  Quantum processing units (QPUs) are currently exclusively available from
cloud vendors. However, with recent advancements, hosting QPUs is soon possible
everywhere. Existing work has yet to draw from research in edge computing to
explore systems exploiting mobile QPUs, or how hybrid applications can benefit
from distributed heterogeneous resources. Hence, this work presents an
architecture for Quantum Computing in the edge-cloud continuum. We discuss the
necessity, challenges, and solution approaches for extending existing work on
classical edge computing to integrate QPUs. We describe how warm-starting
allows defining workflows that exploit the hierarchical resources spread across
the continuum. Then, we introduce a distributed inference engine with hybrid
classical-quantum neural networks (QNNs) to aid system designers in
accommodating applications with complex requirements that incur the highest
degree of heterogeneity. We propose solutions focusing on classical layer
partitioning and quantum circuit cutting to demonstrate the potential of
utilizing classical and quantum computation across the continuum. To evaluate
the importance and feasibility of our vision, we provide a proof of concept
that exemplifies how extending a classical partition method to integrate
quantum circuits can improve the solution quality. Specifically, we implement a
split neural network with optional hybrid QNN predictors. Our results show that
extending classical methods with QNNs is viable and promising for future work.
