3-Qubit Quantum Circuit with 1 CNOT

[jumi]

Ok, I have this circuit, and I'm trying to devise a way to create an 8x8 matrix for any given combination of target qubit and controlled qubit.

(I is the identity matrix, and X is the CNOT operator)

I want it to also include the qubit that passes through untouched because I'm trying to write a program that takes a given state of 3 qubits and runs it through the above circuit.

As of now, for any combination of target and control qubit, I've generated the 8x8 matrices on paper, but I wondering if there's an easier way to generate each case?

If I had to, I suppose I could "brute force" code each individual case (i.e. 1 on 2, 1 on 3, 2 on 3 and their opposites), but it seems like I'm missing something quite easy that wouldn't require that...

Thanks in advance.

 

[azntoon]

The easiest way to generate the 8x8 matrices for any combination of target qubit and controlled qubit is to use a quantum circuit simulator. These simulators allow you to define the number of qubits in your circuit, define the desired circuit operations, and simulate the circuit's output. This will give you the exact 8x8 matrix you need for any given combination of target and controlled qubit.