Help me Read a Paper: Summing Over Superposition Branches
Hello again!
I'm a bit embarrassed to be asking the internet *again* about papers I'm reading, but I've been pretty stumped on this one and Corresponding Author hasn't responded to me. It's an old ish paper so their contact info might be wrong.
I see they are constructing vectors as a uniform superposition of basis-encoded feature-indices and basis-encoded feature-values, and evaluating the index-wise differences with a fairly intuitive adder using basically classical logic but for the fact we are working in superposition.
My hangup is how we are getting to the final Manhattan distance, that needs to be the sum of all these pair wise differences correlated each with their separate branches of the superposition. In the paper they seem to just give that step a single sentence, pointing to the same adder subroutine used to get the individual differences, but since each term is still locked in a different branch of the superposition, I'm not sure how that's possible.
If anyone is familiar with this paper or has time to look it over, I would appreciate some insight.