Space Complexity of Streaming Algorithms on Universal Quantum Computers

TL;DR

This paper investigates the space complexity of data stream problems on universal quantum computers, revealing that classical control bits may negate quantum advantages in space efficiency.

Contribution

It provides an analysis showing that quantum algorithms for certain data stream problems do not reduce space complexity compared to classical algorithms due to classical control requirements.

Findings

Quantum algorithms do not reduce space complexity for PartialMOD and Equality problems.

Classical control bits in quantum algorithms can be as large as classical memory.

No space advantage of quantum over classical algorithms for these problems.

Abstract

Universal quantum computers are the only general purpose quantum computers known that can be implemented as of today. These computers consist of a classical memory component which controls the quantum memory. In this paper, the space complexity of some data stream problems, such as PartialMOD and Equality, is investigated on universal quantum computers. The quantum algorithms for these problems are believed to outperform their classical counterparts. Universal quantum computers, however, need classical bits for controlling quantum gates in addition to qubits. Our analysis shows that the number of classical bits used in quantum algorithms is equal to or even larger than that of classical bits used in corresponding classical algorithms. These results suggest that there is no advantage of implementing certain data stream problems on universal quantum computers instead of classical computers when space complexity is considered.