  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.
