Talk:Qutrit

Other gates

Basically nothing has been written about quantum gates for qutrits AFAIK, but some other gates are possible to deduce for qutrits..

Some CNOT analogs for qutrits:

• $\operatorname {CNOT_{1}} ={\begin{bmatrix}1&0&0&0&0&0&0&0&0\\0&1&0&0&0&0&0&0&0\\0&0&1&0&0&0&0&0&0\\0&0&0&1&0&0&0&0&0\\0&0&0&0&1&0&0&0&0\\0&0&0&0&0&1&0&0&0\\0&0&0&0&0&0&0&1&0\\0&0&0&0&0&0&1&0&0\\0&0&0&0&0&0&0&0&1\end{bmatrix}}$ maps the target 0 → 1, 1 → 0, 2 → 2, if control is 2.
• $\operatorname {CNOT_{2}} ={\begin{bmatrix}1&0&0&0&0&0&0&0&0\\0&1&0&0&0&0&0&0&0\\0&0&1&0&0&0&0&0&0\\0&0&0&1&0&0&0&0&0\\0&0&0&0&1&0&0&0&0\\0&0&0&0&0&1&0&0&0\\0&0&0&0&0&0&0&0&1\\0&0&0&0&0&0&0&1&0\\0&0&0&0&0&0&1&0&0\end{bmatrix}}$ maps the target 0 → 2, 1 → 1, 2 → 0, if control is 2.
• $\operatorname {CNOT_{3}} ={\begin{bmatrix}1&0&0&0&0&0&0&0&0\\0&1&0&0&0&0&0&0&0\\0&0&1&0&0&0&0&0&0\\0&0&0&1&0&0&0&0&0\\0&0&0&0&1&0&0&0&0\\0&0&0&0&0&1&0&0&0\\0&0&0&0&0&0&1&0&0\\0&0&0&0&0&0&0&0&1\\0&0&0&0&0&0&0&1&0\end{bmatrix}}$ maps the target 0 → 0, 1 → 2, 2 → 1, if control is 2.

That flips the target qutrit in various ways only if the control qutrit is $|2\rangle$. Similar gates where the control has to be $|1\rangle$ should also exist.

Any CNOT gate together with the rotation operators and the global phase shift gate should form a universal set of quantum gates for qutrits.

I thought about writing about this in the article. But maybe extrapolation is not good enough, without sources. Besides, it is maybe too much? · · · Omnissiahs hierophant (talk) 21:17, 14 December 2021 (UTC)