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A Panoply of Quantum Algorithms

Bartholomew Furrow
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Abstract

We create a variety of new quantum algorithms that use Grover's algorithm and similar techniques to give polynomial speedups over their classical counterparts. We begin by introducing a set of tools that carefully minimize the impact of errors on running time; those tools provide us with speedups to already-published quantum algorithms, such as improving Durr, Heiligman, Hoyer and Mhalla's algorithm for single-source shortest paths [quant-ph/0401091] by a factor of lg N. The algorithms we construct from scratch have a range of speedups, from O(E)->O(sqrt(VE lg V)) speedups in graph theory to an O(N^3)->O(N^2) speedup in dynamic programming.

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Bartholomew Furrow. 2006-06-15. A Panoply of Quantum Algorithms. https://arxiv.org/abs/quant-ph/0606127

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