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arXiv:quant-ph/0311171

A Hybrid Quantum Search Engine: A Fast Quantum Algorithm for Multiple Matches

Ahmed Younes, Jon Rowe, Julian Francis Miller

Published Nov 25, 2003• 7 citations
arXivHTMLPDF

Abstract

In this paper we will present a quantum algorithm which works very efficiently in case of multiple matches within the search space and in the case of few matches, the algorithm performs classically. This allows us to propose a hybrid quantum search engine that integrates Grover's algorithm and the proposed algorithm here to have general performance better that any pure classical or quantum search algorithm.

DOI
10.48550/arxiv.quant-ph/0311171

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In this paper we will present a quantum algorithm which works very efficiently in case of multiple matches within the search space and in the case of few matches, the algorithm performs classically. This allows us to propose a hybrid quantum search engine that integrates Grover's algorithm and the proposed algorithm here to have general performance better that any pure classical or quantum search algorithm.
Grover's quantum search algorithm is considered as one of the milestone in the field of quantum computing. The algorithm can search for a single match in a database with NNN records in O(N)O(\sqrt{N})O(N​) assuming that the item must exist in the database with quadratic speedup over the best known classical algorithm. This review paper discusses the performance of Grover's algorithm in case of multiple matches where the problem is expected to be easier. Unfortunately, we will find that the algorithm will fail for M>3N/4M>3N/4M>3N/4, where MMM is the number of matches in the list.
The research community has been actively working on the realization of quantum computer. But the large scale commercial quantum computers are not a reality yet quantum computing field has become richer by day with the advent of algorithms and the avenue of its application in multiple domains. Availability of efficient quantum simulators will enable the researchers to quickly verify their results and concepts in order to establish a working proof of correctness. One important algorithm that has become one of the basic ingredients to build other algorithms and models is the Grover's search Algorithm which is known to be the most compute intensive. Our approach highlights the design principles for the fast simulation of Grover's search which can be implemented on a general purpose personal computer. The performance obtained are encouraging when compared to the existing simulators.
Search is one of the most commonly used primitives in quantum algorithm design. It is known that quadratic speedups provided by Grover’s algorithm are optimal, and no faster quantum algorithms for Search exist. While it is known that at least some quantum computation is required to achieve these speedups, the existing bounds do not rule out the possibility of an equally fast hybrid quantum-classical algorithm where most of the computation is classical. In this work, we study such hybrid algorithms, and we show that classical computation, unless it by itself can solve the Search problem, cannot assist quantum computation. In addition, we generalize this result to algorithms with subconstant success probabilities.
Grover's algorithm, orginally conceived as a means of searching an unordered database, can also be used to extract solutions from the result sets generated by quantum computations. The Grover algorithm exploits the concept of an oracle function, which abstracts the process of matching a search item (returning 1 for a match and 0 otherwise), where searching for 1 target item in a search space of size NNN scales as O(N)\mathcal{O}(\sqrt{N})O(N​) oracle queries. In this article, we explore the idea of associating a separate oracle with each bit of the matching condition, obtaining multiple partial oracle functions which can be tested independently. Exploring this idea leads to a multi-stage hybrid search algorithm, whose performance can fall within a wide range, anywhere between O(N)\mathcal{O}(\sqrt{N})O(N​) (same as Grover) or O(log⁡(N))\mathcal{O}(\log(N))O(log(N)). The algorithm is validated against the simplest kind of search scenario, where the incoming index bits are scrambled using a permutation operation.
Abstract In this paper, we consider the problem of searching for an element in a dictionary. Various approaches to solving this problem have been proposed in recent decades: classical and quantum algorithms. We present two algorithms: a hybrid classical-quantum algorithm [1], that implements Grover’s search, and a “pure” quantum algorithm based on the quantum fingerprinting technique. Both algorithms work (a) with a high probability of obtaining the correct result and (b) with a quadratic query acceleration compared to the classical one. Our algorithms are much more memory efficient in terms of the number of qubits used compared to previously known quantum algorithms.