An exact quantum algorithm for testing Boolean functions with one uncomplemented product of two variables

Abstract

In this paper, we propose a novel quantum learning algorithm, based on Younes’ quantum circuit, to find dependent variables of the Boolean function \( f: \left\{ {0, 1} \right\}^{n} \to \left\{ {0, 1} \right\} \) with one uncomplemented product of two variables. Typically, in the worst-case scenario, two dependent variables are found by evaluating the function \( O\left( n \right) \) times. However, our proposed quantum algorithm only requires \( O\left( {\log_{2} n} \right) \) function operations in the worst-case. Additionally, we evaluate the average number to perform the function. In the average case, our algorithm requires \( O\left( 1 \right) \) function operations.

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Correspondence to Chien-Yuan Chen.

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Chen, C. An exact quantum algorithm for testing Boolean functions with one uncomplemented product of two variables. Quantum Inf Process 19, 213 (2020). https://doi.org/10.1007/s11128-020-02711-8

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Keywords

  • Quantum algorithm
  • Quantum learning algorithm
  • The Bernstein–Vazirani algorithm