Unlike the classical circuits, quantum circuits don’t allow loops. And it doesn’t allow FANIN and FANOUT.
We can’t copy qubit, which can be illustrated using CNOT gate. The CNOT gate can be seen as below:
where the top line represents control qubit and the bottom line represents target qubit. It has priority that if the control qubit is set to 0, the target qubit is left alone. Otherwise, the target qubit is flipped.
First we build CNOT circuits which takes a qubit state and initialization states |0> as inputs, the copied qubit states is the output. The process can be seen as below:
Let’s say the input state is |\phi> = a|0> + b |1> and |0>. Thus, the inputs can be written as:
By the priority of CNOT gate, it can be further written into:
Let’s assume the copy success, then the output should be same as Eq.1
However, consider the general case
Eq 1 and Eq 2 is equal iff ab = 0, which is impossible. So copy cannot be done.