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Presentation: I love that each chapter concludes with a section on terminology and a summary.
As a subject theoretical computer science started with Alan Turing and John von Neumann in the 1940ties: Classical computation follows the model of Turing,-- strings of bits, i.e., 0s and 1s; and a mathematical model which is now called the Turing machine.
Instead of bits, why not two-level quantum systems, e.g., models built from electrons or photons? Such an analogues model for computation based on two-level quantum systems, and a quantum version of Turing's machine was suggested in the 1980ties by R.P. Feynman. The form it now has owes much to the author himself, David Deutsch. But it wasn't until Peter Shor's qubit-factoring algorithm in the late 1990ties (not covered in the book) that the subject really took off, and really caught the attention of the mainstream science community, and of the general public: The 'unbreakable' codes might be breakable after all !
That there is a polynomial factoring algorithm, as Shor showed, shook up the encryption community, for obvious reasons, and created headlines in the news. Ideas in the quantum realm, and not part of classical thinking, include superposition of (quantum) states, the EPR paradox (1935), and (quantum) coherence. Although these concepts are at the foundation of quantum theory, they make a drastic change in our whole theoretical framework of computation: Now one passes from the familiar classical notion of bit-registers to that of qubit-registers, and the laws of quantum mechanics take over. Mathematical physicists and computer scientists must revisit the old masters: Bohr, Einstein, Heisenberg, Pauli, and Dirac. In passing from logic gates to quantum gates (unitary matrices), the concept of switching-networks from traditional computer science now changes drastically. The changes introduce brand new scientific challenges, and new truly exciting opportunities. I believe that this book does justice to this, and that it is still a fascinating and thought provoking invitation to some of the most intriguing trends in modern physics.
Review by Palle Jorgensen, July 2005.
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