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}
}
• S. Ben-David, +3 authors Daochen Wang
• Published 2020
• Computer Science, Physics, Mathematics
• 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
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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