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Gottesman refs
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valbert4 committed Jan 21, 2025
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Expand Up @@ -29,7 +29,7 @@ features:
general_gates:
- 'General gates are performed using two-body Hamiltonian rotations \cite{arxiv:quant-ph/0210072}.'
- 'Bosonic gates include beamsplitters \cite{doi:10.1038/s41467-023-41104-0} and Kerr nonlinearities. Universal quantum computing can be achieved using the KLM protocol \cite{doi:10.1038/35051009} with only linear optical elements and photon detectors.'
- 'Bang-bang dynamical decoupling protocol \cite{arxiv:quant-ph/0210072}.'
- 'Dynamical-decoupling protocols \cite{arxiv:quant-ph/0210072,arxiv:0712.1480}.'
- 'A probabilistic CZ gate via a non-linear sign-shift gate, which transforms the Fock states \( \alpha|0\rangle+\beta|1\rangle+\gamma|2\rangle\) into \(\alpha|0\rangle+\beta|1\rangle-\gamma|2\rangle \), followed by measurement \cite{arxiv:quant-ph/0307015}.'
- 'Error-detecting \(CCZ\) and \(cSWAP\) gates using three-level ancilla \cite{arxiv:2212.11196}.'

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2 changes: 1 addition & 1 deletion codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml
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# So information is effectively stored near the boundary of the 2D slice. Measuring slice by slice will teleport it to the next slice.

realizations:
- 'Quantum compututation with cluster states has been realized in the polarizations of photons \cite{arxiv:quant-ph/0503126,arxiv:0906.2233}.'
- 'Quantum computation with cluster states has been realized in the polarizations of photons \cite{arxiv:quant-ph/0503126,arxiv:0906.2233}.'

notes:
- 'See Refs. \cite{arxiv:quant-ph/0602096,doi:10.1002/9783527635283} for a review of cluster states and their applications.'
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2 changes: 1 addition & 1 deletion codes/quantum/qubits/stabilizer/qubit_stabilizer.yml
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Expand Up @@ -42,7 +42,7 @@ description: |
\end{table}
Two qubit stabilizer codes codes are \textit{equivalent} if the codespace of one code can be mapped into that of the other under a tensor product of elements of the \hyperref[topic:clifford]{single-qubit Clifford group} and a qubit permutation.
Equivalence under single-qubit Clifford operations is not the same as the equivalence under a tensor product of arbitrary single-qubit unitary operations \cite{arxiv:0709.1266}.
Equivalence under single-qubit Clifford operations is not the same as equivalence under a tensor product of arbitrary single-qubit unitary operations \cite{arxiv:0709.1266} (see also Ref. \cite{arxiv:0707.4000} about this false LC-LU conjecture).
A qubit stabiilzer code is \textit{decomposable} if there exists a permutation that maps the stabilizer group into a tensor product of two stabilizer groups acting on disjoint sets of qubits.
\subsection{Code representations}
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4 changes: 4 additions & 0 deletions codes/quantum/qudits_galois/stabilizer/css/galois_css.yml
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An \([[n,k,d]]_q\) CSS code can be propagated to an \([[n-2,k,d-1]]_q\) code \cite{arxiv:2208.05353}.
features:
encoders:
- 'Fault-tolerant encoding \cite{arxiv:0712.3223}.'

relations:
parents:
- code_id: galois_true_stabilizer
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