AF: Small: Physics Based Approaches to Quantum Information Science

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Hopefully in the near future quantum computers will be built. These devices could outperform conventional digital computers, not by having faster operations but by reducing the number of operations required to obtain a result. However to date there are only a few known examples of computational tasks where this speedup has been established. The PIs of this proposal are looking for other ways that quantum computers could speed up computationally intensive tasks that now challenge the limits of conventional computers. They are looking at several specific methods for achieving quantum speedup. One such method is the Quantum Adiabatic Algorithm, which relies on a fundamental concept in quantum physics that tells us how to keep a quantum system in its lowest energy state. The PIs are investigating the efficacy of this method on general optimization problems which arise often in practice. Another method uses the physics of quantum coherence on geometric structures to seek algorithmic speed up for search problems. In addition to algorithms, the PIs will investigate quantum cryptographic protocols that might be used on a future quantum internet. Applications of these ideas might include more secure identity protection as well as more secure financial transactions.