Quantum Algorithms via Linear Algebra: A Primer (Hardcover)

Richard J. Lipton, Kenneth W. Regan

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商品描述

This introduction to quantum algorithms is concise but comprehensive, covering many key algorithms. It is mathematically rigorous but requires minimal background and assumes no knowledge of quantum theory or quantum mechanics. The book explains quantum computation in terms of elementary linear algebra; it assumes the reader will have some familiarity with vectors, matrices, and their basic properties, but offers a review of all the relevant material from linear algebra. By emphasizing computation and algorithms rather than physics, this primer makes quantum algorithms accessible to students and researchers in computer science without the complications of quantum mechanical notation, physical concepts, and philosophical issues.

After explaining the development of quantum operations and computations based on linear algebra, the book presents the major quantum algorithms, from seminal algorithms by Deutsch, Jozsa, and Simon through Shor's and Grover's algorithms to recent quantum walks. It covers quantum gates, computational complexity, and some graph theory. Mathematical proofs are generally short and straightforward; quantum circuits and gates are used to illuminate linear algebra; and the discussion of complexity is anchored in computational problems rather than machine models.

Quantum Algorithms via Linear Algebra is suitable for classroom use or as a reference for computer scientists and mathematicians.

商品描述(中文翻譯)

這本介紹量子算法的書籍既簡潔又全面,涵蓋了許多重要的算法。它在數學上嚴謹,但對量子理論或量子力學的背景要求很低,不需要任何相關知識。該書以基本的線性代數來解釋量子計算;它假設讀者對向量、矩陣及其基本性質有一定的熟悉,但提供了線性代數相關材料的回顧。通過強調計算和算法而不是物理學,這本入門書使得計算機科學領域的學生和研究人員能夠理解量子算法,而不需要處理量子力學符號、物理概念和哲學問題的複雜性。

在解釋基於線性代數的量子操作和計算的發展之後,該書介紹了主要的量子算法,從Deutsch、Jozsa和Simon的開創性算法,到Shor和Grover的算法,再到最近的量子行走算法。它涵蓋了量子門、計算複雜性和一些圖論。數學證明通常簡短明了;量子電路和門用於闡明線性代數;而對於複雜性的討論則以計算問題為基礎,而不是機器模型。

《量子算法與線性代數》適合作為課堂教材或計算機科學家和數學家的參考書。