Optimized quantum solutions for vehicle routing problems

Vehicle routing and scheduling are examples of transportation-network operational tasks that can be cast as optimization problems. Solving these problems becomes increasingly challenging with more vehicles or larger networks, as well as when constraints such as vehicle capacity are considered. Existing literature shows that quantum algorithms like QAOA can be used to solve certain transport problems, suggesting that quantum computers may be capable of tackling these applications in the future. However, gate errors and decoherence processes in today’s quantum hardware severely limit the performance of even small-scale demonstrations. We address this issue by constructing algorithms with tailored gates that are robust against typical hardware imperfections. We perform simulations of QAOA for the Mobility as a Service (MaaS) problem with varying network sizes using a pulse-level description of gates and realistic noise models. We probe performance bounds in the presence of different errors including incoherent T1 processes, coherent over-rotation errors, and coherent dephasing, as are common on superconducting quantum computers. Finally, we discuss the results from the standard and robust MaaS QAOA algorithms and compare their performance for each type of error.