On Quantum Linear Algebra for Machine Learning - Quantum Colloquium

Explore quantum linear algebra algorithms for machine learning in this comprehensive lecture from the Quantum Colloquium series. Delve into quantum singular value transformation (QSVT), a unifying framework developed by Gilyén et al., and its applications in achieving quantum speedups for machine learning problems. Examine the typical structure of such applications, barriers to super-polynomial quantum speedup, and current literature addressing these challenges. Discover the intriguing connection between quantum linear algebra and classical sampling and sketching algorithms through "quantum-inspired" classical algorithms. Cover topics including blocking coding, linear algebra on quantum states, linear combinations, literary polynomials, Lipschitz matrix functions, block encoding, and sample query axis. Gain insights into the input and output problems, sample data structures, and composition properties in this in-depth exploration of quantum linear algebra's potential in advancing machine learning techniques.

Introduction
Motivation
Introducing Quantum Linear Algebra
Blocking Coding
Linear Algebra on Quantum States
Linear Combinations
Literary Polynomials
Lipschitz
Matrix Functions
Blocking Codings
Block Encoding
Barriers
Applications
Example
Input problem
Output problem
Sample Query Axis
Sample Data Structure
Composition Properties