Is there a higher order H-gate in Q# language? For example, if I want to apply Hadamard gate to an array(combined state) of 3 qubits. Is there a way to generate a tensor product version of H-gate or other gates?
One way to think of it is to think of the unitary operator H = |+⟩⟨0| + |−⟩⟨1| and the quantum operation H separately.
Taking this view, the unitary H is how we simulate the effect of applying the operation H on an ideal quantum processor.
The quantum operation ApplyToEach(H, _) is then represented by the unitary operator H ⊗ H ⊗ ⋯ ⊗ H in precisely the same way that H is represented by H.
One consequence of this mental model is that the tensor product is defined between unitary operators and not between quantum operations. Rather, the ideal action of quantum operations acting on distinct qubits is represented by the tensor product of the unitary representations of each individual operation.