# I How to synthesize quantum circuits?

1. Feb 26, 2017

### nashed

I wonder if anyone can explain how to actually synthesis a quantum circuit, what I mean by this is that given some requirements, I am able to write the matrix form of the circuit needed, but I have no idea how to turn that into a list of gates.

For example:
Build a circuit that performs the exclusive or operation on three qubits $$|abc\rangle \rightarrow |ab\rangle\otimes|a\oplus b\oplus c\rangle$$ looking at a truth table for the circuit I can see that when a and b are the same then c is conserved, otherwise c is flipped so I can deduce that if I connect c to a controlled not where a is the control and another controlled not where b is the control I get the desired operation.
That said if I try and write the matrix form of the circuit I have no idea how to manipulate it so it looks like the repeated application of controlled not gates.

BTW this is not a homework question but I am not sure this is the correct forum either so feel free to tell me and I"ll delete the post.

2. Feb 27, 2017