Efficient Preparation of Graph States using the Quotient-Augmented Strong Split Tree
Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Graduate School of Science and Technology, Keio University（庆应义塾大学理工学部）；Department of Physics & Astronomy, University College London（伦敦大学学院物理与天文系）；National Institute of Informatics（信息学国立研究所）
Nicholas Connolly, Shin Nishio, Dan E. Browne, William John Munro, Kae Nemoto
备注：
18 pages + 4 page appendix, 10 figures, and 3 tables. Comments are welcome
Graph states are a key resource for measurement-based quantum computation and quantum networking, but state-preparation costs limit their practical use. Graph states related by local complement (LC) operations are equivalent up to single-qubit Clifford gates; one may reduce entangling resources by preparing a favorable LC-equivalent representative. However, exhaustive optimization over the LC orbit is not scalable. We address this problem using the split decomposition and its quotient-augmented strong split tree (QASST). For several families of distance-hereditary (DH) graphs, we use the QASST to characterize LC orbits and identify representatives with reduced controlled-Z count or preparation circuit depth. We also introduce a split-fuse construction for arbitrary DH graph states, achieving linear scaling with respect to entangling gates, time steps, and auxiliary qubits. Beyond the DH setting, we discuss a generalized divide-and-conquer split-fuse strategy and a simple greedy heuristic for generic graphs based on triangle enumeration. Together, these methods outperform direct implementations on sufficiently large graphs, providing a scalable alternative to brute-force optimization.
