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We propose a class of randomized quantum Krylov diagonalization (rQKD) algorithms capable of solving the eigenstate estimation problem with modest quantum resource requirements. Compared to previous real-time evolution quantum Krylov…

Quantum Physics · Physics 2023-03-29 Nicholas H. Stair , Cristian L. Cortes , Robert M. Parrish , Jeffrey Cohn , Mario Motta

Solving differential equations is one of the most computationally expensive problems in classical computing, occupying the vast majority of high-performance computing resources devoted towards practical applications in various fields of…

Quantum Physics · Physics 2024-10-08 Sunheang Ty , Renaud Vilmart , Axel TahmasebiMoradi , Chetra Mang

We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…

Numerical Analysis · Mathematics 2024-11-19 R. Drebotiy , H. Shynkarenko

In this work we present a variant of the fast multipole method (FMM) for efficiently evaluating standard layer potentials on geometries with complex coordinates in two and three dimensions. The complex scaled boundary integral method for…

Numerical Analysis · Mathematics 2025-10-20 Tristan Goodwill , Leslie Greengard , Jeremy Hoskins , Manas Rachh , Yuguan Wang

With the aim of establishing a framework to efficiently perform the practical application of quantum chemistry simulation on near-term quantum devices, we envision a hybrid quantum--classical framework for leveraging problem decomposition…

A general method to generate a centrosymmetric matrix associated with the solving of partial differential equation (PDE) on an irreducible domain by means of a linear equation system is proposed. The method applies to any PDE for which both…

Numerical Analysis · Mathematics 2025-03-12 T. Thuillier

Self-organized semiconductor quantum dots represent almost ideal two-level systems, which have strong potential to applications in photonic quantum technologies. For instance, they can act as emitters in close-to-ideal quantum light…

The Hessian discretisation method (HDM) for fourth order linear elliptic equations provides a unified convergence analysis framework based on three properties namely coercivity, consistency, and limit-conformity. Some examples that fit in…

Numerical Analysis · Mathematics 2020-01-31 Devika Shylaja

Quantum digital signatures (QDS), based on the principles of quantum mechanics, provide information-theoretic security, ensuring the integrity, authenticity, and non-repudiation of data transmission. With present QDS protocols,…

Quantum Physics · Physics 2025-01-10 Jia-Li Zhu , Chun-Hui Zhang , Yue-Ying Wang , Qin Wang

In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some special properties; in…

Quantum Physics · Physics 2016-12-12 David Bermudez , David J. Fernandez C

We focus on a recently developed generalized pseudospectral method for accurate, efficient treatment of certain central potentials of interest in various branches in quantum mechanics, usually having singularity. Essentially this allows…

Quantum Physics · Physics 2019-04-19 Amlan K. Roy

The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…

Numerical Analysis · Mathematics 2025-07-11 Robert Carlson

In this paper we explicate a method of quantum hydrodynamics (QHD) for the study of the quantum evolution of a system of polarized particles. Though we focused primarily on the two-dimension physical systems, the method is valid for…

Mesoscale and Nanoscale Physics · Physics 2013-05-29 P. A. Andreev , L. S. Kuzmenkov , M. I. Trukhanova

A general method for numerical computation of the thermal density matrix of a single-particle quantum system is presented. The Schrodinger equation in imaginary time tau is solved numerically by the finite difference time domain (FDTD)…

Computational Physics · Physics 2009-02-12 I. Wayan Sudiarta , D. J. Wallace Geldart

Variational quantum algorithms are one of the most promising methods that can be implemented on noisy intermediate-scale quantum (NISQ) machines to achieve a quantum advantage over classical computers. This article describes the use of a…

Quantum Physics · Physics 2022-05-10 Wei-Bin Ewe , Dax Enshan Koh , Siong Thye Goh , Hong-Son Chu , Ching Eng Png

We present an efficient second-order finite difference scheme for solving the 2D sine-Gordon equation, which can inherit the discrete energy conservation for the undamped model theoretically. Due to the semi-implicit treatment for the…

Numerical Analysis · Mathematics 2017-06-28 Xiaorong Kang , Wenqiang Feng , Kelong Cheng , Chunxiang Guo

We present an efficient finite difference method for the approximation of second derivatives, with respect to system parameters, of expectations for a class of discrete stochastic chemical reaction networks. The method uses a coupling of…

Quantitative Methods · Quantitative Biology 2012-10-16 Elizabeth Skubak Wolf , David F. Anderson

Quantum key distribution (QKD) offers a reliable solution to communication problems that require long-term data security. For its widespread use, however, the rate and reach of QKD systems must be improved. Twin-field (TF) QKD is a step…

Complex forms of quantum entanglement can arise in two qualitatively different ways; either between many qubits or between two particles with higher-than-qubit dimension. While the many-qubit frontier and the high-dimension frontier both…

Quantum Physics · Physics 2024-09-24 Gabriele Cobucci , Armin Tavakoli

Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…

Quantum Physics · Physics 2021-11-10 Andrew M. Childs , Jin-Peng Liu , Aaron Ostrander