What do we mean by “derive full operator of a quantum circuit” and to describe the mapping from input quantum registers to output quantum registers?

Question

There is a quantum circuit with several Controlled NOT and Controlled swap gates, with two 2-qubit input registers X,Y and two 2-qubit output registers X',Y' where we have to find the mapping of the circuit and what operations it performs.

user1271772 · Accepted Answer

You only have 4 qubits, so the "full operator" is only at most a 16x16 matrix that combines all 7 of those multi-qubit gates. You can derive this "full operator" in MATLAB quite easily by using the "kron" function to build up the multi-qubit gates from 1-qubit and 2-qubit gates (2x2 and 4x4 matrices respectively), and then doing matrix multiplication.

As for the second question: "what operation does this circuit implement", this will become easier to answer once you figure out the 16x16 matrix see what it does to the four input qubits.

As for the second question: "what operation does this circuit implement", this will become easier to answer once you figure out the 16x16 matrix see what it does to the four input  qubits.

What do we mean by “derive full operator of a quantum circuit” and to describe the mapping from input quantum registers to output quantum registers?

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