A Review on Quantum Search Algorithms

TL;DR

This paper reviews quantum search algorithms, especially Grover's algorithm, highlighting their speed advantages over classical methods and discussing various optimizations and extensions.

Contribution

It provides a comprehensive overview of Grover's quantum search algorithms, including their variants and improvements, which is valuable for understanding quantum database search techniques.

Findings

Grover's algorithm achieves quadratic speedup in unstructured search.

Extensions to multiple targets are discussed.

Optimizations like the GRK algorithm improve efficiency.

Abstract

The use of superposition of states in quantum computation, known as quantum parallelism, has significant advantage in terms of speed over the classical computation. It can be understood from the early invented quantum algorithms such as Deutsch's algorithm, Deutsch-Jozsa algorithm and its variation as Bernstein-Vazirani algorithm, Simon algorithm, Shor's algorithms etc. Quantum parallelism also significantly speeds up the database search algorithm, which is important in computer science because it comes as a subroutine in many important algorithms. Quantum database search of Grover achieves the task of finding the target element in an unsorted database in a time quadratically faster than the classical computer. We review the Grover quantum search algorithms for a singe and multiple target elements in a database. The partial search algorithm of Grover and Radhakrishnan and its optimization by Korepin, called GRK algorithm are also discussed.