Articles containing proofs | Integer factorization algorithms | Quantum algorithms

Quantum algorithm for linear systems of equations

The quantum algorithm for linear systems of equations, also called HHL algorithm, designed by Aram Harrow, Avinatan Hassidim, and Seth Lloyd, is a quantum algorithm published in 2008 for solving linear systems. The algorithm estimates the result of a scalar measurement on the solution vector to a given linear system of equations. The algorithm is one of the main fundamental algorithms expected to provide a speedup over their classical counterparts, along with Shor's factoring algorithm, Grover's search algorithm, and the quantum fourier transform. Provided the linear system is sparse and has a low condition number , and that the user is interested in the result of a scalar measurement on the solution vector, instead of the values of the solution vector itself, then the algorithm has a runtime of , where is the number of variables in the linear system. This offers an exponential speedup over the fastest classical algorithm, which runs in (or for positive semidefinite matrices). An implementation of the quantum algorithm for linear systems of equations was first demonstrated in 2013 by Cai et al., Barz et al. and Pan et al. in parallel. The demonstrations consisted of simple linear equations on specially designed quantum devices. The first demonstration of a general-purpose version of the algorithm appeared in 2018 in the work of Zhao et al. Due to the prevalence of linear systems in virtually all areas of science and engineering, the quantum algorithm for linear systems of equations has the potential for widespread applicability. (Wikipedia).

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Andrew Childs - Efficient quantum algorithm for dissipative nonlinear differential equations

Recorded 24 January 2022. Andrew Childs of the University of Maryland presents "Efficient quantum algorithm for dissipative nonlinear differential equations" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: While there has been extensive previous work on efficient quantum alg

From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022

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Linear algebra for Quantum Mechanics

Linear algebra is the branch of mathematics concerning linear equations such as. linear functions and their representations in vector spaces and through matrices. In this video you will learn about #linear #algebra that is used frequently in quantum #mechanics or #quantum #physics. ****

From playlist Quantum Physics

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Rolando Somma - The Quantum Linear Systems Problem - IPAM at UCLA

Recorded 24 January 2022. Rolando Somma of Los Alamos National Laboratory presents "The Quantum Linear Systems Problem" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: The goal of the quantum linear systems problem (QLSP) is to prepare a quantum state proportional to the sol

From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022

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Artificial General Intelligence | Tim Ferriss & Eric Schmidt | GEONOW

✅ Subscribe: https://bit.ly/3slupxs Quantum AI is the use of quantum computing for computation of machine learning algorithms. Thanks to computational advantages of quantum computing, quantum AI can help achieve results that are not possible to achieve with classical computers. Quantum da

From playlist ML & Deep Learning

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Linear Algebra for Computer Scientists. 7. Linear Combinations of Vectors

This computer science video is one of a series on linear algebra for computer scientists. In this video you will learn about linear combinations of vectors, that is, you will learn how to create new vectors by scaling then adding other vectors together. You will also learn that some sets

From playlist Linear Algebra for Computer Scientists

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Intro to Linear Systems: 2 Equations, 2 Unknowns - Dr Chris Tisdell Live Stream

Free ebook http://tinyurl.com/EngMathYT Basic introduction to linear systems. We discuss the case with 2 equations and 2 unknowns. A linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that ar

From playlist Intro to Linear Systems

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Dominic Berry - Optimal scaling quantum linear systems solver via discrete adiabatic theorem

Recorded 25 January 2022. Dominic Berry of Macquarie University presents "Optimal scaling quantum linear systems solver via discrete adiabatic theorem" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: Recently, several approaches to solving linear systems on a quantum compute

From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022

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Andras Gilyen - Quantum Algorithms for Quantum Information Processing Tasks - IPAM at UCLA

Recorded 24 January 2022. Andras Gilyen of the Renyi Institute of Mathematics presents "Quantum Algorithms for Quantum Information Processing Tasks" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: Quantum linear algebra methods, in particular block-encoding and quantum singu

From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022

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Linear Algebra: Systems of Linear Equations

Learn the basics of Linear Algebra with this series from the Worldwide Center of Mathematics. Find more math tutoring and lecture videos on our channel or at http://centerofmath.org/

From playlist Basics: Linear Algebra

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Jin-Peng Liu - Efficient quantum algorithms for nonlinear ODEs and PDEs - IPAM at UCLA

Recorded 27 January 2022. Jin-Peng Liu of the University of Maryland presents "Efficient quantum algorithms for nonlinear ODEs and PDEs" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: Nonlinear dynamics play a prominent role in many domains and are notoriously difficult to

From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022

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Carlos Bravo-Prieto - Variational quantum architectures for linear algebra applications

Recorded 27 January 2022. Carlos Bravo-Prieto of the University of Barcelona presents "Variational quantum architectures for linear algebra applications" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: Current quantum computers typically have a few tens of qubits and are pro

From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022

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HEDS | Using quantum computers to simulate a toy problem of laser-plasma interaction

HEDS Seminar Series- Yuan Shi – August 5th, 2021 LLNL-VIDEO-836250

From playlist High Energy Density Science Seminar Series

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Quantum Metrology II by Girish Agarwal

Dates: Thursday 03 Jan, 2013 - Saturday 05 Jan, 2013 Venue: ICTS-TIFR, IISc Campus, Bangalore The school aims to provide students and researchers an introduction to the field of quantum information, computation and communication. Topics that will be covered include introduction to quantu

From playlist Mini Winter School on Quantum Information and Computation

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David Mazziotti - Contracted Quantum Eigensolver for the Quantum Simulation of Many-electron Systems

Recorded 05 May 2022. David Mazziotti of the University of Chicago, Chemistry, presents "Contracted Quantum Eigensolver for the Quantum Simulation of Many-electron Systems" at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Abstract: We will introduce a novel

From playlist 2022 Large-Scale Certified Numerical Methods in Quantum Mechanics

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Roberto La Scala, Università di Bari

Roberto La Scala, Università di Bari Ciphers and difference equations

From playlist Spring 2021 Online Kolchin Seminar in Differential Algebra

Related pages

Unit vector | Hermitian matrix | Amplitude amplification | Quantum algorithm | Unitary operator | Condition number | Gaussian elimination | Conjugate gradient method | Big data | Computational finance | Hamiltonian simulation | System of linear equations | Born rule | Differentiable programming | Grover's algorithm | Preconditioner | Sparse matrix | BQP | Stefanie Barz | PSPACE | Cloud-based quantum computing