PCMI 2023 Graduate Summer School

The Gradate 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.  These minicourses vary in level of preparation needed, and the schedule is structured so there are good opportunities for students just entering the field as well as courses suitable for more advanced students.  Each course is accompanied by a daily problem session, structured to help students develop facility with the material.

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.  This provides an outstanding way for graduate students to get to know leaders in their field and to interact with them in a leisurely way.  There are also numerous group activities which allow participants in the GSS to interact with people in other groups, including formal and informal social events, and the PCMI Experimental Math Lab, which brings together small groups of participants to work on accessible and open-ended problems.   Graduate students have many opportunities to get good advice about career paths after they complete their PhDs, and can meet mathematicians who are working at a wide variety of institutions, from top research centers to undergraduate-focused colleges.

There are three graduate minicourses scheduled each day (Wednesday afternoons are free) and problem sessions accompanying each minicourse. Participants may attend talks from the other programs as they see fit.

 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.

Prerequisites:  Students should have a solid foundation in linear algebra, probability, and theoretical computer science; basic knowledge of quantum computing will also be helpful.

The PCMI Summer Session will be held July 16-August 5, 2023.