I am wondering what a circuit should look like if I want to prepare the state of the following form: $$ |0\rangle^{\otimes n} \mapsto \dfrac{ |1000\ldots0\rangle + |0100\ldots0\rangle + |0010\ldots0\rangle + \ldots + |00\ldots001\rangle }{\sqrt{n}} $$ Is this something well-known and trivial?
ANSWER
Apparently, this question was asked here.
The Q# realization is provided in katas 15-17 here.