Software simulation of a quantum computer

Question

While we are waiting for our quantum computers, is it possible to write a software simulation of one? I suspect the answer is no, but hope the reasons why not will throw som

Answer 1

Implementing it isn't that hard. The problem is that the computational and memory complexity is exponential in the number of quantum bits you want to simulate.

Basically a quantum computer operates on all possible n-bit states at once. And those grow like 2^n.

The size of an operator grows even faster since it's a matrix. So it grows like (2^n)^2 = 2^(2*n) = 4^n

So I expect a good computer to be able to simulate a quantum computer up to about 20 bits, but it will be rather slow.