Bounds on quantum ordered searching

We prove that any exact quantum algorithm searching an ordered list of N elements requires more than 1 π (ln(N) − 1) queries to the list. This improves upon the previously best known lower bound of 1 12 log 2 (N) − O(1). Our proof is based on a weighted all-pairs inner product argument, and it generalizes to bounded-error quantum algorithms. The currently… (More)