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valbert4 committed Mar 18, 2024
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8 changes: 4 additions & 4 deletions code_extra/bib_preset.yml
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Expand Up @@ -120,10 +120,10 @@ EricZin:
flm: >-
T. Ericson, and V. Zinoviev, eds. \emph{Codes on Euclidean spheres}. Elsevier, 2001.
splag:
_ready_formatted:
flm: >-
10.1007/978-1-4757-6568-7
# splag:
# _ready_formatted:
# flm: >-
# 10.1007/978-1-4757-6568-7

coxeter:
_ready_formatted:
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8 changes: 4 additions & 4 deletions codes/classical/bits/combinatorial_design.yml
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Expand Up @@ -44,13 +44,13 @@ relations:
- code_id: hamming743
detail: 'Weight-three and weight-four codewords of the \([7,4,3]\) Hamming code support combinatorial \(2\)-\((7,3,1)\) and \(2\)-\((7,4,2)\) designs, respectively \cite[Ex. 5.2.5]{preset:HKSdesigns}.'
- code_id: hamming
detail: 'Weight-three codewords of the \([2^r-1,2^r-r-1, 3]\) Hamming code support the Steiner system \(S(2,3,2^r-1)\) \cite[pg. 89]{preset:splag}.'
detail: 'Weight-three codewords of the \([2^r-1,2^r-r-1, 3]\) Hamming code support the Steiner system \(S(2,3,2^r-1)\) \cite[pg. 89]{doi:10.1007/978-1-4757-6568-7}.'
- code_id: extended_hamming
detail: 'Weight-four codewords of the \([2^r,2^r-r-1, 4]\) extended Hamming code support the Steiner system \(S(3,4,2^r)\) \cite[pg. 89]{preset:splag}.'
detail: 'Weight-four codewords of the \([2^r,2^r-r-1, 4]\) extended Hamming code support the Steiner system \(S(3,4,2^r)\) \cite[pg. 89]{doi:10.1007/978-1-4757-6568-7}.'
- code_id: golay
detail: 'The supports of the weight-seven (weight-eight) codewords of the (extended) Golay code support the Steiner system \(S(4,7,23)\) (\(S(5,6,12)\)) \cite[pg. 89]{preset:splag}. Its blocks are called octads.'
detail: 'The supports of the weight-seven (weight-eight) codewords of the (extended) Golay code support the Steiner system \(S(4,7,23)\) (\(S(5,6,12)\)) \cite[pg. 89]{doi:10.1007/978-1-4757-6568-7}. Its blocks are called octads.'
- code_id: ternary_golay
detail: 'The supports of the weight-five (weight-six) codewords of the (extended) ternary Golay code support the Steiner system \(S(4,5,11)\) (\(S(5,6,12)\)) \cite[pg. 89]{preset:splag}. Its blocks are called hexads.'
detail: 'The supports of the weight-five (weight-six) codewords of the (extended) ternary Golay code support the Steiner system \(S(4,5,11)\) (\(S(5,6,12)\)) \cite[pg. 89]{doi:10.1007/978-1-4757-6568-7}. Its blocks are called hexads.'
- code_id: perfect
detail: 'Perfect codes and combinatorial designs are related \cite{doi:10.1137/1016056}.'
- code_id: dual
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2 changes: 1 addition & 1 deletion codes/quantum/qubits/small_distance/small/stab_15_1_3.yml
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Expand Up @@ -22,7 +22,7 @@ description: |
features:
magic_scaling_exponent: 'Magic-state distillation scaling exponent \( \gamma= \log_d (n/k)\approx 2.464\) \cite[Box 2]{arxiv:1612.07330}\cite{arXiv:1703.07847}.'

transversal_gates: 'This code is the smallest qubit stabilizer code with a transversal gate outside of the Clifford group \cite{arxiv:2210.14066}.
transversal_gates: 'This code is the smallest qubit stabilizer code with a (strongly) transversal gate outside of the Clifford group \cite{arxiv:2210.14066}.
A transversal logical \(T^\dagger\) is implemented by applying a \(T\) gate on every qubit \cite{arXiv:quant-ph/9610011,arXiv:1403.2734,arXiv:1612.07330}.
A subsystem version yields a transversal \(CCZ\) gate \cite{arxiv:1304.3709}.
The code fails to have a transversal Hadamard gate; otherwise, it would violate the Eastin-Knill theorem.'
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4 changes: 2 additions & 2 deletions codes/quantum/qubits/small_distance/small/stab_8_3_2.yml
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Expand Up @@ -14,10 +14,10 @@ alternative_names:
- 'Smallest interesting color code'

description: |
Smallest 3D color code whose physical qubits lie on vertices of a cube and which admits a transversal CCZ gate.
Smallest 3D color code whose physical qubits lie on vertices of a cube and which admits a (weakly) transversal CCZ gate.
features:
transversal_gates: 'CZ gates between any two logical qubits \cite{arxiv:1912.10063} and CCZ gate \cite{arxiv:1503.02065,manual:{E. Campbell, “The smallest interesting colour code,” Online available at https://earltcampbell.com/2016/09/26/the-smallest-interesting-colour-code/ (2016), accessed on 2019-12-09.},arxiv:1912.10063}.'
transversal_gates: 'CZ gates between any two logical qubits \cite{arxiv:1912.10063} and (weakly) transversal CCZ gate \cite{arxiv:1503.02065,manual:{E. Campbell, “The smallest interesting colour code,” Online available at https://earltcampbell.com/2016/09/26/the-smallest-interesting-colour-code/ (2016), accessed on 2019-12-09.},arxiv:1912.10063}.'

fault_tolerance:
- 'CCZ gate can be distilled in a fault-tolerant manner \cite{arxiv:2007.07929}.'
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