Expansion Testing using Quantum Fast-Forwarding and Seed Sets
Expansion testing aims to decide whether an $n$-node graph has expansion at least $\Phi$, or is far from any such graph. We propose a quantum expansion tester with complexity $\widetilde{O}(n^{1/3}\Phi^{-1})$. This accelerates the $\widetilde{O}(n^{1/2}\Phi^{-2})$ classical tester by Goldreich and R...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2020-09-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2020-09-16-323/pdf/ |
| _version_ | 1818963253685911552 |
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| author | Simon Apers |
| author_facet | Simon Apers |
| author_sort | Simon Apers |
| collection | DOAJ |
| description | Expansion testing aims to decide whether an $n$-node graph has expansion at least $\Phi$, or is far from any such graph. We propose a quantum expansion tester with complexity $\widetilde{O}(n^{1/3}\Phi^{-1})$. This accelerates the $\widetilde{O}(n^{1/2}\Phi^{-2})$ classical tester by Goldreich and Ron [Algorithmica '02] \cite{goldreich2002property}, and combines the $\widetilde{O}(n^{1/3}\Phi^{-2})$ and $\widetilde{O}(n^{1/2}\Phi^{-1})$ quantum speedups by Ambainis, Childs and Liu [RANDOM '11] and Apers and Sarlette [QIC '19] \cite{apers2019quantum}, respectively. The latter approach builds on a quantum fast-forwarding scheme, which we improve upon by initially growing a seed set in the graph. To grow this seed set we use a so-called evolving set process from the graph clustering literature, which allows to grow an appropriately local seed set. |
| first_indexed | 2024-12-20T12:42:17Z |
| format | Article |
| id | doaj.art-b649b8ae1e924c839687edc39ec2efd4 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-20T12:42:17Z |
| publishDate | 2020-09-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-b649b8ae1e924c839687edc39ec2efd42022-12-21T19:40:25ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2020-09-01432310.22331/q-2020-09-16-32310.22331/q-2020-09-16-323Expansion Testing using Quantum Fast-Forwarding and Seed SetsSimon ApersExpansion testing aims to decide whether an $n$-node graph has expansion at least $\Phi$, or is far from any such graph. We propose a quantum expansion tester with complexity $\widetilde{O}(n^{1/3}\Phi^{-1})$. This accelerates the $\widetilde{O}(n^{1/2}\Phi^{-2})$ classical tester by Goldreich and Ron [Algorithmica '02] \cite{goldreich2002property}, and combines the $\widetilde{O}(n^{1/3}\Phi^{-2})$ and $\widetilde{O}(n^{1/2}\Phi^{-1})$ quantum speedups by Ambainis, Childs and Liu [RANDOM '11] and Apers and Sarlette [QIC '19] \cite{apers2019quantum}, respectively. The latter approach builds on a quantum fast-forwarding scheme, which we improve upon by initially growing a seed set in the graph. To grow this seed set we use a so-called evolving set process from the graph clustering literature, which allows to grow an appropriately local seed set.https://quantum-journal.org/papers/q-2020-09-16-323/pdf/ |
| spellingShingle | Simon Apers Expansion Testing using Quantum Fast-Forwarding and Seed Sets Quantum |
| title | Expansion Testing using Quantum Fast-Forwarding and Seed Sets |
| title_full | Expansion Testing using Quantum Fast-Forwarding and Seed Sets |
| title_fullStr | Expansion Testing using Quantum Fast-Forwarding and Seed Sets |
| title_full_unstemmed | Expansion Testing using Quantum Fast-Forwarding and Seed Sets |
| title_short | Expansion Testing using Quantum Fast-Forwarding and Seed Sets |
| title_sort | expansion testing using quantum fast forwarding and seed sets |
| url | https://quantum-journal.org/papers/q-2020-09-16-323/pdf/ |
| work_keys_str_mv | AT simonapers expansiontestingusingquantumfastforwardingandseedsets |