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CRC Press eBooks

Simple Quantum Algorithms

Mikio Nakahara

Published Mar 11, 2008• 0 citations
Publisher

Abstract

Before we start presenting “useful” but rather complicated quantum algorithms, we introduce a few simple quantum algorithms which will be of help for readers to understand how quantum algorithms are different from and superior to classical algorithms. We follow closely Meglicki [1].
DOI
10.1201/9781420012293-11

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CRC Press eBooks•Mar 11, 2008•0 citations
This authoritative, advanced introduction provides a complete, modern perspective on quantum mechanics. It clarifies many common misconceptions regarding wave/particle duality and the correct interpretation of measurements. The author develops the text from the ground up, starting from the fundamentals and presenting information at an elementary level, avoiding unnecessarily detailed and complex derivations in favor of simple, clear explanations. He begins in the simplest context of a two-state system and shows why quantum mechanics is inevitable, and what its relationship is to classical mechanics. He also outlines the decoherence approach to interpreting quantum mechanics. Distinguishing features: Provides a thorough grounding in the principles and practice of quantum mechanics, including a core understanding of the behavior of atoms, molecules, solids, and light. Utilizes easy-to-follow examples and analogies to illustrate important concepts. Helps develop an intuitive sense for the field, by guiding the reader to understand how the correct formulas reduce to the non-relativistic ones. Includes numerous worked examples and problems for each chapter.
We demonstrated in the previous chapter that there are some quantum algorithms superior to their classical counterparts. It is, however, rather difficult to find any practical use of these algorithms. There are two quantum algorithms, known to date, which are potentially useful: Grover’s search algorithm and Shor’s prime number factorization algorithm. Both of them depend on quantum integral transforms, which will be introduced in the present chapter. We mainly follow [1] in our presentation.