Quantum versus Classical Online Streaming Algorithms with Advice

TL;DR

This paper compares quantum and classical online streaming algorithms, demonstrating quantum advantages in memory-limited settings and showing quantum algorithms outperform classical ones even with advice bits.

Contribution

It introduces problems where quantum online streaming algorithms outperform classical ones with advice, and proves quantum algorithms can surpass classical deterministic algorithms with advice.

Findings

Quantum algorithms outperform classical ones with limited memory.

Quantum algorithms with constant qubits beat classical algorithms with advice.

Quantum advantage persists even with unlimited classical computational power.

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, even if classical online algorithms get advice bits. Furthermore, we show that a quantum online algorithm with a constant number of qubits can be better than any deterministic online algorithm with a constant number of advice bits and unlimited computational power.