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valbert4 committed Mar 28, 2024
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2 changes: 1 addition & 1 deletion codes/quantum/qubits/small_distance/small/stab_10_1_2.yml
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- 'A fault-tolerant universal gate set can be done via code switching between the Steane code and the \([[10,1,2]]\) code \cite{arxiv:2403.13732}.'

realizations:
- 'Fault-tolerant universal gate set via code switching between the Steane code and the \([[10,1,2]]\) code \cite{arxiv:2403.13732}.'
- 'Trapped-ion devices: fault-tolerant universal gate set via code switching between the Steane code and the \([[10,1,2]]\) code on a device from the Monz group \cite{arxiv:2403.13732}.'

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2 changes: 1 addition & 1 deletion codes/quantum/qubits/small_distance/small/stab_6_4_2.yml
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Expand Up @@ -12,7 +12,7 @@ introduced: '\cite{arxiv:quant-ph/9605021,arxiv:quant-ph/9702029,arxiv:quant-ph/

description: |
Error-detecting six-qubit code with rate \(1/3\) whose codewords are cat/GHz states.
Its stabilizer generators are \(XXXXXX\) and \(ZZZZZZ\).
A set of stabilizer generators is \(XXXXXX\) and \(ZZZZZZ\).
It is the unique code for its parameters, up to local equivalence \cite[Tab. III]{arxiv:quant-ph/9608006v5}.
Concatenations of this code with itself yield the \([[6^r,4^r,2^r]]\) level-\(r\) \textit{many-hypercube} code \cite{arxiv:2403.16054}.
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protection: 'The Steane code is a distance 3 code. It detects errors on 2 qubits, corrects errors on 1 qubit.'

realizations:
- 'Trapped-ion qubits: seven-qubit device in Blatt group \cite{arXiv:1403.5426}.
- 'Trapped-ion devices: seven-qubit device in Blatt group \cite{arXiv:1403.5426}.
Ten-qubit QCCD device by Quantinuum \cite{arXiv:2107.07505} realizing repeated syndrome extraction, real-time look-up-table decoding (yielding lower logical SPAM error rate than physical SPAM), and non-fault-tolerant magic-state distillation (see APS Physics Synopsis \cite{doi:10.1103/Physics.14.184}).
Fault-tolerant universal two-qubit gate set using T injection by Monz group \cite{arxiv:2111.12654}.
Logical CNOT gate and Bell-pair creation between two logical qubits (yielding a logical fidelity higher than physical), including rounds of correction and fault-tolerant primitives such as flag qubits and pieceable fault tolerance, on a 20-qubit device by Quantinuum \cite{arxiv:2208.01863}; logical fidelity interval of the combined preparation-CNOT-measurement procedure was higher than that of the unencoded physical qubits.
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