# Defining standard qubit gates for qutrits

I am actually working on quantum computing with qutrits. I am trying to define standard qubit gates for qutrits. The CNOT gate for qubits is defined as follows: $$|x,y\rangle \to |x,y+x \bmod 2\rangle.$$

So the matrix is $$\mathrm{UCN} = \begin{pmatrix} 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & 0 & 1\\ 0 & 0 & 1 & 0 \end{pmatrix}.$$

For the definition of the same type of gate for qutrit I am left with two choices:

$$|x,y\rangle \to |x,y+x \bmod 3\rangle$$ $$|x,y\rangle \to |x,y+2x \bmod 3\rangle$$

Does anyone know if one of the two is more common or more usually defined?

PS: I know that applying one two times is equivalent to apply the other one time.

• Hi, Marco. Welcome to Quantum Computing SE! It is preferable that you use MathJax to typeset your posts. Review How to write a good question?. I've edited the question on your behalf. – Sanchayan Dutta May 7 '19 at 16:18
• Hi Sanchayan, thanks a lot for the edit and the advice. I will make sure that I write a good question next time. – Marco Falso May 7 '19 at 16:21

$$|x,y\rangle \to |x,y+x \bmod 3\rangle$$