Should one learn the math of quantum computing from a "pure" perspective, or is quantum computing texts "good enough"? [closed]

Question

Math for quantum computing includes advanced linear algebra, functional analysis, group and representation theory, probability theory, and more.

There are plenty of pure math books out there for those, but there are also quantum computing/information theory books that contain only the parts relevant for QC.

Is there any advantage to learning the math from a pure math perspective first, then QC, or learning the math directly from quantum computing textbooks? I guess before I crack open Dummit and Foote, I want to make sure I'm not doing overkill.

I ask as someone who is slightly more interested in the math/computer science side of QC, and probably less of the physical implementation.

Answer 1

You should start with a mathematics for quantum computing text which covers at least some of the mathematical background that you need (I like Wolfgang Scherer's Mathematics of Quantum Computing - An Introduction). If you find you need (or just want to develop) a more general mathematical background in certain areas then you can go to mathematics texts for those specific topics.

The problem with approaching from the other direction is that you could spend years doing background reading on all of the mathematical topics that you list before you even get into quantum computing, which is the application that has motivated your interest in the first place.

For example, Scherer covers the all the abstract algebra that you will need in a 60 page appendix on group theory, which is very much focussed on applications of group theory that are relevant to QC rather than purely theoretical results. The 900-odd pages of Dummit and Foote is "overkill" unless you decide you really want to know abstract algebra inside out.