Classical and Quantum Computation (Graduate Studies in Mathematics)

Classical and Quantum Computation (Graduate Studies in Mathematics)

A. Yu. Kitaev

This e-book is an advent to a brand new swiftly constructing thought of quantum computing. It starts with the fundamentals of classical concept 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 publication presents an exposition of quantum computation conception. It begins with the advent of basic quantum formalism (pure states, density matrices, and superoperators), common gate units and approximation theorems. Then the authors research quite a few quantum computation algorithms: Grover's set of rules, Shor's factoring set of rules, and the Abelian hidden subgroup challenge. In concluding sections, numerous similar issues are mentioned (parallel quantum computation, a quantum analog of NP-completeness, and quantum error-correcting codes).

Rapid improvement of quantum computing all started in 1994 with a beautiful advice by way of Peter Shor to take advantage of quantum computation for factoring huge numbers--an tremendous tricky and time-consuming challenge while utilizing a standard computing device. Shor's outcome spawned a burst of task in designing new algorithms and in trying to really construct quantum desktops. at present, the growth is far extra major within the former: a valid theoretical foundation of quantum computing is below improvement and lots of algorithms were steered.

In this concise textual content, the authors offer reliable foundations to the theory--in specific, a cautious research of the quantum circuit model--and disguise chosen subject matters extensive. incorporated are a whole facts of the Solovay-Kitaev theorem with exact set of rules complexity bounds, approximation of unitary operators by way of circuits of doubly logarithmic intensity. between different attention-grabbing themes are toric codes and their relation to the anyon method of quantum computing.

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