Year: 2000
Type: preprint
Abstract: We prove that any exact quantum algorithm searching an ordered list of N elements requires more than \frac{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 best known upper bound for exact searching is roughly 0.526 \log_2(N). We give an exact quantum algorithm that uses \log_3(N) + O(1) queries, which is roughly 0.631 \log_2(N). The main principles in our algorithm are an quantum parallel use of the classical binary search algorithm and a method that allows basis states in superpositions to communicate.
Source: arXiv (Cornell University)
Authors: Hoyer, Peter, Neerbek, Jan
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1575827732