Passcode: please contact albertrico23 at gmail.com
seminar
Speaker: Adam Burchard (Amsterdam)
Abstract
Graph states are a cornerstone of quantum information theory. Existing invariants characterizing the local Clifford (LC) equivalence classes of graph states are however computationally inefficient and call for a more tractable approach. This paper introduces the foliage partition, an easy-to-compute LC-invariant of computational complexity O(n^3) 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.
