Quantum Computing and Math prequisities

[Stealth95]

Hello,
I am a Physics undergraduate, currently beginning my third (out of four) year of studies. I have already taken courses about Real and Complex Analysis, Linear Algebra, ODEs and PDEs (for Maths), Classical Mechanics (Lagrangian and Hamiltonian formalism), Electromagnetism, Special Relativity and some other that I think that are irrelevant for my question. I'm having QM courses in the current and the next semester.

I open the thread, because I managed to finish one of the courses I normally have in this semester from a previous one, so I have time to study something else instead of that one. Currently, I am thinking the Quantum Computing field about the future. Although, I already know some concepts in QM and Dirac's notation (I can solve excercises), I prefer to finish the QM courses before I deal with quantum comptutation. However, I would like to ask if there is any Mathematics subjects I can study, which would be useful for quantum computing.

I also mention that I planned to take a group theory course from the next year, but I cannot do this because it doesn't fit my program, so I have to wait till next year. The only extra course I can now take in my university is Differential Geometry, but from what I read it is not so useful for QC and I do not plan to study General Relativity, at least for now. Another option is to self-study topology, which seems more useful (however self-studying is much harder than taking the course...).

Finally, I would appreciate it if the subject was also useful for other other parts of Physics (like QFT), since I am not 100% that I will work on QC (when I enrolled at Physics Dept. I planned to work on Theoretical Physics, since I am far better on this, but now I'd like it more if I worked on something more applied - that's how I thought of QC).

 

[MisterX]

I came up with a few suggestions.

• functional analysis
• information theory

• advanced statistics
• Numerical calculation course (under "computational science" /engineering/applied math -- if there is one in the physics dept it might assume QM so wait for that one)
• Any computer science course dealing with the kind of advanced algorithms (to understand the classical algorithms that QC is trying to compete with) i.e. don't take the course that teaches about bubble sort, but rather traveling salesman type problems, factoring, etc.

 

[ForensicPhysic]

Linear Algebra, if you are not familiar with it, then don't touch it until you dabble into topics of Functional analysis and information theory (in which LA is a major backbone of such projects.