I've been reading a number of quantum computation research papers that claim quantum cost's that do not add up.
For instance, in this paper - there is a claim that the MTSG gate is a quantum cost of 6. But to actually perform the computation, you need swap gates to get the stuff into the right order!
For instance, to even perform the first gate
V(B, D), you'll need to do the following:
1) U = TENSOR(ID, SWAP, ID)
2) U = TENSOR(ID, ID, VGATE)
3) APPLY (U, R)
4) SWAP BACK
Am I getting something wrong here?