From c7ea38179f515d0645b759d53809ebcf5847123a Mon Sep 17 00:00:00 2001 From: "Victor V. Albert" Date: Mon, 20 Nov 2023 14:37:56 -0500 Subject: [PATCH] subsystem refs --- codes/quantum/qubits/small_distance/small/shor_nine.yml | 2 ++ codes/quantum/qubits/small_distance/small/stab_4_2_2.yml | 2 +- codes/quantum/qubits/subsystem/bacon_shor.yml | 2 +- codes/quantum/qubits/subsystem/subsystem_stabilizer.yml | 4 ++++ .../qudits_galois/subsystem/galois_subsystem_stabilizer.yml | 2 ++ 5 files changed, 10 insertions(+), 2 deletions(-) diff --git a/codes/quantum/qubits/small_distance/small/shor_nine.yml b/codes/quantum/qubits/small_distance/small/shor_nine.yml index a4dab35bd..cea45fee1 100644 --- a/codes/quantum/qubits/small_distance/small/shor_nine.yml +++ b/codes/quantum/qubits/small_distance/small/shor_nine.yml @@ -70,6 +70,8 @@ relations: detail: 'The Shor code is a concatenation of a three-qubit bit-flip with a three-qubit phase-flip repetition code.' - code_id: quantum_concatenated detail: 'The Shor code is a concatenation of a three-qubit bit-flip with a three-qubit phase-flip repetition code.' + - code_id: bacon_shor + detail: 'The \([[9,1,3,3]]\) Bacon-Shor code reduces to the \hyperref[code:shor_nine]{Shor code} for a particular gauge configuration.' - code_id: qecc detail: 'The Shor code is the first quantum error-correcting code.' diff --git a/codes/quantum/qubits/small_distance/small/stab_4_2_2.yml b/codes/quantum/qubits/small_distance/small/stab_4_2_2.yml index 714d06ea3..f0e9d6d7b 100644 --- a/codes/quantum/qubits/small_distance/small/stab_4_2_2.yml +++ b/codes/quantum/qubits/small_distance/small/stab_4_2_2.yml @@ -69,7 +69,7 @@ relations: - code_id: rotated_surface detail: 'Various \([[4,1,2]]\) subcodes are small rotated planar codes \cite{arxiv:2006.03071,arxiv:1912.09410,arXiv:2102.06132,arXiv:2102.13071}.' - code_id: bacon_shor - detail: 'The error-detecting \([[4,1,2]]\) Bacon-Shor code, which reduces to a subcode of the \hyperref[code:stab_4_2_2]{\([[4,2,2]]\) code} for a particular gauge configuration, has gauge operators \(\{XXII,IIXX,ZIZI,IZIZ\}\).' + detail: 'The error-detecting \([[4,1,1,2]]\) Bacon-Shor code, which reduces to a subcode of the \hyperref[code:stab_4_2_2]{\([[4,2,2]]\) code} for a particular gauge configuration, has gauge operators \(\{XXII,IIXX,ZIZI,IZIZ\}\).' - code_id: quantum_parity detail: '\([[4,1,2]]\) subcode \(\{|\overline{00}\rangle,|\overline{01}\rangle\}\) is the smallest member of the sub-family of \([[m^2,1,m]]\) QPC codes.' - code_id: stab_5_1_3 diff --git a/codes/quantum/qubits/subsystem/bacon_shor.yml b/codes/quantum/qubits/subsystem/bacon_shor.yml index 1ddd01ea7..3f773995d 100644 --- a/codes/quantum/qubits/subsystem/bacon_shor.yml +++ b/codes/quantum/qubits/subsystem/bacon_shor.yml @@ -24,7 +24,7 @@ description: | \end{align} Syndrome extraction can be done by measuring these gauge operators, which are on fewer qubits and local. - The shortest error-correcting Bacon-Shor code is \([[9,1,3]]\) with four stabilizer generators + The shortest error-correcting Bacon-Shor code is \([[9,1,3,3]]\), with four stabilizer generators \begin{align} \begin{array}{ccccccccc} X & X & X & X & X & X & I & I & I\\ diff --git a/codes/quantum/qubits/subsystem/subsystem_stabilizer.yml b/codes/quantum/qubits/subsystem/subsystem_stabilizer.yml index 7fa580849..db2292638 100644 --- a/codes/quantum/qubits/subsystem/subsystem_stabilizer.yml +++ b/codes/quantum/qubits/subsystem/subsystem_stabilizer.yml @@ -57,6 +57,10 @@ relations: cousins: - code_id: qubit_stabilizer detail: 'Subsystem stabilizer codes reduce to stabilizer codes when there are no gauge qubits.' + - code_id: q-ary_bch + detail: 'BCH codes yield subsystem stabilizer codes via the subsystem extension of the Hermitian construction \cite[Exam. 1]{arxiv:quant-ph/0610153}.' + - code_id: reed_solomon + detail: 'Primitive RS codes yield subsystem stabilizer codes via the subsystem extension of the Hermitian construction \cite[Exam. 3]{arxiv:quant-ph/0610153}.' # Begin Entry Meta Information diff --git a/codes/quantum/qudits_galois/subsystem/galois_subsystem_stabilizer.yml b/codes/quantum/qudits_galois/subsystem/galois_subsystem_stabilizer.yml index 86f4449a8..6fd19c951 100644 --- a/codes/quantum/qudits_galois/subsystem/galois_subsystem_stabilizer.yml +++ b/codes/quantum/qudits_galois/subsystem/galois_subsystem_stabilizer.yml @@ -14,6 +14,8 @@ description: | Galois-qudit generalization of a subsystem qubit stabilizer code. Can be obtained by taking a Galois-qudit stabilizer code and assigning some of its logical qubits to be gauge qubits. +protection: | + Bounds on code parameters are formulated in Ref. \cite{arxiv:quant-ph/0610153}. relations: parents: