Coherence Fraction in Grover Search Algorithm

TL;DR

This paper investigates the role of coherence fraction in the Grover search algorithm, revealing it as a key resource influencing success probability beyond entanglement.

Contribution

It introduces a generalized Grover algorithm that highlights the importance of coherence fraction, providing new insights into quantum advantage mechanisms.

Findings

Coherence fraction affects Grover success probability.

Success depends on initial state fidelity to equal superposition.

Insights applicable to quantum machine learning algorithms.

Abstract

The question of which resources drive the advantages in quantum algorithms has long been a fundamental challenge. While entanglement and coherence are critical to many quantum algorithms, our results indicate that they do not fully explain the quantum advantage achieved by the Grover search algorithm. By introducing a generalized Grover search algorithm, we demonstrate that the success probability depends not only on the querying number of oracles but also on the coherence fraction, which quantifies the fidelity between an arbitrary initial quantum state and the equal superposition state. Additionally, we explore the role of the coherence fraction in the quantum minimization algorithm, which offers a framework for solving complex problems in quantum machine learning. These findings offer insights into the origins of quantum advantage and open pathways for the development of new quantum algorithms.