Talk:Qutrit

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:

• ${\displaystyle \operatorname {CNOT_{1}} ={\begin{bmatrix}1&0&0&0&0&0&0&0&0\\0&1&0&0&0&0&0&0&0\\0&0&1&0&0&0&0&0&0\\0&0&0&1&0&0&0&0&0\\0&0&0&0&1&0&0&0&0\\0&0&0&0&0&1&0&0&0\\0&0&0&0&0&0&0&1&0\\0&0&0&0&0&0&1&0&0\\0&0&0&0&0&0&0&0&1\end{bmatrix}}}$  maps the target 0 → 1, 1 → 0, 2 → 2, if control is 2.
• ${\displaystyle \operatorname {CNOT_{2}} ={\begin{bmatrix}1&0&0&0&0&0&0&0&0\\0&1&0&0&0&0&0&0&0\\0&0&1&0&0&0&0&0&0\\0&0&0&1&0&0&0&0&0\\0&0&0&0&1&0&0&0&0\\0&0&0&0&0&1&0&0&0\\0&0&0&0&0&0&0&0&1\\0&0&0&0&0&0&0&1&0\\0&0&0&0&0&0&1&0&0\end{bmatrix}}}$  maps the target 0 → 2, 1 → 1, 2 → 0, if control is 2.
• ${\displaystyle \operatorname {CNOT_{3}} ={\begin{bmatrix}1&0&0&0&0&0&0&0&0\\0&1&0&0&0&0&0&0&0\\0&0&1&0&0&0&0&0&0\\0&0&0&1&0&0&0&0&0\\0&0&0&0&1&0&0&0&0\\0&0&0&0&0&1&0&0&0\\0&0&0&0&0&0&1&0&0\\0&0&0&0&0&0&0&0&1\\0&0&0&0&0&0&0&1&0\end{bmatrix}}}$  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 ${\displaystyle |2\rangle }$ . Similar gates where the control has to be ${\displaystyle |1\rangle }$  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)Reply

As the subject. 1.47.138.72 (talk) 03:02, 2 August 2024 (UTC)Reply

It says that the qutrit is a 3-dimensional complex Hilbert space in the article. This means that the quantum state vector of the qutrit (i.e. the value stored in the qutrit) is a vector ${\displaystyle \mathbf {v} }$  in three complex dimensions, ${\displaystyle \mathbf {v} \in \mathbb {C} ^{3}}$ . Because a complex number can be written as two real numbers (a+bi) where a and b are real and i is the imaginary unit, this three-dimensional complex coordinate space is like a 6-dimensional real space ${\displaystyle \mathbb {R} ^{6}.}$  However, the math becomes a lot less cluttery if we use complex numbers instead. Does it need to be clarified in the article that the qutrit is a vector in three complex dimensions? · · · Omnissiahs hierophant (talk) 10:44, 14 September 2024 (UTC)Reply