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Data-driven methods for establishing quantum optimal control (QOC) using time-dependent control pulses tailored to specific quantum dynamical systems and desired control objectives are critical for many emerging quantum technologies. We…

Quantum Physics · Physics 2021-03-29 Andy Goldschmidt , Eurika Kaiser , Jonathan L. Dubois , Steven L. Brunton , J. Nathan Kutz

In this work, we present a numerical method that remedies the instabilities of the conventional FDTD approach for solving Maxwell's equations in a space-time dependent magneto-electric medium with direct application to the simulation of the…

Optics · Physics 2015-06-18 Jason Cornelius , Jinjie Liu , Moysey Brio

Solving high-dimensional parabolic partial differential equations (PDEs) with deep learning methods is often computationally and memory intensive, primarily due to the need for automatic differentiation (AD) to compute large Hessian…

Numerical Analysis · Mathematics 2026-01-13 Wei Cai , Shuixin Fang , Tao Zhou

A previously developed quantum reduced-order model is revised and applied, together with the domain decomposition, to develop the quantum element method (QEM), a methodology for fast and accurate simulation of quantum eigenvalue problems.…

Computational Physics · Physics 2023-04-18 Ming-C. Cheng

We present a fault-tolerant quantum algorithm for implementing the Discrete Variable Representation (DVR) transformation, a technique widely used in simulations of quantum-mechanical Hamiltonians. DVR provides a diagonal representation of…

Quantum Physics · Physics 2025-04-23 Szymon Pliś , Emil Zak

An accurate model of a vertical pillar quantum dot is described. The full three dimensional structure of the device containing the dot is taken into account and this leads to an effective two dimensional model in which electrons move in the…

Mesoscale and Nanoscale Physics · Physics 2008-04-22 P. A. Maksym , Y. Nishi , D. G. Austing , T. Hatano , L. P. Kouwenhoven , H. Aoki , S. Tarucha

We propose a frequency-division multiplexed (FDM) continuous-variable quantum key distribution (CV-QKD) system with enhanced spectral efficiency through dense multiplexing of low-symbol-rate signals. A four-channel 10-Mbaud FDM-CV-QKD…

Quantum Physics · Physics 2026-03-24 Jahyeok Han , Donghyeok Le , Minseok Ryu , Syed Assad , Yong-Su Kim , Sunghyun Bae

Nonlinear Fourier division Multiplexing (NFDM) can be realized from modulating the discrete nonlinear spectrum of an $N$-solitary waveform. To generate an $N$-solitary waveform from desired discrete spectrum (eigenvalue and discrete…

Numerical Analysis · Mathematics 2016-05-23 Vahid Aref

Quantum metrology exploits quantum mechanical laws to improve the precision in estimating technologically relevant parameters such as phase, frequency, or magnetic fields. Probe states are usually tailored on the particular dynamics whose…

At the exceptional point where two eigenstates coalesce in open quantum systems, the usual diagonalization scheme breaks down and the Hamiltonian can only be reduced to Jordan block form. Most of the studies on the exceptional point…

Quantum Physics · Physics 2017-09-22 Kazuki Kanki , Savannah Garmon , Satoshi Tanaka , Tomio Petrosky

Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient numerical technique to solve strongly coupled QFTs in d=2 spacetime dimensions. Further theoretical developments are needed to increase its accuracy and the range…

High Energy Physics - Theory · Physics 2017-12-19 Joan Elias-Miro , Slava Rychkov , Lorenzo G. Vitale

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…

Quantum Physics · Physics 2025-10-22 Vladyslav Bohun , Andrij Kuzmak , Maciej Koch-Janusz

In this study, a fast multipole method (FMM) is used to decrease the computational time of a fully-coupled poroelastic hydraulic fracture model with a controllable effect on its accuracy. The hydraulic fracture model is based on the…

Numerical Analysis · Computer Science 2019-10-23 Ali Rezaei , Fahd Siddiqui , Giorgio Bornia , Mohamed Y. Soliman

A so-called grid-overlay finite difference method (GoFD) was proposed recently for the numerical solution of homogeneous Dirichlet boundary value problems of the fractional Laplacian on arbitrary bounded domains. It was shown to have…

Numerical Analysis · Mathematics 2025-03-05 Jinye Shen , Bowen Shi , Weizhang Huang

An extremely fast time-harmonic finite element solver developed for the transmission analysis of photonic crystals was applied to mask simulation problems. The applicability was proven by examining a set of typical problems and by a…

Optics · Physics 2009-05-28 S. Burger , R. Köhle , L. Zschiedrich , W. Gao , F. Schmidt , R. März , C. Nölscher

We compare the long-time error bounds and spatial resolution of finite difference methods with different spatial discretizations for the Dirac equation with small electromagnetic potentials characterized by $\varepsilon \in (0, 1]$ a…

Numerical Analysis · Mathematics 2021-05-24 Yue Feng , Jia Yin

The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…

Numerical Analysis · Mathematics 2018-10-09 Jerome Droniou , Neela Nataraj , Devika Shylaja

Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate methods for problems with curved interfaces and internal…

Numerical Analysis · Mathematics 2022-06-14 Zhilin Li , Kejia Pan , Juan Ruiz

In this paper, we analyze the convergence of Alternating Direction Method of Multipliers (ADMM) on convex quadratic programs (QPs) with linear equality and bound constraints. The ADMM formulation alternates between an equality constrained…

Optimization and Control · Mathematics 2015-10-06 Arvind U. Raghunathan , Stefano Di Cairano

Double quantum dots (DQDs) hold great promise as building blocks for quantum technology as they allow for two electronic states to coherently couple. Defining QDs with materials rather than using electrostatic gating allows for QDs with a…

Mesoscale and Nanoscale Physics · Physics 2021-09-08 David Barker , Sebastian Lehmann , Luna Namazi , Malin Nilsson , Claes Thelander , Kimberly A. Dick , Ville F. Maisi