A Quantum Advantage for a Natural Streaming Problem

TL;DR

This paper presents a one-pass quantum streaming algorithm for triangle counting, demonstrating a quantum advantage in space complexity for a well-studied natural problem, resolving a longstanding open question.

Contribution

It introduces the first quantum streaming algorithm for triangle counting that uses less space than classical algorithms in certain cases, advancing the understanding of quantum advantages in natural streaming problems.

Findings

Quantum algorithm uses polynomially less space in some parameter regions.

Resolves a question about quantum advantages for natural streaming problems.

Provides almost-tight bounds for classical triangle counting in streaming.

Abstract

Data streaming, in which a large dataset is received as a "stream" of updates, is an important model in the study of space-bounded computation. Starting with the work of Le Gall [SPAA `06], it has been known that quantum streaming algorithms can use asymptotically less space than their classical counterparts for certain problems. However, so far, all known examples of quantum advantages in streaming are for problems that are either specially constructed for that purpose, or require many streaming passes over the input. We give a one-pass quantum streaming algorithm for one of the best studied problems in classical graph streaming - the triangle counting problem. Almost-tight parametrized upper and lower bounds are known for this problem in the classical setting; our algorithm uses polynomially less space in certain regions of the parameter space, resolving a question posed by Jain and Nayak in 2014 on achieving quantum advantages for natural streaming problems.