# Expansion Testing using Quantum Fast-Forwarding and Seed Sets

arXiv: https://arxiv.org/abs/1907.02369 · HTML: https://mlsanity.com/paper/1907.02369/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2019.

## Built on by (most cited first, 1 of 1)

- [FairGen: Towards Fair Graph Generation](https://mlsanity.com/paper/2303.17743/) (2023)

## Abstract (arXiv)

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 widetildeO(n1/3Phi-1). This accelerates the widetildeO(n1/2Phi-2) classical tester by Goldreich and Ron [Algorithmica '02], and combines the widetildeO(n1/3Phi-2) and widetildeO(n1/2Phi-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 use a so-called evolving set process from the graph clustering literature, which allows to grow an appropriately local seed set.