Binary Quantum Search

TL;DR

This paper introduces a binary quantum search method that optimizes the process of finding target items or groups within a database by reducing the number of oracle queries needed, improving efficiency over previous partial search algorithms.

Contribution

It demonstrates that directly partitioning the database into sub-blocks and applying the GRK algorithm is faster than sequentially searching through partitions.

Findings

Direct partitioning reduces query complexity.

Optimized binary search outperforms sequential partial searches.

The method is applicable to various database sizes.

Abstract

Database search has wide applications and is used as a subroutine in many important algorithms. We shall consider a database with one target item. Quantum algorithm finds the target item in a database faster than any classical algorithm. It frequently occurs in practice that only a portion of information about the target item is interesting, or we need to find a group of items sharing some common feature as the target item. This problem is in general formulated as search for a part of the database [a block] containing the target item, instead of the item itself. This is partial search. Partial search trades accuracy for speed, i.e. it works faster than a full search. Partial search algorithm was discovered by Grover and Radhakrishnan. We shall consider optimized version of the algorithm and call it GRK. It can be applied successively [in a sequence]. First the database is partitioned into blocks and we use GRK to find the target block. Then this target block is partitioned into sub-blocks and we use GRK again to find the target sub-block. [We can call it binary quantum search.] Another possibility is to partition the database into sub-blocks directly and use GRK to find the target sub-block in one time. In this paper we prove that the latter is faster [makes less queries to the oracle].