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arXiv:quant-ph/0010040

Grover's quantum search algorithm

Samuel J. Lomonaco

Published Oct 10, 2000• 2 citations
arXivHTMLPDF

Abstract

This paper is a written version of a one hour lecture given on Lov Grover's database search algorithm. Table Of Contents 1 ... Problem Definition 2 ... The quantum mechanical perspective 3 ... Properties of the inversion I_|psi> 4 ... The method in Lov's "madness" 5 ... Summary of Grover's algorithm 6 ... An example of Grover's algorithm References

DOI
10.48550/arxiv.quant-ph/0010040

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This paper is a written version of a one hour lecture given on Lov Grover's database search algorithm. Table Of Contents 1 ... Problem Definition 2 ... The quantum mechanical perspective 3 ... Properties of the inversion I_|psi> 4 ... The method in Lov's "madness" 5 ... Summary of Grover's algorithm 6 ... An example of Grover's algorithm References
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The development of programming languages for quantum computing has increased rapidly over the last few years, making it practical for a hands-on approach in teaching quantum computation. In this paper, I introduce the standard textbook example of searching for one item out of four using Grover's search algorithm and extend it by including a quantum database. In addition to explaining how to include a quantum database using a quantum circuit model, I give a complete program implementing the algorithm written in the quantum computing language Qiskit from IBM. If presented in the classroom, this extension of Grover's search algorithm alleviates some unsatisfying aspects of the standard textbook example. If given as an exercise to students, it allows them to extend the standard example and provides experience in developing quantum algorithms. I also outline searching for one (or more) items out of eight with a quantum database, which could be used for student projects.
Abstract Quantum superposition is a powerful computational tool to have at one’s disposal – in fact, a phrase along the lines quantum computers evaluate a function for every possible input in superposition and hence achieve a massive speed-up appears in virtually every popular and media article on the subject. The reality is, however, a little more complicated. In this chapter, we look at what is probably the closest quantum algorithm to the naive idea of ‘evaluating for every possibility at once’, namely Lov Grover’s quantum search algorithm. Grover’s algorithm is one of the oldest and most important quantum algorithms and offers a quadratic advantage over the best possible classical algorithm for the problem of searching an unstructured database. Notably, a quadratic quantum advantage is the best one can hope for in certain problems that exhibit a lack of structure, which is proven by considering the performance of the best possible quantum algorithm tackling the OR problem.