By A. Yu. Kitaev, A. H. Shen, M. N. Vyalyi

This ebook is an advent to a brand new and quickly constructing subject: the speculation of quantum computing. It starts with the fundamentals of classical conception of computation: Turing machines, Boolean circuits, parallel algorithms, probabilistic computation, NP-complete difficulties, and the belief of complexity of an set of rules. the second one a part of the ebook offers an exposition of quantum computation idea. It starts off with the creation of basic quantum formalism (pure states, density matrices, and superoperators), common gate units and approximation theorems. Then the authors learn a number of quantum computation algorithms: Grover's set of rules, Shor's factoring set of rules, and the Abelian hidden subgroup challenge. In concluding sections, a number of comparable subject matters are mentioned (parallel quantum computation, a quantum analog of NP-completeness, and quantum error-correcting codes).

Rapid improvement of quantum computing began in 1994 with a gorgeous advice via Peter Shor to exploit quantum computation for factoring huge numbers--an tremendous tough and time-consuming challenge whilst utilizing a standard laptop. Shor's outcome spawned a burst of job in designing new algorithms and in trying to really construct quantum pcs. presently, the growth is way extra major within the former: a valid theoretical foundation of quantum computing is less than improvement and lots of algorithms were steered.

In this concise textual content, the authors supply reliable foundations to the theory--in specific, a cautious research of the quantum circuit model--and disguise chosen themes intensive. the various effects haven't seemed in other places whereas others increase on latest works. integrated are a whole facts of the Solovay-Kitaev theorem with actual set of rules complexity bounds, approximation of unitary operators via circuits of doubly logarithmic intensity. between different attention-grabbing issues are toric codes and their relation to quantum computing.

Prerequisites are very modest and comprise linear algebra, parts of workforce conception and chance, and the concept of a proper or an intuitive set of rules. this article is appropriate for a path in quantum computation for graduate scholars in arithmetic, physics, or laptop technological know-how. greater than a hundred difficulties (most of them with whole suggestions) and an appendix summarizing the required effects are a truly worthy addition to the e-book.

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### Classical and Quantum Computation (Graduate Studies in Mathematics) by A. Yu. Kitaev, A. H. Shen, M. N. Vyalyi

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