Efficient Preparation of Graph States using the Quotient-Augmented Strong Split Tree
This work addresses scalability limitations in quantum state preparation, offering practical improvements for quantum computing and networking applications, though it appears incremental with domain-specific focus.
The paper tackles the problem of efficiently preparing graph states for quantum computation by reducing entangling resources through local complement equivalence. It introduces methods using split decomposition and split-fuse construction that achieve linear scaling for certain graph families and outperform direct implementations on large graphs.
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.