David J. Rosenbaum

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We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G ∼ = H. For several decades, the n log p n+O(1) generator-enumeration bound (where p is the smallest prime dividing the order of the group) has been the best worst-case result for general groups. In this work, we show the first(More)
We consider the isomorphism problem for groups specified by their multiplication tables. Until recently, the best published bound for the worst-case was achieved by the n log p n+O(1) generator-enumeration algorithm. In previous work with Fabian Wagner, we showed an n (1/2) log p n+O(log n/ log log n) time algorithm for testing isomorphism of p-groups by(More)
We consider a generalization of the standard oracle model in which the oracle acts on the target with a permutation which is selected according to internal random coins. We show new exponential quantum speedups which may be obtained over classical algorithms in this oracle model. Even stronger, we describe several problems which are impossible to solve(More)
This paper presents a new quantum array that can be used to control a single-qudit hermitian operator for an odd radix r > 2 by n controls using Θ n log 2 r+2 single-qudit controlled gates with one control and no an-cilla qudits. This quantum array is more practical than existing quantum arrays of the same complexity because it does not require the use of(More)