Work

The Foliage Partition: An Easy-to-Compute LC-Invariant for Graph States

Year: 2025

Type: article

Abstract: This paper introduces the foliage partition, an easy-to-compute LC-invariant for graph states, of computational complexity O(n3) in the number of qubits. Inspired by the foliage of a graph, our invariant has a natural graphical representation in terms of leaves, axils, and twins. It captures both, the connection structure of a graph and the 2 -body marginal properties of the associated graph state. We relate the foliage partition to the size of LC-orbits and use it to bound the number of LC-automorphisms of graphs. We also show the invariance of the foliage partition when generalized to weighted graphs and qudit graph states.

Source: Quantum

DOI: 10.22331/q-2025-04-24-1720

Authors: Adam Burchardt, Frederik Hahn

Institutions: Centrum Wiskunde & Informatica, QuSoft, University of Amsterdam, Technische Universität Berlin, Freie Universität Berlin

Language: English

Topic: Quantum Information and Cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $215

Funders: European Commission, Deutsche Forschungsgemeinschaft, Nederlandse Organisatie voor Wetenschappelijk Onderzoek