This seems like something that can be done with indexing, but I
haven't found the solution.

out is a 2D array is initialized to zeros.  x is a 1D array whose
values correspond to the columns of out.  For each row in out, set
out[row,x[row]] = 1.  Here is working code:
def orthogonal_mod (x, nbits):
    out = np.zeros ((len(x), 1<<nbits), dtype=complex)
    for e in range (len (x)):
        out[e,x[e]] = 1
    return out

Any idea to do this without an explicit python loop?