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Reviewer: Alessandro Berni

Computing, generally speaking, relies on physical processes executed by machines that are, in turn, bound by certain physical laws. In a more specific sense, the underlying principles of the classic theory of computation, shaped by the work of pioneers such as Turing and von Neumann, are based on the concept of the Turing machine, which idealizes a mechanical device subject to the laws of classical physics. Instead, quantum computing is based on an alternative paradigm in which quantum mechanical phenomena such as superposition and entanglement are used to represent data (in qubits) and perform data operations. Although this discipline is still in its infancy (Nobel laureate Richard Feynman published his seminal paper on quantum computing in 1982 [1]), a great deal of theoretical and experimental research is being conducted to address important problems in domains such as signal processing, artificial intelligence, and cryptoanalysis. This review presents the tenth anniversary edition of this classic textbook, commonly referred to as "Mike and Ike," which remains an authoritative reference for those interested in this promising and fascinating field of research. The contents are organized in three parts. The first one provides a general introduction, showing how quantum computers may solve some computational problems much more efficiently than classical computers (the quantum version of the Fourier transform, quantum search, and quantum simulation, in which a quantum computer is used to simulate a quantum system). The second part details the aspects related to quantum computation, including quantum circuits, applications of the quantum Fourier transform, and approaches toward the physical realization of quantum computers (harmonic oscillator, optical photon quantum computer, ion traps, and nuclear magnetic resonance). The third part covers quantum information. Starting from the effect of quantum noise, the authors present quantum operations and error-correction methods aimed at achieving fault-tolerant quantum computation. Beyond that, after a refresher on the concept of entropy, they deliver a distilled high-level discussion on quantum information theory, touching on topics such as data compression and cryptography. As one would expect, this is not an easy book, given the mathematics and physics topics it includes. In any case, the authors have composed an excellent work, delivering a convincing and comprehensive treatment of quantum computation and quantum information-a work characterized by both breadth and depth that still stands the test of time very well. This tenth anniversary edition contains a new introduction and afterword, and incorporates up-to-date coverage of topics such as entanglement measures, which are key to effects such as quantum teleportation and error correction, distributed quantum computation, and the experimental implementation of actual quantum computers. The self-contained and modular structure of the book makes it usable by independent readers as a reference text; the book can also be used as a textbook in support of graduate studies. Each chapter comes with a large number of exercises and problems, although the worked solutions are not always provided. It would probably be useful to couple this excellent reference text with an exercise book containing worked examples and problems. The "History and Further Reading" sections provided at the end of each chapter give useful input toward the definition of a proper context for the concepts exposed and suggest useful references for in-depth analysis. In conclusion, "Mike and Ike" is still the authoritative reference point for anybody studying or researching in the field of quantum computing. Online Computing Reviews Service