Expansion Testing using Quantum Fast-Forwarding and Seed Sets - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year :

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.

Dates and versions

hal-02436647 , version 1 (13-01-2020)

Identifiers

Cite

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

Collections

INRIA INRIA2
16 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More