Quantum computers hold the promise of solving problems which classical computers find intractable. The resulting interest in quantum computers has led to the formulation of an intractability conjecture-that there are problems whose solution in polynomial time will defy even quantum computers. This project will attempt to advance our understanding of the physical implications of this and related conjectures, broadly whether hardness/intractability/glassiness is an emergent property of quantum mechanical systems of recognizable physical interest. To this end we will carry out theoretical investigations of a set of specific questions as well as mobilize a larger and interdisciplinary group of theorists for a set of meetings to focus attention on this topic. Concrete outputs will consist of a set of papers. We believe this enterprise can help uncover quantum systems with robustly slow dynamics at large system size as well as shed light on live issues in quantum computer science such as the prospects for a PCP theorem.