Related papers: High order schemes for solving partial differentia…
In this work, in order to obtain higher-order schemes for solving forward backward stochastic differential equations, we adopt the high-order multi-step method in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36(4) (2014),…
In this paper a class of higher order finite element methods for the discretization of surface Stokes equations is studied. These methods are based on an unfitted finite element approach in which standard Taylor-Hood spaces on an underlying…
We propose several methods for optimizing the number of qubits in a quantum circuit while preserving the number of non-Clifford gates. One of our approaches consists in reversing, as much as possible, the gadgetization of Hadamard gates,…
Simulating the time evolution of a physical system at quantum mechanical levels of detail -- known as Hamiltonian Simulation (HS) -- is an important and interesting problem across physics and chemistry. For this task, algorithms that run on…
In this paper, we consider effective discretization strategies and iterative solvers for nonlinear PDE-constrained optimization models for pattern evolution within biological processes. Upon a Sequential Quadratic Programming linearization…
We introduce an algorithm to compute Hamiltonian dynamics on digital quantum computers that requires only a finite circuit depth to reach an arbitrary precision, i.e. achieves zero discretization error with finite depth. This finite number…
High-order spatial discretisations and full discretisations of parabolic partial differential equations on evolving surfaces are studied. We prove convergence of the high-order evolving surface finite element method, by showing high-order…
Scaling the size of monolithic quantum computer systems is a difficult task. As the number of qubits within a device increases, a number of factors contribute to decreases in yield and performance. To meet this challenge, distributed…
Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…
The discrete gradient methods are integrators designed to preserve invariants of ordinary differential equations. From a formal series expansion of a subclass of these methods, we derive conditions for arbitrarily high order. We derive…
Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…
We investigate high-order finite difference schemes for the Hamilton-Jacobi equation continuum limit of nondominated sorting. Nondominated sorting is an algorithm for sorting points in Euclidean space into layers by repeatedly removing…
In this report, we propose a novel quantum diagonalization algorithm based on the optimization of variational quantum circuits. Diagonalizing a quantum state is a fundamental yet computationally challenging task in quantum information…
A novel class of hybrid quantum-classical algorithms based on the variational approach have recently emerged from separate proposals addressing, for example, quantum chemistry and combinatorial problems. These algorithms provide an…
We investigate high-order Convolution Quadratures methods for the solution of the wave equation in unbounded domains in two dimensions that rely on Nystr\"om discretizations for the solution of the ensemble of associated Laplace domain…
The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods…
Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…
In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…
We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…