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Is partial quantum search of a database any easier?

Lov K. Grover·Jaikumar Radhakrishnan
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Abstract

In this paper, we consider the partial database search problem where given a database on N items, we are required to determine the first k bits of an address x such that f(x)=1. We derive an algorithm and a lower bound for this problem in the quantum circuits model. Let q(k,N) be the minimum number of queries needed to find the first k bits of the required address x. We show that there exist constants c_k and d_k such that (pi/4) (1 - d_k/sqrt{K}) sqrt{N} <= q(k,n) <= (pi/4) (1 - c_k/sqrt{K}) sqrt{N}, where K=2^k. Thus, it is always easier to determine a few bits of the target address than to find the entire address, but as k becomes large this advantage reduces rapidly.

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Lov K. Grover, Jaikumar Radhakrishnan. 2005-02-07. Is partial quantum search of a database any easier?. https://arxiv.org/abs/quant-ph/0407122

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