I read "Minds, Machines, and the Multiverse" (reprinted in paperback as "The Quest for the Quantum Computer") alongside David Deutsch's "The Fabric of Reality," thinking that Julian Brown's journalism would help elucidate Deutsch's text, which I assumed would be more difficult. Ironically, not only did I find "The Fabric of Reality" far more exciting and readable, but, even on its own terms, Brown's book was often monotonous and unimaginative.
While the first and last chapters are quite fascinating, the meat of the book reads like an endless serious of abstracts of articles excerpted from mathematical, physics, and computing journals, separated by droll subheads ("Beam Me Up, Atom by Atom"). The major problem is that Brown doesn't seem to have any particular audience in mind. On the one hand, it's hard to imagine most lay readers sitting through his detailed expositions on various mathematics and physics concepts; on the other, math-savvy readers don't need to be told (to cite just one example) what ASCII is.
It's not just that Brown's book is knee-deep in mathematics, however. In fact, the math presented is really not that difficult--it's just boringly presented. The endless series of Alice, Bob, Carol, and Eve stories has all the verve of the litany of questions on the SAT. (Several times I found myself asking, "Which Bob is this?"). Likewise, the descriptions of logic gates are about as exciting as my college textbooks on linear algebra and number theory. Brown's presentation is hampered further by the lack of a glossary; he repeatedly expects the reader to remember terms he discussed over 100 pages earlier.
In sum, computer programmers and armchair mathematicians looking for a primer on the theoretical underpinnings of quantum computation might find this book a helpful introduction. The general reader, however, will have to wait for a well-written overview of the subject. In the meantime, I recommend "The Fabric of Reality" as a starting point.