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

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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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References

  1. Lu, Z.Q.: The elements of statistical learning: data mining, inference, and prediction. J. R. Stat. Soc. Ser. A 173(3), 693–694 (2010)

    Article  Google Scholar 

  2. Mossel, E., O’Donnell, R., Servedio, R.P.: Learning juntas. In: Proc. 35th Ann. ACM Symp. Theo. Comp., pp. 206–212 (2003)

  3. Atıcı, A., Servedio, R.A.: Quantum algorithms for learning and testing juntas. Quantum Inf. Process. 6(5), 323–348 (2007)

    Article  MathSciNet  Google Scholar 

  4. Floess, D.F., Andersson, E., Hillery, M.: Quantum algorithms for testing Boolean functions. arXiv:1006.1423 (2010)

  5. Bernstein, E., Vazirani, U.: Quantum complexity theory. SIAM J. Comput. 26(5), 1411–1473 (1997)

    Article  MathSciNet  Google Scholar 

  6. Boyer, M., Brassard, G., Høyer, P., Tapp, A.: Tight bounds on quantum searching. Fortschr. Phys.-Prog. Phys. 46(4–5), 493–505 (1998)

    Article  ADS  Google Scholar 

  7. Ambainis, A., Belovs, A., Regev, O., de Wolf, R.: Efficient quantum algorithms for (gapped) group testing and junta testing. In: Proc. 27th Ann. ACM-SIAM Symp. Discr. Alg., pp. 903–922 (2016)

  8. El-Wazan, K., Younes, A., Doma, S.B.: A quantum algorithm for testing juntas in Boolean functions. arXiv:1710.10495 (2017)

  9. Younes, A.: A fast quantum algorithm for the affine Boolean function identification. Eur. Phys. J. Plus 130(2), 34 (2015)

    Article  Google Scholar 

Download references

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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 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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  • DOI: https://doi.org/10.1007/s11128-020-02711-8

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