The following are recommended sources for an introduction to quantum computing.
This is an article by Barenco, Ekert, Sanpera and Machiavello, and is most suitable for the general scientific reader. It forms part of the Centre for Quantum Computation site, which contains useful information and links elsewhere.
For a more complete and technical discussion, at a level suitable for a graduate physicist, we can warmly recommend a review written by Andrew Steane for Reports on Progress in Physics:
Andrew Steane,
Quantum Computing
Reports on Progress in Physics vol 61, pp 117-173 (1998).
Preprint: quant-ph/9708022
The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarise not just quantum computing, but the whole subject of quantum information theory. It turns out that information theory and quantum mechanics fit together very well. In order to explain their relationship, the review begins with an introduction to classical information theory and computer science, including Shannon's theorem, error correcting codes, Turing machines and computational complexity. The principles of quantum mechanics are then outlined, and the EPR experiment described. The EPR-Bell correlations, and quantum entanglement in general, form the essential new ingredient which distinguishes quantum from classical information theory, and, arguably, quantum from classical physics. Basic quantum information ideas are described, including key distribution, teleportation, data compression, quantum error correction, the universal quantum computer and quantum algorithms. The common theme of all these ideas is the use of quantum entanglement as a computational resource. Experimental methods for small quantum processors are briefly sketched, concentrating on ion traps, high Q cavities, and NMR. The review concludes with an outline of the main features of quantum information physics, and avenues for future research.Introduction