computational challenge is due to the nature…
This article is a brief introduction to quantum algorithms for the eigenvalue problem in quantum many-body systems. Rather than a broad survey of topics, we focus on providing a conceptual understanding of several quantum algorithms that…
In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…
In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV - functions. The space of the…
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…
The variational quantum-classical algorithms are the most promising approach for achieving quantum advantage on near-term quantum simulators. Among these methods, the variational quantum eigensolver has attracted a lot of attention in…
In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…
This paper is an algorithmic study of quantum phase estimation with multiple eigenvalues. We present robust multiple-phase estimation (RMPE) algorithms with Heisenberg-limited scaling. The proposed algorithms improve significantly from the…
The induction motor behaviour is represented by a fifth order differential equation model. Addition of a torque correction factor to the model accurately reproduces the transient torques and instantaneous real and reactive power flows of…
Constrained problems are frequently encountered in classical and quantum optimization. Particle conservation, in particular, is commonly imposed when studying energy spectra of chemical and solid state systems. Though particle…
In this paper, we present a fast and accurate numerical scheme for the solution of fifth-order boundary-value problems. We apply the reproducing kernel Hilbert space method (RKHSM) for solving this problem. The analytic results of the…
In this paper, we define arbitrarily high-order energy-conserving methods for Hamiltonian systems with quadratic holonomic constraints. The derivation of the methods is made within the so-called line integral framework. Numerical tests to…
We propose a Multilevel Monte-Carlo (MLMC) method for computing entropy measure valued solutions of hyperbolic conservation laws. Sharp bounds for the narrow convergence of MLMC for the entropy measure valued solutions are proposed. An…
Many optimal control problems are formulated as two point boundary value problems (TPBVPs) with conditions of optimality derived from the Hamilton-Jacobi-Bellman (HJB) equations. In most cases, it is challenging to solve HJBs due to the…
Environmental management optimizing a long-run objective is an ergodic control problem whose resolution can be achieved by solving an associated non-local Hamilton-Jacobi-Bellman (HJB) equation having an effective Hamiltonian. Focusing on…
Characterizing the Hamiltonians of continuous-variable (CV) quantum systems is a fundamental challenge laden with difficulties arising from infinite-dimensional Hilbert spaces and unbounded operators. Existing protocols for achieving the…
Solutions to many-body problem instances often involve an intractable number of degrees of freedom and admit no known approximations in general form. In practice, representing quantum-mechanical states of a given Hamiltonian using available…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
We show that symplectic Runge-Kutta methods provide effective symplectic integrators for Hamiltonian systems with index one constraints. These include the Hamiltonian description of variational problems subject to position and velocity…