Analysis on the hypercube with applications to quantum computing

June 6 to June 10, 2022

at the

American Institute of Mathematics, San Jose, California

organized by

Polona Durcik, Irina Holmes Fay, and Paata Ivanisvili

Original Announcement

This workshop will be devoted to analysis on the hypercube. The set of vertices of a unit cube is called the hypercube. It consists of vectors with coordinates zeros and ones. Series of open questions in computer science, especially in quantum computing such as Aaronson-Ambainis conjecture, can be formulated as mathematical problems on the hypercube which do not require any a priori knowledge of computer science to start solving them. It turns out that these questions have certain Fourier-analytic nature if one considers the hypercube as a Cantor group equipped with uniform measure. Unlike the classical case of the unit circle, many fundamental results in classical Fourier analysis and approximation theory, including Markov-Bernstein type inequalities, are not yet developed well enough to solve the problems raised in computer science. The goal of the workshop is to bring researchers with different backgrounds, including analysis, probability, combinatorics, and computer science, in order to introduce them to open problems on the hypercube, give lectures on the subject, strengthen the bridges between fields that overlap with the hypercube, and describe the recent results in this area

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.