It's just an exponential overhead. The state of a quantum computer is a superposition over all bitstrings, i.e. a vector of size 2^n for n qubits, and you have to implement quantum operators by multiplying with 2^n x 2^n unitary matrices (you better do that implicitly whenever possible or it will be very slow).

After taking a lecture on quantum computing, it was actually a weekend project to implement a basic quantum simulator myself, very useful to confirm that I actually understood the model as well as I thought.