It is often asserted that Hamiltonian simulation (given some Hermitian matrix, $H$) is BQP-complete.
I don't see how the input to such an algorithm is done without the use of some block-encoding or something similar.
We could encode a Hermitian matrix as an adjacency matrix of an undirected graph, but the weights could only be real numbers. I think this idea was the inspiration for quantum walks.
But is this real-value only variant of hamiltonian simulation still BQP-complete?