From 9528562558863e33f88e8a78a2e49a15979b9b44 Mon Sep 17 00:00:00 2001 From: "Victor V. Albert" Date: Sat, 30 Mar 2024 09:36:53 -0400 Subject: [PATCH] ~ --- .../qubits/nonstabilizer/cws/non_stabilizer.yml | 6 +++--- .../nonstabilizer/cws/quantum_goethals_preparata.yml | 12 +++++++----- .../quantum/qubits/nonstabilizer/cws/qubit_5_6_2.yml | 2 +- .../nonstabilizer/galois_non_stabilizer.yml | 4 ++-- 4 files changed, 13 insertions(+), 11 deletions(-) diff --git a/codes/quantum/qubits/nonstabilizer/cws/non_stabilizer.yml b/codes/quantum/qubits/nonstabilizer/cws/non_stabilizer.yml index 5f46e1e3e..d8adefa09 100644 --- a/codes/quantum/qubits/nonstabilizer/cws/non_stabilizer.yml +++ b/codes/quantum/qubits/nonstabilizer/cws/non_stabilizer.yml @@ -8,7 +8,7 @@ physical: qubits logical: qubits name: 'Union stabilizer code' -introduced: '\cite{arXiv:quant-ph/9703016,arxiv:quant-ph/0210097,arxiv:0801.2144}' +introduced: '\cite{arXiv:quant-ph/9703002,arXiv:quant-ph/9703016,arxiv:quant-ph/9710031,arxiv:quant-ph/0210097,arxiv:0801.2144}' # First ref discusses unions of general codes alternative_names: @@ -16,9 +16,9 @@ alternative_names: # arxiv:quant-ph/0210097 description: | - Extension of stabilizer codes whose codespace consists of a direct sum of a stabilizer codespace and one or more of that stabilizer code's error spaces. + A qubit code whose codespace consists of a direct sum of a qubit stabilizer codespace and one or more of that stabilizer code's error spaces. - Union stabilizer codes constructed in Ref. \cite{arxiv:quant-ph/0210097} include \(((33, 155, 3))\), \(((15, 8, 3))\). + Union stabilizer codes constructed in Ref. \cite{arxiv:quant-ph/0210097} include the \(((33, 155, 3))\) and \(((15, 8, 3))\) codes. features: diff --git a/codes/quantum/qubits/nonstabilizer/cws/quantum_goethals_preparata.yml b/codes/quantum/qubits/nonstabilizer/cws/quantum_goethals_preparata.yml index 758c56418..4796d0043 100644 --- a/codes/quantum/qubits/nonstabilizer/cws/quantum_goethals_preparata.yml +++ b/codes/quantum/qubits/nonstabilizer/cws/quantum_goethals_preparata.yml @@ -16,18 +16,20 @@ description: | They can be viewed as union stabilizer codes constructed from the codespace of a \([[2^m,2^m-7m+3,8]]\) code (which itself is obtained from the Steane enlargement construction) and the coset representatives used to obtain the Goethals and Preparata codes \cite[Thm. 10.3]{doi:10.1017/CBO9781139034807.012}. The Goethals and Preparata codes can each be used to obtain families of union stabilizer codes with distance 8 and 6, respectively \cite{arxiv:0801.2144}. - Plugging the \(\mathbb{Z}_4\) versions of these codes into the modular-qudit CSS construction and applying the Gray map yields qubit code families with similar parameters \cite{manual:{S. Ling and P. Sole. 2008. Nonadditive quantum codes from Z4-codes. http://hal.archives-ouvertes.fr/hal-00338309/fr/.}}. + A construction using the \(\mathbb{Z}_4\) versions of these codes and the Gray map yields qubit code families with similar parameters \cite{manual:{S. Ling and P. Sole. 2008. Nonadditive quantum codes from Z4-codes. http://hal.archives-ouvertes.fr/hal-00338309/fr/.}}. relations: parents: - - code_id: cws + - code_id: non_stabilizer cousins: - code_id: goethals + detail: 'The \(((2^m,2^{2^m−5m+1},8))\) Goethals-Preparata code is constructed using the classical Goethals and Preparata codes \cite{arXiv:0801.2144,arxiv:0801.2150}. + A construction using the \(\mathbb{Z}_4\) versions of the Goethals and Preparata codes and the Gray map yields qubit code families with similar parameters \cite{manual:{S. Ling and P. Sole. 2008. Nonadditive quantum codes from Z4-codes. http://hal.archives-ouvertes.fr/hal-00338309/fr/.}}.' - code_id: preparata + detail: 'The \(((2^m,2^{2^m−5m+1},8))\) Goethals-Preparata code is constructed using the classical Goethals and Preparata codes \cite{arXiv:0801.2144,arxiv:0801.2150}. + A construction using the \(\mathbb{Z}_4\) versions of the Goethals and Preparata codes and the Gray map yields qubit code families with similar parameters \cite{manual:{S. Ling and P. Sole. 2008. Nonadditive quantum codes from Z4-codes. http://hal.archives-ouvertes.fr/hal-00338309/fr/.}}.' - code_id: gray - detail: 'Plugging the \(\mathbb{Z}_4\) versions of the Kerdock and Preparate codes into the modular-qudit CSS construction and applying the Gray map yields qubit code families with similar parameters as the \(((2^m,2^{2^m−5m+1},8))\) Goethals-Preparata codes \cite{manual:{S. Ling and P. Sole. 2008. Nonadditive quantum codes from Z4-codes. http://hal.archives-ouvertes.fr/hal-00338309/fr/.}}.' - - code_id: qudit_css - detail: 'Plugging the \(\mathbb{Z}_4\) versions of the Kerdock and Preparate codes into the modular-qudit CSS construction and applying the Gray map yields qubit code families with similar parameters as the \(((2^m,2^{2^m−5m+1},8))\) Goethals-Preparata codes \cite{manual:{S. Ling and P. Sole. 2008. Nonadditive quantum codes from Z4-codes. http://hal.archives-ouvertes.fr/hal-00338309/fr/.}}.' + detail: 'A construction using the \(\mathbb{Z}_4\) versions of the Goethals and Preparata codes and the Gray map yields qubit code families with similar parameters as the \(((2^m,2^{2^m−5m+1},8))\) Goethals-Preparata code \cite{manual:{S. Ling and P. Sole. 2008. Nonadditive quantum codes from Z4-codes. http://hal.archives-ouvertes.fr/hal-00338309/fr/.}}.' diff --git a/codes/quantum/qubits/nonstabilizer/cws/qubit_5_6_2.yml b/codes/quantum/qubits/nonstabilizer/cws/qubit_5_6_2.yml index 1f3777a7b..5cbeed5f5 100644 --- a/codes/quantum/qubits/nonstabilizer/cws/qubit_5_6_2.yml +++ b/codes/quantum/qubits/nonstabilizer/cws/qubit_5_6_2.yml @@ -24,7 +24,7 @@ relations: detail: 'The \(((5,6,2))\) code is the \(((n,1+n(q-1),2))_q\) union stabilizer code for \(n=5\) and \(q=2\) \cite{arxiv:quant-ph/0210097}.' - code_id: quantum_cyclic - code_id: non_stabilizer - detail: 'The six-qubit CWS code is a union stabilizer code \cite{arxiv:quant-ph/0210097}.' + detail: 'The six-qubit CWS code is a union stabilizer code \cite{arXiv:quant-ph/9703002,arxiv:quant-ph/0210097}.' # Begin Entry Meta Information diff --git a/codes/quantum/qudits_galois/nonstabilizer/galois_non_stabilizer.yml b/codes/quantum/qudits_galois/nonstabilizer/galois_non_stabilizer.yml index 01fe29aa0..cf30cbd4e 100644 --- a/codes/quantum/qudits_galois/nonstabilizer/galois_non_stabilizer.yml +++ b/codes/quantum/qudits_galois/nonstabilizer/galois_non_stabilizer.yml @@ -8,7 +8,7 @@ physical: galois logical: galois name: 'Galois-qudit union stabilizer code' -introduced: '\cite{arXiv:quant-ph/9703016,arxiv:quant-ph/0210097,arxiv:0801.2144}' +introduced: '\cite{arXiv:quant-ph/9703002,arXiv:quant-ph/9703016,arxiv:quant-ph/9710031,arxiv:quant-ph/0210097,arxiv:0801.2144}' # First ref discusses unions of general codes alternative_names: @@ -16,7 +16,7 @@ alternative_names: # arxiv:quant-ph/0210097 description: | - Extension of Galois-qudit stabilizer codes whose codespace consists of a direct sum of a Galois-qudit stabilizer codespace and one or more of that stabilizer code's error spaces. + A Galois-qudit code whose whose codespace consists of a direct sum of a Galois-qudit stabilizer codespace and one or more of that stabilizer code's error spaces. The projection onto a stabilizer code is proportional to an equal sum over all elements of the stabilizer group \(\mathsf{S}\). Union stabilizer codes generalize stabilizer codes by modifying the code projection with elements of a subset \(\mathsf{B}\subset\mathsf{S}\) called the \textit{Fourier description} \cite[Thm. 2.7]{arxiv:quant-ph/0210097}.