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An exact quantum logarithmic time algorithm for the 3-junta problem

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Abstract

To tackle the \(3\)-junta problem, this work provides an exact quantum learning algorithm for discovering three dependent variables. A 3-junta is a Boolean function \(f:{\left\{\text{0,1}\right\}}^{n}\to \left\{0, 1\right\}\) that is dependent on just three of the \(n\) variables. Chen suggested an exact quantum learning method in 2021 for solving the 3-junta problem with one uncomplemented product by executing the function operation \(O\left(\text{log}_{2}n\right)\) times in the worst-case. In this work, the modified black-box function is used to solve the \(3\)-junta problem. In the worst-case, our proposed quantum algorithm takes \(O\left(\text{log}_{2}n\right)\) function operations. Furthermore, the average number of function operations is calculated. Our algorithm requires at most \(3.41\) function operations on average.

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Acknowledgements

This work was supported in part by the National Science and Technology Council of the Republic of China under contract NSTC 112-2221-E-390-013.

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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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Correspondence to Chien-Yuan Chen.

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Chen, CY. An exact quantum logarithmic time algorithm for the 3-junta problem. Quantum Inf Process 23, 232 (2024). https://doi.org/10.1007/s11128-024-04402-0

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