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Rapid sampling through quantum computing

Lov K. Grover
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Abstract

This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space. This yields new applications - an algorithm is presented that can create an arbitrarily specified quantum superposition on a space of size N in O(sqrt(N)) steps. By making a measurement on this superposition, it is possible to obtain a sample according to an arbitrarily specified classical probability distribution in O(sqrt(N)) steps. A classical algorithm would need O(N) steps.

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Lov K. Grover. 2000-02-18. Rapid sampling through quantum computing. https://arxiv.org/abs/quant-ph/9912001

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