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arXiv · 2403.04126

Optimal Scheduling of Graph States via Path Decompositions

Samuel J. Elman·Jason Gavriel·Ryan L. Mann
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Abstract

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 $\textsf{NP}$-hard, while for graphs with bounded spatial cost, we establish an efficient algorithm for computing an optimal measurement schedule.

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Samuel J. Elman, Jason Gavriel, Ryan L. Mann. 2024-03-07. Optimal Scheduling of Graph States via Path Decompositions. https://doi.org/10.1103/physreva.111.012627

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