Corpus ID: 216562599

Quantum Implications of Huang's Sensitivity Theorem

@article{Aaronson2020QuantumIO,
  title={Quantum Implications of Huang's Sensitivity Theorem},
  author={Scott Aaronson and Shalev Ben-David and Robin Kothari and Avishay Tal},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={2020},
  volume={27},
  pages={66}
}
  • Scott Aaronson, Shalev Ben-David, +1 author Avishay Tal
  • Published 2020
  • Mathematics, Computer Science, Physics
  • Electronic Colloquium on Computational Complexity (ECCC)
  • Based on the recent breakthrough of Huang (2019), we show that for any total Boolean function $f$, the deterministic query complexity, $D(f)$, is at most quartic in the quantum query complexity, $Q(f)$: $D(f) = O(Q(f)^4)$. This matches the known separation (up to log factors) due to Ambainis, Balodis, Belovs, Lee, Santha, and Smotrovs (2017). We also use the result to resolve the quantum analogue of the Aanderaa-Karp-Rosenberg conjecture. We show that if $f$ is a nontrivial monotone graph… CONTINUE READING

    Figures, Tables, and Topics from this paper.

    Paper Mentions

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 51 REFERENCES

    Towards Optimal Separations between Quantum and Randomized Query Complexities

    • Avishay Tal
    • Mathematics, Computer Science, Physics
    • Electronic Colloquium on Computational Complexity
    • 2019

    On Fractional Block Sensitivity

    THE QUANTUM ADVERSARY METHOD AND CLASSICAL FORMULA SIZE LOWER BOUNDS