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Gottesman refs
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valbert4 committed Jan 21, 2025
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3 changes: 3 additions & 0 deletions codes/quantum/qubits/majorana/fermions.yml
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Admissible codewords include fermionic states, a subset of which is the Gaussian fermionic states \cite{arxiv:quant-ph/0108033,arxiv:quant-ph/0108010,arxiv:quant-ph/0404180,arxiv:2010.15518,arxiv:2409.11628}.
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Majorana analogues of common qubit noise channels have been developed \cite{arxiv:1806.01275}.
features:
encoders:
- 'A fermionic code using fermion-number eigenstates as codewords does not admit fermionic logical operators \cite{arxiv:2411.08955}.'
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2 changes: 1 addition & 1 deletion codes/quantum/qubits/qubits_into_qubits.yml
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The Clifford group is the normalizer of the \hyperref[topic:pauli]{Pauli group}.
The group consists of the Pauli group as well as elements that permute Pauli operators amongst themselves.
Up to any phases and Pauli strings, the group is equivalent to the symplectic group \(Sp(2n,\mathbb{Z}_2)\).
See Refs. \cite{arxiv:quant-ph/0304125,arxiv:0811.0898,arxiv:1310.6813,preset:GottesmanBook} for generators, relations, and normal form.
See Refs. \cite{arxiv:quant-ph/0304125,arxiv:0811.0898,arxiv:1310.6813,arxiv:1810.10259,preset:GottesmanBook} for generators, relations, and normal form.
The group cannot be expressed as a semidirect product of the Pauli and symplectic groups \cite{arxiv:2406.09951}.
There is a canonical form for Clifford circuits \cite{arxiv:2003.09412,arxiv:2408.15202}.
Restricting the group to real-valued elements yields the \textit{real Clifford group}.
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