Part 4 Introducing quantum-inspired linear algebra | Ewin Tang (University of Washington)
Channel: IAS | Park City Mathematics Institute | PCMI
Date: 27/07/2023

Quantum and quantum-inspired linear algebra
Part 4 Introducing quantum-inspired linear algebra
Lecture 4 notes
https://www.ias.edu/sites/default/files/Tang%20qsvt_lect_4.pdf
Problem set 4
https://www.ias.edu/sites/default/files/Tang%20Qsvt_pset_4_0.pdf

An exciting recent line of work unifies many interesting quantum algorithms under a powerful linear algebraic framework known as "quantum singular value transformation" (QSVT). We'll introduce this framework, build some tools in polynomial approximation that are helpful for applying it, and investigate what kinds of results it can achieve. Our goal will be to understand how and when to use QSVT in quantum algorithm design, and ultimately, whether it can reveal new quantum speedups for interesting problems in data analysis, machine learning, or quantum simulation.

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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
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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