Projects
Finding new quantum algorithms is one of the biggest challenges in quantum
computation. Recent progress in the area includes solving Pell's equation
and its generalization, the unit group of a number field, and problems from
computational algebraic number theory. Long term goals include finding
quantum algorithms for graph isomorphism and the unique shortest lattice
vector problem, as well as the more general hidden subgroup problem.
Methods for the stabilization of quantum systems against
errors are essential for quantum information processing. Quantum codes
allow detecting and correcting errors that are due to incoherence effects.
Long term goals include the search for new constructions of quantum codes
and the analysis of the threshold required for fault-tolerant quantum
computing.
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