Pseudo-polynomial algorithms for bounded instances

Develop pseudo-polynomial algorithms for the QEC-aware spatio-temporal path optimization problem in suitably bounded instances, leveraging the fact that the established NP-hardness result does not preclude such approaches.

Background

The paper proves that finding a minimum-cost feasible strategy for QEC-protected direct transmission is NP-hard, even for a single request with a fixed protection scheme. The reduction establishes hardness through constrained path selection, using zero physical noise, rather than through the nonlinear logical-error evolution specific to the quantum model.

Because the hardness result is a worst-case complexity result, it does not rule out pseudo-polynomial algorithms for instances whose relevant numerical parameters—such as cost, propagation-time, or constraint budgets—are suitably bounded. The paper identifies this algorithmic possibility but does not develop such an approach; instead, it proceeds with a discretized label-correcting framework that provides relaxed feasibility guarantees.