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arXiv · 0809.1538

Asymptotic Quantum Search and a Quantum Algorithm for Calculation of a Lower Bound of the Probability of Finding a Diophantine Equation That Accepts Integer Solutions

R. V. Ramos·J. L. de Oliveira
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Abstract

Several mathematical problems can be modeled as a search in a database. An example is the problem of finding the minimum of a function. Quantum algorithms for solving this problem have been proposed and all of them use the quantum search algorithm as a subroutine and several intermediate measurements are realized. In this work, it is proposed a new quantum algorithm for finding the minimum of a function in which quantum search is not used as a subroutine and only one measurement is needed. This is also named asymptotic quantum search. As an example, we propose a quantum algorithm based on asymptotic quantum search and quantum counting able to calculate a lower bound of the probability of finding a Diophantine equation with integer solution.

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R. V. Ramos, J. L. de Oliveira. 2008-10-07. Asymptotic Quantum Search and a Quantum Algorithm for Calculation of a Lower Bound of the Probability of Finding a Diophantine Equation That Accepts Integer Solutions. https://arxiv.org/abs/0809.1538

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