We study the optimal scheduling of graph states in measurement-based quantum computation, establishing an equivalence between measurement schedules and path decompositions of graphs. We define the spatial cost of a measurement schedule based on the number of simultaneously active qubits and prove that an optimal measurement schedule corresponds to a path decomposition of minimal width. Our analysis shows that approximating the spatial cost of a graph is NP-hard, while for graphs with bounded spatial cost, we establish an efficient algorithm for computing an optimal measurement schedule.
@article{arxiv.2403.04126,
title = {Optimal Scheduling of Graph States via Path Decompositions},
author = {Samuel J. Elman and Jason Gavriel and Ryan L. Mann},
journal= {arXiv preprint arXiv:2403.04126},
year = {2025}
}