!Long Rant!!
Got inspired by Ewin Tang's paper on figuring out a classical computer algorithm for recommendation systems inspired by quantum computers and started to write up an email to a professor in some Quantum research I'm interested in doing. As a high school student, it's VERY daunting to start. Been researching the prof and I'm super excited but it's nerve racking! Like what if she doesn't even open her research projects to high school students and I'm wasting my time? In case, I am planning on asking if there is anyone else I should contact. I'm focused on doing this research with McMaster since it's nearby but I'm really doubting myself. People my age who do this stuff are phenomenal and I feel like I wouldn't live up to that. You guys are probably a lot more experienced in this so if you've got any advice or tips, let me know.
>.<

Well I don't know about asking profs, and I don't know how much you know and all but here's what you need to start on quantum stuff:

Nielsen and Chuang's book is the Bible for quantum computation. It's pretty well written too. But that book is fairly advanced, especially for high school (I tried to tackle it in high school, failed miserably).

To understand the book, you need these as prerequisites:

Hardcore maths. Especially linear algebra (Strang), advanced calculus(Thomas and Finney), Fourier transforms, probability and statistics (Sheldon Ross).

Knowledge of basic quantum theory. Brian Greene's Fabric of the Cosmos is great for intuition, and David Griffiths' book for the actual quantum physics.

Information theory, at least the basics, since a lot of quantum computation is about managing quantum information (plus cool stuff like quantum cryptography and coding). Can't point to a resource, sorry, I basically just Googled till I understood what I needed.

I'm assuming you already have a fairly okay grounding in classical physics - your studies of calculus and linear algebra should provide some very powerful tools for physics (Lagrangian mechanics, Noether's theorem, tensors, etc.). I would recommend studying at least a bit of Lagrangian/Hamiltonian mechanics - it's kinda hard to see the point of using Hamiltonians in Schrödinger's equation without that.

And finally you'll need some "classical" computer science. Fundamental algorithms (searching, sorting, etc.), complexity theory, formal systems (automata and the oft-misunderstood Turing machine), grammars, compression and coding theory, etc.

Sources for these are all over the web, just Google it up.

This is where I am right now, so I can't advise you on what you'll need after this. If it looks very intimidating, it really isn't. Just a lot of data. And you'll have a lot of fun studying this stuff. Just keep at it.

If you already know this stuff, or if this wasn't what you were asking for, then, well, crap. I hope this helps somebody else. I may also have missed some stuff, really sleepy right now.

Another thing. Quantum stuff is usually extremely weird and non intuitive. When you're starting out, even the very basic algorithms like Deutsch-Jozsa, Grover's algorithm, or quantum teleportation look like black magic or mathematical trickery. It's important that you think about what's really going on and not get too lost in abstract mathematical details, though it's extremely confusing at first because it doesn't confom to our intuitions about reality.

Only on Twatter this would be a long post 😅 but I'll take the ! before Long as a NOT operator 😛

I don't have any experience with quantum computers other than that IBM (iirc) provides a 5 qubit quantum computer that you can play with online through their web app.

Regarding the professor, University professors might take a look but I wouldn't bet on the chance that she'll respond. If I look at myself, I often have people contacting me on Facebook with questions and I don't always respond there either. Reason being that many people only say "hi" "I have question" "please help" without mentioning what exactly it is that they need help with, or what their experience is.

Many people that I do end up accepting the message requests of to see what they're worth end up knowing jack shit and only want me to be their personal search engine.

Properly formulating what exactly you'd like to know more or even just talk about, and mentioning or showing in the formulation of the question what you already know about the topic on the other hand goes a long way.

For example, if you'd like to talk about the security of a web server, mentioning things like the particular server package and OS you're running, as well as the general configuration so far (firewall, IDS, running it as user "nobody" and whatnot) are all positive triggers in this case. Similarly, you'll want to be elaborate about your experience in the quantum research field and your questions/remarks as well.

Good luck!

@Condor a five qubit computer becomes useless pretty fast, and you can very easily simulate it because you need just 2^5 = 32 doubles of data to store the system state with reasonable accuracy (for a n-qubit system you have 2^n state-combinations).

Because of the exponential growth it gets out of hand pretty fast though (in fact, simulation of quantum systems is one thing quantum computers are way better at than classical systems). Largest simulation I've done was running Shor's factorization algorithm using 31 qubits, that's 2^31 doubles, things got pretty hairy, I can tell you! (Ran into numerical accuracy problems too)

@RememberMe Great point. I've never done any research into quantum systems myself so I don't know about the accuracy of simulations or how feasible they are (i.e. I just didn't do the math 😛) but yeah that's a very valid argument against the use of that online playground.

@RememberMe It was JUST what I needed. The power of Devrant! You practically just coached me to it and I appreciate the time it must of took you to write this up. I'll definitely go through all this for the rest of summer and over into school when needed (highschool is LITE so I'll be fine) Again, you're friggin amazing thank you!!!

@Condor that sounds like great help! I'm mostly emailing her to figure out whether or not I can take part in one of her researches that I am very intrested in rather than milking questions out of her, for that, @RememberMe gave great resources.

PS. no, it was not an operator. If i ever right something like that, someone better delete my account