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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 learning 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. The goal would be to read/understand research papers in the field and possibly contribute.

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    $\begingroup$ Before this gets closed, I will comment that I know many practitioners who "get by" without having ever studied quantum theory from a rigorous mathematical perspective. Over time you'll find that the more rigorous base will help with a number of nuances, but you can definitely start working on QC with little more than linear algebra $\endgroup$ Commented Dec 14, 2021 at 1:21
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    $\begingroup$ I second @quantummechanic. Also, representation theory is nice but it’s not super critical to quantum computing problems afaik. If you have some knowledge of linear algebra - and probability! and can accept the postulates of quantum mechanics then you’re well on your way to knowing much about quantum computing, and indeed potentially contributing. $\endgroup$ Commented Dec 14, 2021 at 2:11
  • $\begingroup$ @MarkS I don't quite see this as a duplicate of the other question either, but isn't this a sort of "career advise question"? Last time this was discussed, quantumcomputing.meta.stackexchange.com/q/319/55, there seemed to be a consensus towards these being off-topic $\endgroup$
    – glS
    Commented Dec 15, 2021 at 11:09
  • $\begingroup$ Close voters: This is a different question from the duplicate. Also, it's on topic in my opinion. The Meta post glS refers to is from when the site was less than 6 months old. $\endgroup$ Commented Dec 15, 2021 at 19:22
  • $\begingroup$ @user1271772 is there reason to believe consensus changed in the meantime? $\endgroup$
    – glS
    Commented Dec 15, 2021 at 19:35

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This is just my opinion...

There is certainly an advantage in understanding the mathematics used in quantum information and computation from a pure mathematics perspective. I wrote a book on quantum information, and I included only the mathematical background I needed to explain the material on quantum information I wanted to cover, and nothing more. That sort of background material is not intended to give the reader a deep understanding of the subject matter, it's just meant to explain to the reader the tools that are needed for the rest of the book. New discoveries will surely require additional background material, and it can only be an advantage to know more.

However, that does not mean that you should study this material first. If you try to do that, your career might be half over by the time you get to quantum information. My recommendation is to focus your studies on what you find to be interesting, and to think of strengthening your background as a continual ongoing process that will never be finished.

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