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An Exact Quantum Algorithm for the 2-Junta Problem

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Abstract

This paper proposes a novel quantum learning algorithm based on Bernstein and Vazirani’s quantum circuit to find the dependent variables of the 2-junta problem. Typically, for a given Boolean function f : {0, 1}n → {0, 1} that depends on only 2 out of n variables, the dependent variables are obtained by evaluating the function 4n times in the worst-case. However, the proposed quantum algorithm only requires O(log2n) function operations in the worst-case. Moreover, the algorithm requires an average of 5.3 function operations at the most when n ≥ 8.

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  1. Department of Computer Science and Information Engineering, National University of Kaohsiung, No.700, Kaohsiung University Rd, Kaohsiung, Taiwan

    Chien-Yuan Chen

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  1. Chien-Yuan Chen
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Correspondence to Chien-Yuan Chen.

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Chen, CY. An Exact Quantum Algorithm for the 2-Junta Problem. Int J Theor Phys 60, 80–91 (2021). https://doi.org/10.1007/s10773-020-04662-3

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  • DOI: https://doi.org/10.1007/s10773-020-04662-3

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