# Gate definitions for quantum random access codes

I would like to know how the gates are defined in quantum random access codes? Consider the $$2 \to 1$$ code described in Lemma 3.1 of this paper.

The section defines the encoding and decoding circuits. But it is not clear to me how to define gates. Say, I want to apply an $$Rz(\theta)$$ on the first qubit or a CNOT gate on both qubits.

How do I do that?

• I was able to make some progress. For single qubit gates, applying it directly means applying on the first encoded qubit. To apply it on the second qubit, you have to conjugate it with the H gate. I am still not sure how to apply the CNOT gate. – Omar Shehab Aug 18 '20 at 23:08