How to Design a Quantum Streaming Algorithm Without Knowing Anything About Quantum Computing

TL;DR

This paper introduces a simple quantum sketching technique that enables classical algorithms to achieve quantum advantages in streaming models without requiring prior quantum computing knowledge.

Contribution

It provides a universal quantum sketch that simplifies deriving quantum streaming algorithms from classical ones, accessible to non-quantum experts.

Findings

Quantum sketch unifies previous quantum streaming results.

Classical algorithms can be enhanced with quantum techniques using the sketch.

Accessible to readers with minimal quantum background.

Abstract

A series of work [GKK+08, Kal22, KPV24] has shown that asymptotic advantages in space complexity are possible for quantum algorithms over their classical counterparts in the streaming model. We give a simple quantum sketch that encompasses all these results, allowing them to be derived from entirely classical algorithms using our quantum sketch as a black box. The quantum sketch and its proof of correctness are designed to be accessible to a reader with no background in quantum computation, relying on only a small number of self-contained quantum postulates.