Quantum Algorithms for Quantum Information Processing Tasks

Explore quantum algorithms for quantum information processing tasks in this lecture by Andras Gilyen from the Renyi Institute of Mathematics. Delve into the efficient tools provided by quantum linear algebra methods, particularly block-encoding and quantum singular value transformation, for processing coherent quantum information. Discover how these new tools and understanding enable solving various problems with greater generality or efficiency than previously known. Examine applications in estimation, testing, and tomography tasks related to quantum states, as well as the implementation of Petz recovery channels—a quantum generalization of Bayes' inference. Learn about topics such as block-encoding, density operators with purified access, Quantum Singular Value Transformation (OSVT), direct implementation of HHL and pseudoinverse, singular vector transformation and projection, quantum speed-ups for distribution testing, fidelity estimation, and implementing Petz recovery channels. Gain insights into the various applications and speed-ups achieved through these quantum algorithms in this comprehensive presentation from IPAM's Quantum Numerical Linear Algebra Workshop.

Intro
A bird's eye view on quantum inear algebra
Block-encoding
Example: density operator with purified access
Quantum Singular Value Transformation (OSVT)
Direct implementation of HHL / the pseudoinverse
Singular vector transformation and projection
Quantum speed-ups for distribution testing
Fidelity estimation
Implementing Petz recovery Channels
Summarizing the various applications and speed-ups