English
Related papers

Related papers: Quantum Iterative Methods for Solving Differential…

200 papers

We propose and experimentally demonstrate sequential quantum computing (SQC), a paradigm that utilizes multiple homogeneous or heterogeneous quantum processors in hybrid classical-quantum workflows. In this manner, we are able to overcome…

A versatile and efficient variational approach is developed to solve in- and out-of-equilibrium problems of generic quantum spin-impurity systems. Employing the discrete symmetry hidden in spin-impurity models, we present a new canonical…

Strongly Correlated Electrons · Physics 2018-07-13 Yuto Ashida , Tao Shi , Mari Carmen Bañuls , J. Ignacio Cirac , Eugene Demler

Partial differential equations (PDEs) are fundamental across numerous scientific fields. As these problems scale to high dimensions, classical numerical schemes introduce severe computational bottlenecks, known as the curse of…

Quantum Physics · Physics 2026-04-29 Chih-Kang Huang , Giacomo Antonioli , Frédéric Barbaresco

It is well known that the choice of the iterative method is crucial in determining the speed of the converged solution. This article presents a detailed comparison between several iterative techniques for solving incmopressible…

Numerical Analysis · Mathematics 2019-07-31 Mohamed Mohsen Ahmed

The theoretical analysis of the Adiabatic Quantum Computation protocol presents several challenges resulting from the difficulty of simulating, with classical resources, the unitary dynamics of a large quantum device. We present here a…

Quantum Physics · Physics 2024-03-11 Giuseppe Carleo , Bela Bauer , Matthias Troyer

This paper is devoted to the derivation of a digital quantum algorithm for the Cauchy problem for symmetric first order linear hyperbolic systems, thanks to the reservoir technique. The reservoir technique is a method designed to avoid…

Quantum Physics · Physics 2018-04-10 F. Fillion-Gourdeau , E. Lorin

We explore how a continuous-variable (CV) quantum computer could solve a classic differential equation, making use of its innate capability to represent real numbers in qumodes. Specifically, we construct variational CV quantum circuits…

Quantum Physics · Physics 2020-12-23 Martin Knudsen , Christian B. Mendl

In this manuscript, we show how flow equation methods can be used to study localisation in disordered quantum systems, and particularly how to use this approach to obtain the non-equilibrium dynamical evolution of observables. We review the…

Disordered Systems and Neural Networks · Physics 2020-02-27 S. J. Thomson , M. Schiró

The paper presents a variational quantum algorithm to solve initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum…

Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited,…

Quantum Physics · Physics 2023-11-07 Lucas T. Brady , Stuart Hadfield

We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…

At the heart of quantum technology development is the control of quantum systems at the level of individual quanta. Mathematically, this is realised through the study of Hamiltonians and the use of methods to solve the dynamics of quantum…

Quantum Physics · Physics 2022-10-24 Sofia Qvarfort , Igor Pikovski

We introduce an approach for quantum computing in continuous time based on the Lewis-Riesenfeld dynamic invariants. This approach allows, under certain conditions, for the design of quantum algorithms running on a nonadiabatic regime. We…

Quantum Physics · Physics 2011-08-18 M. S. Sarandy , E. I. Duzzioni , R. M. Serra

Computing electronic structures of quantum systems is a key task underpinning many applications in photonics, solid-state physics, and quantum technologies. This task is typically performed through iterative algorithms to find the energy…

Quantum Physics · Physics 2026-02-03 Shaobo Zhang , Akib Karim , Harry M. Quiney , Muhammad Usman

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Machine Learning · Computer Science 2022-10-04 Ayano Kaneda , Osman Akar , Jingyu Chen , Victoria Kala , David Hyde , Joseph Teran

Differential equations (DEs) serve as the cornerstone for a wide range of scientific endeavors, their solutions weaving through the core of diverse fields such as structural engineering, fluid dynamics, and financial modeling. DEs are…

Quantum Physics · Physics 2025-06-10 Josephine Hunout , Sylvain Laizet , Lorenzo Iannucci

In this article, we introduce an original hybrid quantum-classical algorithm based on a variational quantum algorithm for solving systems of differential equations. The algorithm relies on a spectral decomposition of the trial functions…

In this paper we present an extension of standard iterative splitting schemes to multiple splitting schemes for solving higher order differential equations. We are motivated by dynamical systems, which occur in dynamics of the electrons in…

Numerical Analysis · Mathematics 2012-04-17 Juergen Geiser , Thomas Zacher

Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by…

Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…

Systems and Control · Electrical Eng. & Systems 2025-12-23 Jan Schneider , Julian Berberich