7 papers · 1 filter
The Structure of Circle Graph States
Frederik Hahn, Rose McCarty, Hendrik Poulsen Nautrup +1
Circle graph states are a structurally important family of graph states. The family's entanglement is a priori high enough to allow for universal measurement-based quantum computat…
The 27-qubit Counterexample to the LU-LC Conjecture is Minimal
Nathan Claudet
It was once conjectured that two graph states are local unitary (LU) equivalent if and only if they are local Clifford (LC) equivalent. This so-called LU-LC conjecture was disprove…
Local Equivalences of Graph States
Nathan Claudet
Graph states form a large family of quantum states that are in one-to-one correspondence with mathematical graphs. Graph states are used in many applications, such as measurement-b…
Deciding Local Unitary Equivalence of Graph States in Quasi-Polynomial Time
Nathan Claudet, Simon Perdrix
We describe an algorithm with quasi-polynomial runtime for deciding local unitary (LU) equivalence of graph states. The algorithm builds on a recent graphical…
Local equivalence of stabilizer states: a graphical characterisation
Nathan Claudet, Simon Perdrix
Stabilizer states form a ubiquitous family of quantum states that can be graphically represented through the graph state formalism. A fundamental property of graph states is that a…
Covering a Graph with Minimal Local Sets
Nathan Claudet, Simon Perdrix
Local sets, a graph structure invariant under local complementation, have been originally introduced in the context of quantum computing for the study of quantum entanglement withi…