Quantum versus Classical Online Streaming Algorithms with Logarithmic Size of Memory

TL;DR

This paper compares quantum and classical online streaming algorithms, demonstrating that quantum algorithms outperform classical ones when using logarithmic or sublogarithmic memory sizes.

Contribution

It introduces problems where quantum streaming algorithms surpass classical counterparts with limited memory, highlighting advantages of quantum computation in online settings.

Findings

Quantum algorithms outperform classical ones with logarithmic memory.

Quantum streaming algorithms solve certain problems more efficiently.

Classical algorithms are less effective with sublogarithmic memory.

Abstract

We consider online algorithms with respect to the competitive ratio. Here, we investigate quantum and classical one-way automata with non-constant size of memory (streaming algorithms) as a model for online algorithms. We construct problems that can be solved by quantum online streaming algorithms better than by classical ones in a case of logarithmic or sublogarithmic size of memory.