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TamaraCopilot
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CRAWLER
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
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codes/classical/spherical/polytope/2d/polygon.yml

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name: 'Polygon code'
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description: |
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Spherical \((1,q,4\sin^2 \frac{\pi}{q})\) code for any \(q\geq1\) whose codewords are the vertices of a \(q\)-gon. Special cases include the line segment (\(q=2\)), triangle (\(q=3\)), square (\(q=4\)), pentagon (\(q=5\)), and hexagon (\(q=6\)).
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Spherical \((1,q,4\sin^2 \frac{\pi}{q})\) code for any \(q\geq2\) whose codewords are the vertices of a \(q\)-gon. Special cases include the line segment (\(q=2\)), triangle (\(q=3\)), square (\(q=4\)), pentagon (\(q=5\)), and hexagon (\(q=6\)).
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\begin{figure}
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\includegraphics{polygon.svg}

codes/quantum/qubits/stabilizer/qldpc/balanced_product/tensor/singlesector/hypergraph/quantum_expander.yml

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- 'Dimensional jump protocols between various quantum expander codes \cite{arxiv:2510.06760}.'
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decoders:
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- 'Small set-flip linear-time decoder, which corrects \hyperref[topic:asymptotics]{order} \(\Omega(n^{1/2})\) adversarial errors \cite{arxiv:1504.00822}. The decoder has been generalized to hypergraph products of 3 or more expander codes \cite{arxiv:2510.06760}'
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- 'Small set-flip linear-time decoder, which corrects \hyperref[topic:asymptotics]{order} \(\Omega(n^{1/2})\) adversarial errors \cite{arxiv:1504.00822}. The decoder has been generalized to hypergraph products of 3 or more expander codes \cite{arxiv:2510.06760}.'
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- 'Log-time decoder \cite{arxiv:1808.03821}.'
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- 'Constant-time decoder \cite{manual:{A. Grospellier. Constant time decoding of quantum expander codes and application to fault-tolerant quantum computation. PhD thesis, Inria Paris (2019)}}.'
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- '2D geometrically local syndrome extraction circuits acting on a patch of \(N\) physical qubits have to be of depth of \hyperref[topic:asymptotics]{order} \(\Omega(n/\sqrt{N})\) or deeper. More generally, there is a tradeoff between the depth \(D\) and width \(W\) of a syndrome extraction circuit, namely, \(D \geq n/\sqrt{W}\) \cite{arxiv:2109.14599}.'
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- '2D geometrically local syndrome extraction circuits acting on a patch of \(N\) physical qubits must have depth of \hyperref[topic:asymptotics]{order} \(\Omega(n/\sqrt{N})\) or greater. More generally, there is a tradeoff between the depth \(D\) and width \(W\) of a syndrome extraction circuit, namely, \(D \geq n/\sqrt{W}\) \cite{arxiv:2109.14599}.'
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fault_tolerance:
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- 'Fault-tolerance with constant overhead can be achieved \cite{arxiv:1808.03821}.'

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