Work

Variational learning algorithms for quantum query complexity

Year: 2024

Type: article

Abstract: Quantum query complexity is pivotal in the analysis of quantum algorithms, encompassing well-known examples like search and period-finding algorithms. These algorithms typically involve a sequence of unitary operations and oracle calls dependent on an input variable. In this study, we introduce a variational learning approach to explore quantum query complexity. Our method employs an efficient parameterization of the unitary operations and utilizes a loss function derived from the algorithm’s error probability. We apply this technique to various quantum query complexities, notably devising a new algorithm that resolves the 5-bit Hamming modulo problem with four queries, addressing an open question from Cornelissen et al (2021 arXiv: 2112.14682 ). This finding is corroborated by a semidefinite programming (SDP) approach. Our numerical method exhibits superior memory efficiency compared to SDP and can identify quantum query algorithms (QQAs) that require a smaller workspace register dimension, an aspect not optimized by SDP. These advancements present a significant step forward in the practical application and understanding of QQAs.

Source: New Journal of Physics

DOI: 10.1088/1367-2630/ad309c

Authors: Zipeng Wu, Shi-Yao Hou, Chao Zhang, Lvzhou Li, Bei Zeng

Institutions: Hong Kong University of Science and Technology, Sichuan Normal University, Sun Yat-sen University

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,485

Funders: National Natural Science Foundation of China, Basic and Applied Basic Research Foundation of Guangdong Province