Part 1 Overview of quantum learning theory | Srinivasan Arunachalam (IBM Quantum)
Channel: IAS | Park City Mathematics Institute | PCMI
Date: 2023-07-19

Lecture 1 notes
https://www.ias.edu/sites/default/files/PCMI_Arunachalam_lecture1.pdf

Problem set 1
https://www.ias.edu/sites/default/files/PCMI_Arunachalam_exercise1.pdf

Overview of quantum learning theory
Srinivasan Arunachalam (IBM Quantum)

In recent times, there have been several exciting results in the field of quantum learning. In these lectures, I'll focus on three flavors of results in this field: 

(i) Learning Boolean functions. Here there is an unknown class of Boolean functions, what are the strengths and weaknesses of quantum examples for learning these concept classes? 

(ii) Learning quantum states. Here there is an unknown class of quantum states, and the goal is to learn the unknown state given copies of the state.  There have also been results for learning structured classes of quantum states, reducing the sample and time complexity of learning. 

(iii) More recently, there has been few works on learning distributions obtained from quantum circuits and separations for learning tasks given access to entangled and separable measurements. 

The goal of these lectures is to introduce these directions of research, give an overview of the main results in these areas and discuss the main proof techniques used towards proving them. I will not be assuming any prior knowledge of quantum learning.

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iThe 2023 PCMI 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