Coherence fraction in Grover's search algorithm

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. Published by the American Physical Society 2024

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Publication Details

Journal
Physical review. A/Physical review, A
Published
2024-12-31
DOI
https://doi.org/10.1103/physreva.110.062429
Citations
3
Primary Topic
Quantum Computing Algorithms and Architecture
Type
article
Field-Weighted Citation Impact
1.04

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article

Coherence fraction in Grover's search algorithm

Yunlong Xiao, Jin‐Min Liang, Hai Jin, Shao-Ming Fei et al.
3 citations
Physical review. A/Physical review, A
Quantum Computing Algorithms and Architecture
1.04
article

Coherence fraction in Grover's search algorithm

Yunlong Xiao, Jin‐Min Liang, Hai Jin, Shao-Ming Fei, Zhihao Ma, Suyuan Zhou
article en
3 citations

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. Published by the American Physical Society 2024

Physical review. A/Physical review, AVol. 110(6)
Agency for Science, Technology and Research (SG), Shanghai Jiao Tong University (CN), Peking University (CN), Institute of High Performance Computing (SG), Southern University of Science and Technology (CN), Japan Science and Technology Agency (JP), Max Planck Institute for Mathematics in the Sciences (DE), SGIDI Engineering Consulting (China) (CN), Max Planck Institute for Mathematics (DE), Capital Normal University (CN)
National Research Foundation, Agency for Science, Technology and Research, National Research Foundation Singapore, National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities
Openalex Percentile: Top 18%
Quantum Computing Algorithms and Architecture
1.04
DOIOpen Access PDFOpenAlex
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