General framework for quantum search algorithms

TL;DR

This paper presents a generalized framework for quantum search algorithms, extending Grover's method by incorporating more flexible transformations and control mechanisms, leading to potential speedups especially in spatial search problems.

Contribution

It introduces a unified framework that generalizes previous quantum search algorithms and demonstrates how controlling transformations via an ancilla qubit can enhance performance.

Findings

Framework encompasses previous generalizations of Grover's algorithm.

Controlling transformations with an ancilla qubit improves search efficiency.

Achieves faster spatial search in two dimensions.

Abstract

Grover's quantum search algorithm drives a quantum computer from a prepared initial state to a desired final state by using selective transformations of these states. Here, we analyze a framework when one of the selective trasformations is replaced by a more general unitary transformation. Our framework encapsulates several previous generalizations of the Grover's algorithm. We show that the general quantum search algorithm can be improved by controlling the transformations through an ancilla qubit. As a special case of this improvement, we get a faster quantum algorithm for the two-dimensional spatial search.