  Distributed quantum applications impose requirements on the quality of the
quantum states that they consume. When analyzing architecture implementations
of quantum hardware, characterizing this quality forms an important factor in
understanding their performance. Fundamental characteristics of quantum
hardware lead to inherent tradeoffs between the quality of states and
traditional performance metrics such as throughput. Furthermore, any real-world
implementation of quantum hardware exhibits time-dependent noise that degrades
the quality of quantum states over time. Here, we study the performance of two
possible architectures for interfacing a quantum processor with a quantum
network. The first corresponds to the current experimental state of the art in
which the same device functions both as a processor and a network device. The
second corresponds to a future architecture that separates these two functions
over two distinct devices. We model these architectures as Markov chains and
compare their quality of executing quantum operations and producing entangled
quantum states as functions of their memory lifetimes, as well as the time that
it takes to perform various operations within each architecture. As an
illustrative example, we apply our analysis to architectures based on
Nitrogen-Vacancy centers in diamond, where we find that for present-day device
parameters one architecture is more suited to computation-heavy applications,
and the other for network-heavy ones. Besides the detailed study of these
architectures, a novel contribution of our work are several formulas that
connect an understanding of waiting time distributions to the decay of quantum
quality over time for the most common noise models employed in quantum
technologies. This provides a valuable new tool for performance evaluation
experts, and its applications extend beyond the two architectures studied in
this work.
