Work

Expansion Testing using Quantum Fast-Forwarding and Seed Sets

Year: 2020

Type: article

Abstract: Expansion testing aims to decide whether an n -node graph has expansion at least Φ , or is far from any such graph. We propose a quantum expansion tester with complexity O~(n1/3Φ−1) . This accelerates the O~(n1/2Φ−2) classical tester by Goldreich and Ron [Algorithmica '02] \cite{goldreich2002property}, and combines the O~(n1/3Φ−2) and O~(n1/2Φ−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.

Source: Quantum

DOI: 10.22331/q-2020-09-16-323

Author: Simon Apers

Institutions: Centre National de la Recherche Scientifique, Centrum Wiskunde & Informatica, Institut de Recherche en Informatique Fondamentale

Language: Latvian

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $215

Funders: European Commission, Agence Nationale de la Recherche, Fonds De La Recherche Scientifique - FNRS, QuantERA