Part 3: Data Processing for Quantum Relative Entropy - Omar Fawzi

Quantum Information Theory Lecture 3 notes https://www.ias.edu/sites/default/files/Fawzi%20Lecture%203%20July%2019.pdf Problem set 3 https://www.ias.edu/sites/default/files/Fawzi%20Problem%20Set%203%20July%2019.pdf Shannon laid the foundations of information theory in 1948 by formulating a mathematical theory for studying information storage and transmission. In particular, his noisy channel coding theorem characterizes the fundamental limits of information transmission in the presence of noise. The guiding question for this course will be to explore the analogous quantum problem: information transmission in the presence of quantum noise. In order to be able to formulate and provide answers to this question, we will introduce many fundamental notions about state discrimination, quantum channels and quantum entropy measures. --- The 2023 Program: Quantum Computation Organizers: David Gosset, University of Waterloo; Aram Harrow, MIT; Stacey Jeffery, CWI and QuSoft; Ryan O'Donnell, Carnegie Mellon University; and Thomas Vidick, Caltech. Very recently we have seen experiments at the boundary of the "quantum computing advantage", where quantum computers can massively outperform classical ones at certain tasks.  These advances highlight the need for further mathematical understanding of the computational power of near-term quantum devices.  The goal of the 2023 GSS is to dive deeply into the mathematics relevant for building near-term quantum computers, analyzing their power, and putting them to use.  Minicourses will include: overviews of quantum learning, information theory, and linear-algebraic algorithms; recent advances in quantum error-correcting codes; and, the complexity theory of random circuits and Hamiltonians. Structure: The Graduate Summer School at PCMI consists of a series of several interwoven minicourses on different aspects of the main research theme of that summer.  These courses are taught by leading experts in the field, chosen not only for their stature in the field but their pedagogical abilities. Each minicourse comprises three to five lectures. Each course is accompanied by a daily problem session, structured to help students develop facility with the material. 2023 Schedule Week 1   Andras: Quantum Fourier transform beyond Shor's algorithm   Omar: Quantum information theory   Srinivasan: Overview of quantum learning theory Week 2   Ewin: Quantum and quantum-inspired linear algebra   Nicolas: Quantum LDPC codes   Yassine: Quantum query complexity Week 3   Bill: Computational complexity of near-term quantum experiments   Jeongwan: Topological aspects of quantum codes   Sandy: Quantum Hamiltonian complexity — The GSS takes place within the broader structure of PCMI, so there are many researchers at all levels in the field in attendance, as well as participants in the other PCMI programs. ias.edu/PCMI