This completely depends on what you are up to. Different areas of quantum physics may require anything from Fortran over C++ over Python/Matlab to Mathematica/ML/LISP etc. Your best bet is to become a competent programmer; for that you typically want to start with one or two languages (e.g., C++ and Python or C++ and Mathematica seem like good combinations to me).
Some notes on the languages:
- Fortran: Ugly language, very bad to start with. Used for hardcore number crunching in many areas (e.g., quantum chemistry, solid state physics, and other electronic structure stuff).
- C++: The most complicated language ever invented. Very powerful if used right, able to create horrific abominations if used wrong. Useful for all kinds of high-performance code (if used right), low-level to high-level. Useful for building *large* applications with many million lines of code (most major Programs in Windows, and a great part of Windows itself are written in C++).
- Python/Matlab: Can be used more-or-less interchangably in the numerics department (Python with numpy and scipy). Both are very powerful and very easy to use "glue" languages (languages you mainly use to glue library functions together). Usually the best way to get something to work, fast. Python has the advantage of being somewhat cleaner and freely available and also being useful for many things besides numerics; but in the numerics department it is less powerful than Matlab.
- Mathematica/ML/LISP: Functional languages which are mainly useful for symbolic algebra. (that is, if you have to write your symbolic algebra routines yourself, which, in fact, often happens).