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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.

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  • $\begingroup$ Hi and welcome to Quantum computing SE. Could you please add more details, e.g. a circuit picture? Thank you. $\endgroup$ Commented Apr 12, 2020 at 16:07
  • $\begingroup$ I didnt want to directly ask the question as the guidelines dont allow me but you asked so i have edited the ques and posted a picture of the ques. You dont need to answer the whole ques just give me an explanation because i am totally new to this and just started. $\endgroup$ Commented Apr 13, 2020 at 17:25
  • $\begingroup$ @ArpitSingh Why edit the question to make it less informative? $\endgroup$
    – Rammus
    Commented Mar 18, 2021 at 19:19

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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.

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