  We study a job shop scheduling problem for an automatized robot in a
high-throughput laboratory and a travelling salesperson problem with recently
proposed digitized counterdiabatic quantum optimization (DCQO) algorithms. In
DCQO, we find the solution of an optimization problem via an adiabatic quantum
dynamics, which is accelerated with counterdiabatic protocols. Thereafter, we
digitize the global unitary to encode it in a digital quantum computer. For the
job-shop scheduling problem, we aim at finding the optimal schedule for a robot
executing a number of tasks under specific constraints, such that the total
execution time of the process is minimized. For the traveling salesperson
problem, the goal is to find the path that covers all cities and is associated
with the shortest traveling distance. We consider both hybrid and pure versions
of DCQO algorithms and benchmark the performance against digitized quantum
annealing and the quantum approximate optimization algorithm (QAOA). In
comparison to QAOA, the DCQO solution is improved by several orders of
magnitude in success probability using the same number of two-qubit gates.
Moreover, we experimentally implement our algorithms on superconducting and
trapped-ion quantum processors. Our results demonstrate that circuit
compression using counterdiabatic protocols is amenable to current NISQ
hardware and can solve logistics scheduling problems, where other digital
quantum algorithms show insufficient performance.
