From df24e35edfb7d4885b4910735f9ff48041caf127 Mon Sep 17 00:00:00 2001 From: Nathan Claudet Date: Thu, 11 Jun 2026 18:46:45 +0200 Subject: [PATCH 1/3] updated the state of the art for LU-LC equivalence, harmonisation and references "cluster state" was written instead of "graph state" everywhere but at one place, I replaced it to "cluster state" added reference to arxiv:1611.06938 for the 27-vertex counterexample to LU=LC, because the paper presents an equivalent but more elegant counterexample --- codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml b/codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml index ef7f78618..ebd3c8478 100644 --- a/codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml +++ b/codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml @@ -33,9 +33,9 @@ description: | Fault-tolerant MBQC based on topological error correction uses the three-dimensional RBH cluster state on the bcc lattice \cite{arxiv:quant-ph/0510135,arxiv:quant-ph/0610082}. Since they are stabilizer states, two cluster states are considered local-Clifford equivalent if they can be mapped into each other under a tensor product of arbitrary \hyperref[topic:clifford]{single-qubit Clifford} operations. - For graph states, any such equivalence can be generated by a finite sequence of local complementations (LCs), where local complementation about a vertex complements the induced subgraph on its neighborhood \cite{arxiv:quant-ph/0307130,arxiv:quant-ph/0308151}. + For cluster states, any such equivalence can be generated by a finite sequence of local complementations (LCs), where local complementation about a vertex complements the induced subgraph on its neighborhood \cite{arxiv:quant-ph/0307130,arxiv:quant-ph/0308151}. More generally, any two local-unitary equivalent cluster states can be mapped into each other by operations at some level of the hierarchy \cite{arxiv:2409.20183}, meaning that general tensor-product unitaries are not needed. - Cluster states on \(\leq 19\) qubits are LC equivalent if and only if they are local-unitary equivalent \cite{arxiv:2409.20183}, and there exists a cluster state on \(27\) qubits that is local-unitary but not LC equivalent \cite{arxiv:0709.1266,arxiv:0812.4625,arxiv:1910.03969}. + Cluster states on \(\leq 26\) qubits are LC equivalent if and only if they are local-unitary equivalent \cite{arxiv:2603.25219}, and there exists a pair of cluster states on \(27\) qubits that are local-unitary but not LC equivalent \cite{arxiv:0709.1266,arxiv:0812.4625,arxiv:1910.03969,arxiv:1611.06938}. Local complementation has been generalized to graphically characterize local unitary equivalence under local Clifford operations and, more generally, at other levels of the \term{Clifford hierarchy} \cite{arxiv:2409.20183}. protection: | From 60ba24eb1ffd14cd35818589dd4c1a93b986027d Mon Sep 17 00:00:00 2001 From: Nathan Claudet Date: Thu, 11 Jun 2026 19:14:42 +0200 Subject: [PATCH 2/3] Add user id --- users/users_db.yml | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/users/users_db.yml b/users/users_db.yml index 5b816fd99..f386aa38e 100644 --- a/users/users_db.yml +++ b/users/users_db.yml @@ -34,6 +34,12 @@ # +- user_id: NathanClaudet + name: 'Nathan Claudet' + gscholaruser: 'f7wBxrcAAAAJ' + githubusername: nathanclaudet + pageurl: 'nathanclaudet.fr' + - user_id: ArdaAydin name: 'Arda Aydin' gscholaruser: B1IwuFcAAAAJ From 47e7f765994e8ca6fd68b3df6f5ad8e5d235e936 Mon Sep 17 00:00:00 2001 From: Nathan Claudet Date: Thu, 11 Jun 2026 19:23:11 +0200 Subject: [PATCH 3/3] changelog --- codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml | 2 ++ 1 file changed, 2 insertions(+) diff --git a/codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml b/codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml index ebd3c8478..c36016d7a 100644 --- a/codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml +++ b/codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml @@ -177,6 +177,8 @@ relations: _meta: # Change log - most recent first changelog: + - user_id: NathanClaudet + date: '2026-06-11' - user_id: VictorVAlbert date: '2026-06-08' - user_id: DavidTStephen