Quamtum Computing Home : www.sharetechnote.com 
Quamtum Gate  X (PauliX)
Quantom Gate X is similar to NOT gate in classical computing. As NOT gate in classical computing convert bit 0 to bit 1 and convert bit 1 to bit 0, X gate in quantum computing convert the quatum bit 0> to 1> and convert the quatum bit 1> to 0>.
In symbol and mathematical form, it is presented as follows. It takes 1 bit as input and return 1 bit as output. If you look into the matrix form, you would notice that it takes 2x1 vector (representing 1 qubit) and swap the elements within the vector.
If I you plug in the state vector for 0> and 1> into X gate matrix equation, you can get the output as follows. You would see that the element in the statevector get swaped by the gate X matrix.
Quamtum Gate  Y (PauliY)
Quamtum Gate  Z (PauliZ)
