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Overview of Quantum Learning Theory - Lecture 1

IAS | PCMI Park City Mathematics Institute via YouTube

Overview

Explore quantum learning theory fundamentals in this comprehensive lecture from IBM Quantum researcher Srinivasan Arunachalam, focusing on three key areas: Boolean function learning, quantum state learning, and quantum circuit distribution learning. Delve into the strengths and limitations of quantum examples in Boolean function learning, discover techniques for learning unknown quantum states with reduced sample and time complexity, and examine recent developments in learning distributions from quantum circuits and the distinctions between entangled and separable measurements. Master essential concepts through accompanying lecture notes and problem sets, with no prior quantum learning knowledge required. Part of the 2023 PCMI Graduate Summer School program on Quantum Computation, this lecture covers crucial topics including quantum PAC learning, VC dimension, sample complexity comparisons between classical and quantum approaches, Pretty Good Measurement techniques, and agnostic learning scenarios.

Syllabus

Intro
Quantum machine learning
Quantum learning theory
A Theory of the Learnable
Classical learner using classical examples
Learning model: classical PAC learning
Quantum PAC learning
Vapnik and Chervonenkis (VC) dimension
VC dimension characterizes PAC sample complexity
Quantum sample complexity = Classical sample complexity
Proof approach: Pretty Good Measurement
Sample complexity lower bound via PGM
Random classification noise
Agnostic learning

Taught by

IAS | PCMI Park City Mathematics Institute

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