Can we build a working quantum computer big enough to do things ordinary computers can easily do?
This question is to some extent impacted by the previous one, but it also has a strong engineering aspect to it. Some physicists think quantum computers are impossible in principle; more think they are possible in principle, but are still unsure if they will ever be practical. Here are some ways to learn more about quantum computation: • Centre for Quantum Computation home page. • John Preskill, course notes on quantum computation. • Michael A. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information, Cambridge U. Press, Cambridge, 2000. Errata, table of contents and Chapter 1 available here.