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

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Abstract

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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Authors and Affiliations

  1. Institute of Quantum Computing and Computer Theory, School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, 510006, China

    Ze-Kun Ye & Lv-Zhou Li

  2. Ministry of Education Key Laboratory of Machine Intelligence and Advanced Computing, Sun Yat-sen University, Guangzhou, 510006, China

    Lv-Zhou Li

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  1. Ze-Kun Ye
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  2. Lv-Zhou Li
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Correspondence to Lv-Zhou Li.

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Ye, ZK., Li, LZ. Characterization of Exact One-Query Quantum Algorithms for Partial Boolean Functions. J. Comput. Sci. Technol. 38, 1423–1430 (2023). https://doi.org/10.1007/s11390-022-1361-0

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