"First, I'm not aware of any proof that Brassard et al.'s algorithm is optimal." Also, it's really not clear from this post why you can't play the same kind of

"First, I'm not aware of any proof that Brassard et al.'s algorithm is optimal." Also, it's really not clear from this post why you can't play the same kind of parallelization game. (IE if the underlying thing it provides is a faster way to do x, why can't you parallelize that x in the same way) Actually, it looks like bernstein points out you can do this, so the author of this post is essentially comparing a crappy technique to a good one, and saying "The good one is better". It turns out they are the same in the end and it's just cheaper to build normal machines than quantum ones. That seems more reasonable to me than "this technique is slower than the best classical one". It's not. It's just cheaper. That's all. He also says bernstein brilliantly explains why even better quantum algorithms will never win, but actually, bernstein just conjectures that :) " there are several obvious ways to combine quantum search with the rho method, but I have not found any such combinations that improve performance, and I conjecture that—in a suitable generic model—no such improvements are possible." That's a pretty easy conjecture to always make - "i haven't found a way to make this faster, so i conjecture a way to make it faster doesn't exist". These types of conjectures are often very wrong, which is why we have proofs ;)