Randomized query complexity can beat certificate complexity
- We construct a function with R(f) = O~(sqrt{C(f)}), which is optimal up to log factors.
- The same function also has $Q(f) = O~(C(f)^{1/4}), where Q(f) is the bounded-error quantum query complexity of f, which is also nearly optimal.
Unverified
- We construct a function with R(f) = O~(sqrt{C(f)}), which is optimal up to log factors.
- The same function also has $Q(f) = O~(C(f)^{1/4}), where Q(f) is the bounded-error quantum query complexity of f, which is also nearly optimal.
Sources: Arxiv