> A n-bit pure quantum state can be fully described using 2^n complex numbers
Why 2^n? Isn't it 2 numbers per state (real and imaginary parts)? So it would be 2+2+2...+2 (n times) = 2n total numbers
Why 2^n? Isn't it 2 numbers per state (real and imaginary parts)? So it would be 2+2+2...+2 (n times) = 2n total numbers
Which one of the basis states we end up measuring depends on the squared of the complex amplitude of that state (Born rule). Therefore, if you were to simulate a quantum computer, in the general case you would need to keep track of these complex amplitudes belonging to the states, every 2^n of them. Because of the real and imaginary parts this amounts to 2*2^n=2^(n+1) numbers.