Small- to medium-scale quantum computers are around the corner, and the biggest upcoming challenges are expected to be algorithmic. What computational tasks can such computers speed up? And how can we test them? More specifically, what are the prospects for quantum simulation, quantum machine learning, and protocols for testing quantum devices? The answers to these questions touch on deep issues and will require an unprecedented collaboration between theoretical computer science (algorithms, complexity theory, cryptography) and physics, chemistry, and mathematics. This summer cluster brought together researchers from these fields to collaborate on formalizing and answering these questions. The third week of the eight-week program, June 11 to 15, was devoted to a workshop exploring the state of the art related to these challenges.