Symmetries, Graph Properties, and Quantum Speedups

@article{BenDavid2020SymmetriesGP,
  title={Symmetries, Graph Properties, and Quantum Speedups},
  author={Shalev Ben-David and Andrew M. Childs and Andr'as Gily'en and William Kretschmer and Supartha Podder and Daochen Wang},
  journal={2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)},
  year={2020},
  pages={649-660}
}
Aaronson and Ambainis (2009) and Chailloux (2018) showed that fully symmetric (partial) functions do not admit exponential quantum query speedups. This raises a natural question: how symmetric must a function be before it cannot exhibit a large quantum speedup? In this work, we prove that hypergraph symmetries in the adjacency matrix model allow at most a polynomial separation between randomized and quantum query complexities. We also show that, remarkably, permutation groups constructed out of… Expand

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