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# Expansion Testing using Quantum Fast-Forwarding and Seed Sets

Abstract : 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], 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], 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 borrow a so-called evolving set process from the graph clustering literature, which allows to grow an appropriately local seed set.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.inria.fr/hal-02436647
Contributor : Simon Apers Connect in order to contact the contributor
Submitted on : Monday, January 13, 2020 - 11:43:23 AM
Last modification on : Wednesday, June 8, 2022 - 12:50:07 PM

### Identifiers

• HAL Id : hal-02436647, version 1
• ARXIV : 1907.02369

### Citation

Simon Apers. Expansion Testing using Quantum Fast-Forwarding and Seed Sets. 2020. ⟨hal-02436647⟩

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