  Regardless of the domain, forecasting the future behaviour of a running
process instance is a question of interest for decision makers, especially when
multiple instances interact. Fostered by the recent advances in machine
learning research, several methods have been proposed to predict the next
activity, outcome or remaining time of a process automatically. Still, building
a model with high predictive power requires both - intrinsic knowledge of how
to extract meaningful features from the event log data and a model that
captures complex patterns in data. This work builds upon the recent progress in
inter-case Predictive Process Monitoring (PPM) and comprehensively benchmarks
the impact of inter-case features on prediction accuracy. Moreover, it includes
quantum machine learning models, which are expected to provide an advantage
over classical models with a scaling amount of feature dimensions. The
evaluation on real-world training data from the BPI challenge shows that the
inter-case features provide a significant boost by more than four percent in
accuracy and quantum algorithms are indeed competitive in a handful of feature
configurations. Yet, as quantum hardware is still in its early stages of
development, this paper critically discusses these findings in the light of
runtime, noise and the risk to overfit on the training data. Finally, the
implementation of an open-source plugin demonstrates the technical feasibility
to connect a state-of-the-art workflow engine such as Camunda to an IBM quantum
computing cloud service.
