Efficient Preparation of Graph States using the Quotient-Augmented Strong Split Tree

2026-03-24

AI Summary

The high resource cost of preparing graph states hinders their application in measurement-based quantum computing and quantum networks. This work addresses this challenge for distance-hereditary graphs by proposing a split-and-fuse construction method based on quotient-augmented strong split trees (QASST). By integrating local complementation equivalence analysis with split decomposition, the approach yields an efficient preparation scheme featuring low circuit depth and minimal entangling gates, which is further generalized to arbitrary graph structures. A divide-and-conquer strategy combined with a triangle-enumeration heuristic is introduced to substantially reduce the number of controlled-Z gates and overall circuit depth. Empirical evaluations across multiple graph families demonstrate that the method outperforms direct implementation, achieving linear resource scaling and favorable scalability.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

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.

Problem

• graph states
• local complementation
• state preparation
• scalability
• entangling gates

Innovation

• graph states
• local complementation
• split decomposition
• quotient-augmented strong split tree
• distance-hereditary graphs