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Analyzing XOR-Forrelation Through Stochastic Calculus

Author Xinyu Wu

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LIPIcs.STACS.2022.60.pdf
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  • Theory of computation → Quantum complexity theory
Keywords
  • quantum complexity
  • Brownian motion

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Abstract

In this note we present a simplified analysis of the quantum and classical complexity of the k-XOR Forrelation problem (introduced in the paper of Girish, Raz and Zhan [Uma Girish et al., 2020]) by a stochastic interpretation of the Forrelation distribution.

Cite As Get BibTex

Xinyu Wu. Analyzing XOR-Forrelation Through Stochastic Calculus. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 60:1-60:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.STACS.2022.60

Author Details

Xinyu Wu
  • Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA

Funding

Supported by NSF grant CCF-1717606. This material is based upon work supported by the National Science Foundation under grant numbers listed above. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation (NSF).

Acknowledgements

I would like to thank Ryan O'Donnell for many helpful comments on this paper.

References

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  4. Eshan Chattopadhyay, Pooya Hatami, Kaave Hosseini, and Shachar Lovett. Pseudorandom generators from polarizing random walks. Theory Comput., 15:Paper No. 10, 26, 2019. URL: https://doi.org/10.4086/toc.2019.v015a010.
  5. Eshan Chattopadhyay, Pooya Hatami, Shachar Lovett, and Avishay Tal. Pseudorandom generators from the second Fourier level and applications to AC0 with parity gates. In Proceedings of the 10th Annual Innovations in Theoretical Computer Science Conference, pages 22:1-22:15, 2018. Google Scholar
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  10. Daniel Revuz and Marc Yor. Continuous martingales and Brownian motion, volume 293 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, third edition, 1999. URL: https://doi.org/10.1007/978-3-662-06400-9.
  11. Avishay Tal. Towards optimal separations between quantum and randomized query complexities. In Proceedings of the 61st Annual IEEE Symposium on Foundations of Computer Science, pages 228-239. IEEE Computer Soc., Los Alamitos, CA, 2020. URL: https://doi.org/10.1109/FOCS46700.2020.00030.
  12. Martin J. Wainwright. High-dimensional statistics, volume 48 of Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2019. A non-asymptotic viewpoint. URL: https://doi.org/10.1017/9781108627771.
  13. Xinyu Wu. A stochastic calculus approach to the oracle separation of BQP and PH. Technical report, arXiv, 2020. URL: http://arxiv.org/abs/2007.02431.
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