Quantum Computing [Paperback]

Though probably best used by those with a solid background in mathematics and quantum physics, this book can be useful to the technologically curious due to the fact that the author successfully distills less-than-obvious proofs into meaningful basic concepts. Warning: some of the introductory 'basics' are not. This, however, does not diminish the usefulness of this book.

There is, by now, some variety of textbooks to choose from, covering quantum computing and quantum information;-- the output of research papers has been explosive since Peter Shor discovered his algorithm. From the start, one book stood out as being especially ready for use in the class room, the one by Nielsen-Chuang, but by now there are others.

The present one covers more ground in physics (theory), but it has fewer exercises;-- other books (for example Hirvensalo) stress more the math and the CS side of the subject;-- the other books also have more worked examples, and are perhaps more immediately readily for the classroom. This book should still go over well with well motivated students in both math and in CS.

The level is even, and a beginning student can progress in steps, following the text.

Background: On the classical side, the subject started with Alan Turing and John von Neumann: Classical computation, as is well known, follows the model of A. Turing,-- strings of bits, i.e., 0s and 1s; a mathematical model, now called the Turing mashine. Why not two-level quantum systems? The thought was long in coming. It finally arrived, and with vengeance. An analogues model for computation based on two-level quantum

systems was suggested in the 1980ties by R.P. Feynman and D. Deutsch. But it wasn't until Peter Shor's qubit-factoring algorithm in the mid 1990ties that the subject really took off, and really caught the attention of the math community. The 'unbreakable' codes might be breakable afterall! That there is a polynomial factoring algorithm, as Shor showed, shook up the encryption community as well, for obvious reasons. New elements of thinking in the quantum realm, and not part

of the classical frame of mind, include superposition of (quantum) states, the EPR paradox, and (quantum) coherence. Although these concepts are at the foundation of quantum theory, they make a drastic change in the whole theoretical framework as far as computation is concerned: Now when one passes from the familiar classical notion of bit-registers to that of qubit-registers, the rather non-intuitive laws of quantum mechanics take over. Mathematical physicist and computer scientists 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 computer science changes drastically. The changes introduce new challenges, and new truely exciting opportunities. It is not

easy for authors who break with tradition to make everyone happy;-- this is especially so in a new field,--one which has grabbed headlines, and one which is at the same time interdisiplinary. This is a great book to start with!

Reviewed by Palle Jorgensen, August 2004.

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