Characterization and Control in Large Hilbert spaces.

Abstract

Computational devices built on and exploiting quantum phenomena have the potential to revolutionize our understanding of computational complexity by being able to solve certain problems faster than the best known classical algorithms. Unfortunately, unlike the digital computers quantum information processing devices hope to replace, quantum information is fragile by nature and lacks the inherent robustness of digital logic. Indeed, for whatever we can do to control the evolution, nature can also do in some random and unknown fashion ruining the computation. This thesis explores the task of building the classical control architecture to control a large quantum system and how to go about characterizing the behaviour of the system to determine the level of control reached. Both these tasks appear to require an exponential amount of resources as the size of the system grows. The inability to efficiently control and characterize large scale quantum systems will certainly militate against their potential computational usefulness making these important problems to solve. The solutions presented in this thesis are all tested for their practical usefulness by implementing them in either liquid- or solid-state nuclear magnetic resonance.