Articles containing proofs | Integer factorization algorithms | Quantum algorithms
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).
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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