Speed Limits for Annealing in Open Quantum Systems

In quantum annealing, an initial state is driven toward a final state by specifying a control function referred to as the "annealing schedule." Speed limits can provide lower bounds for the minimum time required for an anneal, and only recently has a schedule-independent speed limit been derived in the closed quantum system setting. Here we derive a similar speed limit for annealing in the open quantum system setting, i.e. quantum dynamics in the presence of dissipation. In incorporating the nonunitary effects of an environment on the system, this derivation generalizes the previous closed quantum result while maintaining the schedule-independence absent from other bounds in the literature. We then analyze the interplay between coherent control and dissipation in simplified examples, demonstrating that our bound captures key scaling behavior with respect to the strength of the dissipator. We also explore numerically the scaling of our bound with respect to system size for thermal state preparation of an Ising model.

SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525. SAND2025-13361A.