EMT/QIS: Physics Based Approaches to Quantum Algorithms

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Quantum computation lies at the intersection of computer science and physics and is a promising emerging technology. Quantum algorithms take advantage of quantum effects not available to conventional computers. There are striking examples where a quantum algorithm, running on a quantum computer, would outperform any classical computer attempting the same task. These include finding the prime factors of a number, searching an unordered list and determining who wins a game. The discovery of new algorithms is key to the growth of this field. The investigators hope to develop new algorithms as well as study the performance of certain known algorithms whose run time is not yet established. The hope is to continue to develop a fruitful synergy between techniques used in physics and conventional algorithm design. The research here would bridge the fields of computer science and physics looking for new algorithms as well as deepening our understanding of the physics which underlies the quantum speedups. The development of a large scale functioning quantum computer would change the world of computation and this research attempts to aid the effort to develop such a machine. The topics to be investigated include quantum walk algorithms, algorithms for evaluating the Jones polynomial and other related quantities, as well as cryptographic protocols for unforgeable identification. The adiabatic algorithm will be studied using a Matrix Product State ansatz as well as by large scale numerical simulation and the fault tolerance of this algorithm will also be investigated.