Today I read a paper titled “A better lower bound for quantum algorithms searching an ordered list”
The abstract is:
We show that any quantum algorithm searching an ordered list of n elements needs to examine at least 1/12 log n-O(1) of them.
Classically, log n queries are both necessary and sufficient.
This shows that quantum algorithms can achieve only a constant speedup for this problem.
Our result improves lower bounds of Buhrman and de Wolf(quant-ph/9811046) and Farhi, Goldstone, Gutmann and Sipser (quant-ph/9812057).