Quantum search in a dictionary based on fingerprinting-hashing

TL;DR

This paper introduces a quantum search algorithm for dictionaries that uses fingerprinting-hashing to improve memory efficiency and incorporates a novel amplitude amplification step, achieving similar query complexity with fewer qubits.

Contribution

The paper presents a quantum search algorithm based on fingerprinting-hashing, reducing memory requirements compared to previous methods while maintaining optimal query complexity.

Findings

Uses $O( oot n)$ queries similar to prior algorithms.

Requires only $O( ext{log} n + ext{log} m)$ qubits, less than previous methods.

Incorporates a new amplitude amplification step with fingerprinting-hashing.

Abstract

In this work, we present a quantum query algorithm for searching a word of length $m$ in an unsorted dictionary of size $n$. The algorithm uses $O(\sqrt{n})$ queries (Grover operators), like previously known algorithms. What is new is that the algorithm is based on the quantum fingerprinting-hashing technique, which (a) provides a first level of amplitude amplification before applying the sequence of Grover amplitude amplification operators and (b) makes the algorithm more efficient in terms of memory use -- it requires $O(\log n + \log m)$ qubits. Note that previously developed algorithms by other researchers without hashing require $O(\log n + m)$ qubits.