In this post: Superposition of quantum circuits, the two states are qubits. Is it possible to generalize this question to two qudit case? ie, given quantum circuits $C_1$ and $C_2$ that generates $\vert \psi\rangle$ and $\vert\phi\rangle$ respectively, where $\vert \psi\rangle$ and $\vert\phi\rangle$ belong to a d-dimensional Hilbert space, is it possible to generate the superposition of them, $c(\vert \psi\rangle+\vert\phi\rangle)$, for some normalization constant $c$?
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