Efficient Preparation of Graph States using the Quotient-Augmented Strong Split Tree
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911555425140736 |
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| author | Connolly, Nicholas Nishio, Shin Browne, Dan E. Munro, William John Nemoto, Kae |
| author_facet | Connolly, Nicholas Nishio, Shin Browne, Dan E. Munro, William John Nemoto, Kae |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_23892 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient Preparation of Graph States using the Quotient-Augmented Strong Split Tree Connolly, Nicholas Nishio, Shin Browne, Dan E. Munro, William John Nemoto, Kae Quantum Physics Discrete Mathematics Combinatorics 05C76(Primary) 05C30, 05C83, 05C90 (Secondary) G.2.1; G.2.2; F.2.1 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. |
| title | Efficient Preparation of Graph States using the Quotient-Augmented Strong Split Tree |
| topic | Quantum Physics Discrete Mathematics Combinatorics 05C76(Primary) 05C30, 05C83, 05C90 (Secondary) G.2.1; G.2.2; F.2.1 |
| url | https://arxiv.org/abs/2603.23892 |