Stephen Parrott of Quantum Computation and Quantum Information

My first acquaintance with this book came from a copy which I ordered through interlibrary loan after seeing favorable comments on the internet. The loan period was only two weeks, so I wasn’t able to study this 600-page book in detail. But I learned quite a bit just by skimming it. After I saw that it was a book that would repay study, I purchased it. The first chapter of 58 pages nicely introduces many of the important ideas, leaving the more difficult details to later chapters. For example, I learned about quantum teleportation, which I had never understood from popular accounts. I read it from cover to cover and was able to follow almost all of it in detail. Since I read it as someone learning this material for the first time, I’ll review it from a student’s perspective. Chapter 2 gives a nice (with one possible exception ) summary of basic quantum mechanics. It includes an introduction to necessary concepts from abstract linear algebra, including important specific applications (e.g., the Schmidt decomposition) which are not likely to be covered even in advanced linear algebra courses. The authors wisely limit the treatment to finite-dimensional Hilbert spaces. This is adequate for nearly all the book’s applications, and it vastly simplifies the mathematics. The treatment is mathematically accurate and more rigorous than most physics texts, but is generally too coordinate-dependent to full exploit the conceptual simplifications of abstract linear algebra. For example, I never got used to the authors’ notation for the (orthogonal) projector from a Hilbert space H to a subspace E with orthonormal basis {ei}i=1. Most mathematicians would use some notation like PE , but most physics texts (including this one) use the more cumbersome (expressed in the Dirac “ket” notation which is used throughout the book):