Puzzler 5: When states 0 and 7 are connected, we get a loop graph.
The section entitled "Compiling Loop Graphs", in
arXiv:0706.0479, gives an
exact compilation. If 0 and 7 are not connected,
quant-ph/0701088 gives
an approximate compilation that uses Trotter's trick.
Puzzler 6:
quant-ph/9902062
shows how to compile a diagonal unitary matrix exactly (For N rows, it requires
O(N) elementary operations).