A Time/Utility Function for Scheduling Quantum Applications

We introduce the concept of quantum time/utility functions (TUF) to enable effective scheduling decisions when executing quantum applications. The quantum TUF captures the relationship between the projected execution quality of an application and its execution time, enabling real-time, noise-aware scheduling. We consider different strategies for computing the TUF while addressing practical constraints, and introduce the Haar TUF, a simple, application-agnostic formula for random circuits. We implement the Haar TUF for a delegated quantum computing application, where we showcase both its ability to capture meaningful behaviour and its limitations in describing application-specific instances.