From bf2f4f9019122b45fbc06a3b8fda37f6306009f2 Mon Sep 17 00:00:00 2001 From: sdoygb Date: Thu, 13 Aug 2026 17:33:53 +0800 Subject: [PATCH 1/3] Add self-orthogonal CSS(RM(r,m),RM(r,m)) family and certified distance to quantum_reed_muller entry --- .../quantum/qubits/stabilizer/rm/quantum_reed_muller.yml | 9 +++++++++ users/users_db.yml | 5 +++++ 2 files changed, 14 insertions(+) diff --git a/codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml b/codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml index 391d810ad..c4ede8950 100644 --- a/codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml +++ b/codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml @@ -20,6 +20,9 @@ description: | Non-CSS codes can be derived from such codes by modifying the \(X\)-type stabilizers \cite{arxiv:quant-ph/9608026}. + CSS codes formed from a single RM code are also possible: CSS\((\text{RM}(r,m), \text{RM}(r,m))\), valid whenever \(2r < m-1\) (so that \(\text{RM}(r,m) \subset \text{RM}(r,m)^{\perp} = \text{RM}(m-r-1,m)\)), has parameters \([[2^m, 2^m - 2\sum_{j=0}^{r} {m \choose j}, 2^{r+1}]]\). + Its distance \(2^{r+1}\) follows from the RM minimum-weight theorem \cite[Ch. 13]{preset:MacSlo}: \(X\)-type logicals are cosets of \(C \setminus C^{\perp}\), whose minimum weight is that of \(\text{RM}(m-r-1,m)\), i.e., \(2^{m-(m-r-1)} = 2^{r+1}\); \(Z\)-type logicals follow by symmetry. + protection: 'Detects errors on \(d-1\) qubits, corrects errors on \(\left\lfloor (d-1)/2 \right\rfloor\) qubits.' features: @@ -33,6 +36,10 @@ features: rate: 'Dimension is \(k = 2^r - {r \choose t} + 2 \sum_{i=0}^{t-1} {r \choose i}\). CSS codes formed from RM codes achieve channel capacity on erasure channels \cite{doi:10.1109/ISIT.2016.7541599}.' + distance: + - 'CSS codes formed from a single RM code, CSS\((\text{RM}(r,m),\text{RM}(r,m))\) with \(2r < m-1\), have distance \(d = 2^{r+1}\) \cite[Ch. 13]{preset:MacSlo}.' + - 'The distance of this family admits a certificate that can be checked without enumerating the exponentially many error patterns: for \(r \geq 1\), column-distinctness of the RM check matrix rules out weight-2 logicals; the RM minimum-weight theorem \cite[Ch. 13]{preset:MacSlo} rules out weights \(3,\ldots,2^{r+1}-1\); and indicator vectors of affine \((r+1)\)-flats are weight-\(2^{r+1}\) vectors in \(\text{RM}(m-r-1,m)\setminus\text{RM}(r,m)\), saturating the bound.' + fault_tolerance: - 'Gate switching protocol for universal computation \cite{arxiv:1403.2734}.' - 'Fault-tolerant universal computation can be achieved via \hyperref[topic:code-switching]{code switching} between the \([[127,1,15]]\) self-dual doubly even punctured quantum RM code and the \([[127,1,7]]\) triply even punctured quantum RM code \cite{arxiv:2410.23263}.' @@ -62,6 +69,8 @@ relations: _meta: # Change log - most recent first changelog: + - user_id: sdoygb + date: '2026-08-13' - user_id: VictorVAlbert date: '2026-06-08' - user_id: VictorVAlbert diff --git a/users/users_db.yml b/users/users_db.yml index 3ab0e5227..92c16a5be 100644 --- a/users/users_db.yml +++ b/users/users_db.yml @@ -716,3 +716,8 @@ githubusername: LeonidPryadko pageurl: "https://faculty.ucr.edu/~leonid/" avatarurl: "builtinavatar:LeonidPryadko" + +- user_id: sdoygb + name: 'Ouyang Guobin' + githubusername: sdoygb + From 9dbd64d43aa16c7756f36bb4c778a66bf07d13d1 Mon Sep 17 00:00:00 2001 From: sdoygb Date: Thu, 13 Aug 2026 18:35:31 +0800 Subject: [PATCH 2/3] Remove features.distance key (violates code_features schema); distance statement kept in description --- codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml | 3 --- 1 file changed, 3 deletions(-) diff --git a/codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml b/codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml index c4ede8950..d575bfa65 100644 --- a/codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml +++ b/codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml @@ -36,9 +36,6 @@ features: rate: 'Dimension is \(k = 2^r - {r \choose t} + 2 \sum_{i=0}^{t-1} {r \choose i}\). CSS codes formed from RM codes achieve channel capacity on erasure channels \cite{doi:10.1109/ISIT.2016.7541599}.' - distance: - - 'CSS codes formed from a single RM code, CSS\((\text{RM}(r,m),\text{RM}(r,m))\) with \(2r < m-1\), have distance \(d = 2^{r+1}\) \cite[Ch. 13]{preset:MacSlo}.' - - 'The distance of this family admits a certificate that can be checked without enumerating the exponentially many error patterns: for \(r \geq 1\), column-distinctness of the RM check matrix rules out weight-2 logicals; the RM minimum-weight theorem \cite[Ch. 13]{preset:MacSlo} rules out weights \(3,\ldots,2^{r+1}-1\); and indicator vectors of affine \((r+1)\)-flats are weight-\(2^{r+1}\) vectors in \(\text{RM}(m-r-1,m)\setminus\text{RM}(r,m)\), saturating the bound.' fault_tolerance: - 'Gate switching protocol for universal computation \cite{arxiv:1403.2734}.' From c4ab75cb19abeb30e825a824d97a70787754b0b0 Mon Sep 17 00:00:00 2001 From: sdoygb Date: Thu, 13 Aug 2026 18:36:01 +0800 Subject: [PATCH 3/3] tidy: remove stray blank line --- codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml | 1 - 1 file changed, 1 deletion(-) diff --git a/codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml b/codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml index d575bfa65..da420c460 100644 --- a/codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml +++ b/codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml @@ -36,7 +36,6 @@ features: rate: 'Dimension is \(k = 2^r - {r \choose t} + 2 \sum_{i=0}^{t-1} {r \choose i}\). CSS codes formed from RM codes achieve channel capacity on erasure channels \cite{doi:10.1109/ISIT.2016.7541599}.' - fault_tolerance: - 'Gate switching protocol for universal computation \cite{arxiv:1403.2734}.' - 'Fault-tolerant universal computation can be achieved via \hyperref[topic:code-switching]{code switching} between the \([[127,1,15]]\) self-dual doubly even punctured quantum RM code and the \([[127,1,7]]\) triply even punctured quantum RM code \cite{arxiv:2410.23263}.'