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arXiv:1507.08947

Quantum search followed by classical search versus quantum search alone

P. R. M. Sousa, F. V. Mendes, Rubens Viana Ramos

Published Jul 31, 2015• 0 citations
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Abstract

In this work, we show that the usage of a quantum gate that gives extra information about the solution searched permits to improve the performance of the search algorithm by switching from quantum to classical search in the appropriated moment. A comparison to the case where only quantum search is used is also realized.
DOI
10.48550/arxiv.1507.08947

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The quantum search algorithm (QSA) is one of the most recent developments in the era of quantum signal processing (QSP) and quantum information theory (QIT). It shows a faster performance in finding the solutions of system such as multiple-input multiple-output (MIMO) communication system, quantum error correction and others with a polynomial order over the classical one. Grover's algorithm is one of the first proposed QSA in identifying the index number of the solution of a system, whose solutions are known to the oracle. A further improved QSA called Boyer-Brassard-Høyer-Tapp (BBHT) is followed by the Durr-Hoyer algorithm (DHA), which proposes to find the solutions, while the exact number of the solutions is not known. In this treatise, we propose two modifications to the existing DHA and BBHT algorithms. In DHA, we propose a semi-quantum framework, where after each iteration in DHA, the non-solution points are removed in classical framework. This makes the data set iteratively shorter. In the case of BBHT algorithm, we propose to choose the Grover search number based on the Gamma distribution instead of the uniform one, which gives more chances to the new larger values to improve probability of success. The performance of the proposed QSAs demonstrates plausible improvement in search success performance as compared to their existing BBHT and DHA counterparts. Numerical simulations are conducted with the proposed QSA algorithms on a MIMO orthogonal frequency division multiplexing (OFDM) system to demonstrate the performance improvement.
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