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)

How many dimension of basis?

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

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 $\mathbf {v}$ in three complex dimensions, $\mathbf {v} \in \mathbb {C} ^{3}$. 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 $\mathbb {R} ^{6}.$ 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)