Worst Case Execution Time (WCET) are important data elements to feed any safety and schedulability analysis of safety critical real-time systems for which any default can jeopardize the life of the system or even threaten the life of human beings. WCET is particularly important in the context of real-time autonomous systems (e.g. robotics, self-driving cars). The problem of computing safe upper bonds of execution time is well known, but the challenge is also to have them tight to avoid over-engineering of real-time systems and mastering their costs. But this challenge is still not fully reached and moreover tends to pursue a moving target as the hardware and software architecture of real-time systems also moves forward (pipelines, cache memories, multi-cores, etc.).
The goal of this PhD Thesis is to explore what quantum computing can do to simplify the problem, bring for more precision and capacity of analysis of these issues. This work will be supported by existing state of the art, and could explore a bit further than the strict domain of usual WCET analysis.
Depending on the candidate profile, the subject will bend more towards either implementation aspects - How to best implement a WCET algorithm onto an available quantum simulator (eg. QX simulator, Quantum Learning Machine), or computational complexity theory aspects.