So quick question, it's probably been asked before. But

>>9034120
No idea, but I'm guessing that you are going to need a major on it unless you already have a degree on some of those fields. If that's the case, ask some professor in your university or something.

Or even if not, go to your nearest university, they'll guide you better.

>>9034120
for quantum, in addition to knowing vector calculus and differential equations, you will also need to know partial differential equations. The best way to learn PDEs, though, is by learning something like quantum right along with it.

While probability used in quantum mechanics is the same probability used by statisticians in a sense, they focus on different things and seem to speak different languages. All the stats you will need to get started can be learned while learning intro quantum. Really, it's mostly how to compute things like expectation values given a continuous probability distribution and some measurable quantity (hint: multiply and integrate), or finding the variance of the same thing.

Group theory you won't need until you already have your feet wet with basic quantum, like Schroedinger equation without spin. Once you get to spin, you can go a few ways because the topic is notoriously tricky. The correct way is to learn about continuous group theory (lie groups) and understand spin from that perspective. Alternatively, you can get handwavey and gloss over the details, but you'll miss out on a fascinating and brain-twisting subject and won't understand really what's going on.

Until you get really comfortable with decomposing quantum systems into modes, computing is a ways away.

By all means though, you sound like you are at the level needed to start learning about quantum (linear algebra, calculus, diff eq.)

>>9034120
>Learn Proofs
A Transition to Advanced Mathematics by Smith, Eggen, and St. Andre
>Learn Probability
Introduction to Probability by Bertsekas and Tsitsiklis
Introduction to Probability by Blitzstein and Hwang
>Learn Group Theory
Visual Group Theory by Carter
>Learn Linear Algebra mk.II
Linear Algebra by Shilov

>>9034120
>my book has the pre requisites of group theory, linear algebra, and abstract algebra
>I already have linear algebra under my belt up to calculus III and DFQ.
If those subjects appear together in the same sentence like that, you can be pretty certain it doesn't mean cookbook linear algebra, but rather a course heavily laden in rigorous proof writing, based on a book like Shilov's.
>when researching group theory, it seems like I need to know set theory, probability, and discrete
I mean, not really. Books on basic group theory, analysis, topology, etc at the "advanced undergraduate" level most often have no real prerequisites, but assume a certain amount of "mathematical maturity" - being comfortable with abstraction and proof reading/writing. Many strive to be "self-contained" and build up set-theoretic preliminaries in an introductory chapter - see the introductions to Munkres' topology or Rosenlicht's analysis, or Smith's Introductory Mathematics: Algebra and Analysis for a more thorough, in-depth treatment of foundational material. Far as group theory/algebra in general goes, Artin is quite readable and friendly for newcomers. But read your book's preface closely to see precisely what prereqs/background it assumes of you

>>9034120
You don't need any probability for abstract algebra. I'm really not sure how that got listed. And all the rest is just basic math competency anyways, so you probably be fine just going in on your own without any real preparation. Besides, most algebra textbooks are made for undergrads anyways, so you'll get a good overview of those "required" topic from the text babying you.

Aside from all that, you really don't need much abstract algebra for quantum computing in my experience. Just be good a linear algebra and matrix shit.

>>9034120
if you're a physics student just read the book straight away, if you know qm the formalism shouldn't be a huge stretch. If you're in cs or math the most efficient way imo is to learn QM, it will touch on the math topics needed. If you start reading the math literature it will take you months because of the autism of math books

>>9034488
mathfags are really autistic, do you think you need to read 4 books to read before quantum computing? Even cs majors learn it, it can't be too hard

>>9035439
>do you think you need to read 4 books to read before quantum computing?
>to read 4 books to read
lel
What you need to know of course depends on what level of "quantum computing" you're doing. If OP's book says it has mathematical prereqs, it probably does.
That's not to say you can't learn anything about the subject at a lower level of sophistication

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>>9034120
I cannot stress the importance of graph theory enough.

Just for the record IBM gives you access to a computer to run experiments. You design an experiment, they run it on their quantum computer and you get the results back. They also have some material and resources to get you started. With all you already know they'll give you an account for sure. In case it's not clear it's a physical quantum computer and not a half assed one like D Wave. Of course you can run a limited number of experiments but it's pretty cool. There's also a software processor that simulates the results and doesn't spend any credits.