That depends on the number of qbits you want to simulate. Doing the calculations on classical computers has an exponential slowdown as you need 2^n classical bits to store n qbits. It's pretty unlikely that you will ever be able to simulate a quantum computer with more than a few dozen qbits.
Indeed. I'd expect this to top of at about 64 qbits with smart maths. (Mostly due to pointer limitations.) You could try to extend addressing but it'll be even slower...
Just as a data point: Current state-of-the-art methods for Lanczos-type methods on state vectors are around 40 spins/qubits incorporating many symmetries and additional shortcuts one does not have in a generic "quantum computer simulator". Without those symmetries/shortcuts, the limit is likely closer to 30 qubits (i.e. approx. 16-64 GB per state vector), as it’s not only necessary to store these beasts but also do operations on them.
If you don’t insist on a single dense state vector but a sparser tensor network-based formulation, you can go to much larger systems (hundreds or thousands of spins) but will be limited by the amount of entanglement you can represent in your system.
