While traveling to and fro (2000 road miles) and at the amateur chamber music festival I got through 75 of the 328 pages of “Quantum Computing a Gentle Introduction” by Rieffel and Polak. I think it’s worth a shot for the readership. It is the real stuff and not a popularization.
10 years ago I tried getting through “Quantum Computation and Quantum Information” by Nielsen and Chuang (607 pages), ignoring the warning in the preface saying that it was at a level “comprehensible to readers with a background at least the equal of a beginning graduate student in” computer sciences, mathematics and physics. I had none of these back then, although my math background probably fits now.
The background needed for Rieffel still falls in the three fields but is much less.
l. Physics: quantum mechanics is approached from an axiomatic point of view. No differential equations or their series solutions of the Schrodinger equation appears. The physics used is quite simple when viewed as postulates (but Feynman warns us not to think — how can it be like that).
2. Mathematics:
a. You need to know tensors (or learn them from the book), but not the indexladen horrors that appear when you try to change the basis. They are crucial to understanding entanglement which is crucial for quantum computation. I think I did a better job of explaining them than Reiffel — https://luysii.wordpress.com/2014/12/28/how-formal-tensor-mathematics-and-the-postulates-of-quantum-mechanics-give-rise-to-entanglement/
b. You need to know enough linear algebra to understand vectors and matrices. Not to worry. I took QM twice once in the spring of 1961 as a Chemistry grad student and 50 years later auditing a course at Smith. In 1961 we ground through the Schrodinger equation solving the hydrogen atom completely showing how the quantum numbers and atomic orbitals arose from the recursion relations of the infinite series solving the equation. It was like seeing the face of God — https://luysii.wordpress.com/2009/10/15/recursion-relations/https://luysii.wordpress.com/2009/10/15/recursion-relations/. The second time around Mathematica had changed everything and Iye https://luysii.wordpress.com/2009/09/22/what-hath-mathematica-wrought/
I was amazed at how the Smith course ignored the linear algebra underlying QM so I wrote series of 9 posts on the subject
It should be all you need, explaining things such as Hermitian operators, and just why matrix multiplication is the way it is.
c. Complex numbers. You just need to understand how a unit complex number lies on the circle with radius 1, and how multiplication by them moves them around on the circle. No differentiation. No Cauchy Reimann equations etc. etc. The wikipedia page should tell you more than you need to know — https://en.wikipedia.org/wiki/Complex_plane
3. Computer science. I’ve never officially studied it but picked up programming when the apple Lisa came out 40 years ago. I think most readers know what a register is and how to program.
So give it a shot. Two caveats and a shoutout
First: The ‘introduction’ is not gentle. In the preface to Reiffel’s book the following appears. She presented the initial work to two groups in Palo Alto (FX Palo Alto Laboratory and Palo Alto Research Center) and describes their ‘struggles’ learning the material. I doubt that any of them were dumb.
Second: It is not a math book where important concepts are initially fully defined. Example: the crucial definition of qubit
On p. 3 we are told that a qubit can take on a continuum of values
On p. 13 we are told that a qubit is also called a quantum bit
We are also told on that page that for a two dimensional complex vector space to be viewed as a qubit two linearly independent states called |0 > and | 1 > must be distinguished
On p. 14 we are told that qubits can take on not only the values of |0 > and | 1 > but also any superposition of these values (a |0 > + b | 1 >) where a and b are complex numbers and |a|^2 + |b|^2 = 1
Shoutout: Her writing is quite clear and unambiguous.
I may post my notes on the book as I take them if people think the first dose is helpful.
