Characterization of Exact One-Query Quantum Algorithms for Partial Boolean Functions

The query model (or black-box model) has attracted much attention from the communities of both classical and quantum computing. Usually, quantum advantages are revealed by presenting a quantum algorithm that has a better query complexity than its classical counterpart. In the history of quantum algo...

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Bibliographic Details
Published in:Journal of computer science and technology Vol. 38; no. 6; pp. 1423 - 1430
Main Authors: Ye, Ze-Kun, Li, Lv-Zhou
Format: Journal Article
Language:English
Published: Singapore Springer Nature Singapore 01.12.2023
Springer
Springer Nature B.V
Subjects:
Algorithms
Analysis
Artificial Intelligence
Boolean
Boolean functions
Codes
Computer Science
Data Structures and Information Theory
Information Systems Applications (incl.Internet)
Mathematical models
Quantum computing
Queries
Regular Paper
Software Engineering
Theory of Computation
quantum query complexity
quantum algorithm
quantum computing
ISSN:1000-9000, 1860-4749
Online Access:Get full text
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Summary:The query model (or black-box model) has attracted much attention from the communities of both classical and quantum computing. Usually, quantum advantages are revealed by presenting a quantum algorithm that has a better query complexity than its classical counterpart. In the history of quantum algorithms, the Deutsch algorithm and the Deutsch-Jozsa algorithm play a fundamental role and both are exact one-query quantum algorithms. This leads us to consider the problem: what functions can be computed by exact one-query quantum algorithms? This problem has been addressed in the literature for total Boolean functions and symmetric partial Boolean functions, but is still open for general partial Boolean functions. Thus, in this paper, we continue to characterize the computational power of exact one-query quantum algorithms for general partial Boolean functions. First, we present several necessary and sufficient conditions for a partial Boolean function to be computed by exact one-query quantum algorithms. Second, inspired by these conditions, we discover some new representative functions that can be computed by exact one-query quantum algorithms but have an essential difference from the already known ones. Specially, it is worth pointing out that before our work, the known functions that can be computed by exact one-query quantum algorithms are all symmetric functions and the quantum algorithm used is essentially the Deutsch-Jozsa algorithm, whereas the functions discovered in this paper are generally asymmetric and new algorithms to compute these functions are required. Thus, this expands the class of functions that can be computed by exact one-query quantum algorithms.
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ISSN:1000-9000
1860-4749
DOI:10.1007/s11390-022-1361-0