PIRSA:20120020

Video URL

https://pirsa.org/20120020

Symmetries, graph properties, and quantum speedups

Podder, S. (2020). Symmetries, graph properties, and quantum speedups. Perimeter Institute for Theoretical Physics. https://pirsa.org/20120020

Podder, Supartha. Symmetries, graph properties, and quantum speedups. Perimeter Institute for Theoretical Physics, Dec. 09, 2020, https://pirsa.org/20120020 

          @misc{ scivideos_PIRSA:20120020,
            doi = {10.48660/20120020},
            url = {https://pirsa.org/20120020},
            author = {Podder, Supartha},
            keywords = {Quantum Information},
            language = {en},
            title = {Symmetries, graph properties, and quantum speedups},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2020},
            month = {dec},
            note = {PIRSA:20120020 see, \url{https://scivideos.org/pirsa/20120020}}
          }

Supartha Podder University of Ottawa

Talk numberPIRSA:20120020
DOI10.48660/20120020
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

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 these symmetries are essentially the only permutation groups that prevent super-polynomial quantum speedups. We prove this by fully characterizing the primitive permutation groups that allow super-polynomial quantum speedups. In contrast, in the adjacency list model for bounded-degree graphs (where graph symmetry is manifested differently), we exhibit a property testing problem that shows an exponential quantum speedup. These results resolve open questions posed by Ambainis, Childs, and Liu (2010) and Montanaro and de Wolf (2013). Based on: arxiv:2006.12760