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codes/classical/properties/block/checksum.yml

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protection: 'The checksum can be calculated from the message via a formula and verified against the appended checksum in order to flag certain misread messages.'
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notes:
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- 'See Ref. \cite{doi:10.1147/sj.141.0016} for a history.'
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relations:
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parents:

codes/classical/rings/checksum/isbn.yml

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name: 'International Standard Book Number (ISBN) code'
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short_name: 'ISBN'
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introduced: '\cite{manual:{}}'
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description: |
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relations:
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parents:
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- code_id: rings_into_rings
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detail: 'The last digit of a particular ISBN is a check digit that is evaluated modulo 11 \cite{preset:Hill}.'
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- code_id: q-ary_digits_into_q-ary_digits
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detail: 'The last digit of a particular ISBN is a check digit that is evaluated modulo 11 \cite{preset:Hill}.'
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- code_id: checksum
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detail: 'The last digit of a particular ISBN is a check digit that is evaluated modulo 11 \cite{preset:Hill}.'
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# Begin Entry Meta Information

codes/classical/spherical/sharp_config/cgs_spherical.yml

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description: |
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Member of a \((q(q^2-q+1),(q+1)(q^3+1),2-2/q^2)\) family of spherical codes for any prime-power \(q\).
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Constructed from generalized quadrangles, which in this case correspond to sets of totally isotropic points and lines in the projective space \(PG_{5}(q)\) \cite[Exam. 9.4.5]{preset:EricZin}.
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There exist multiple distinct spherical codes using this construction for \(q>3\) \cite{arxiv:math/0607446}.
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There exist multiple distinct spherical codes using this construction for \(q>3\) \cite{arxiv:math/0607446,arxiv:2403.16874}.
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protection: 'CGS isotropic subspace codes saturate the Levenshtein bound \cite[pg. 64]{preset:EricZin}.'
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codes/quantum/oscillators/fock_state/rotation/squeezed_vacuum.yml

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- 'Multi-legged squeezed code'
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description: |
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A squeezed Fock-state code constructed from a coherent superposition of \(m\) squeezed vacuum states, each squeezed along evenly-spaced axes in phase space.
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A squeezed Fock-state code constructed from a coherent superposition of \(m\) squeezed vacuum states, each squeezed along equiangular axes in phase space.
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For an even integer \(m > 0\) (the number of ``legs'') and squeezing strength \(r\), the two logical codewords are defined as
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\begin{align}
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|0_L\rangle & \propto \sum_{j=0}^{m-1} S\left(r, \frac{\pi j}{m}\right) \ket{\vac}, \\
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|1_L\rangle & \propto \sum_{j=0}^{m-1} (-1)^{j} S\left(r, \frac{\pi j}{m}\right) \ket{\vac},
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|0_L\rangle & \propto \sum_{j=0}^{m-1} S\left(r, \frac{\pi j}{m}\right) \ket{0}, \\
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|1_L\rangle & \propto \sum_{j=0}^{m-1} (-1)^{j} S\left(r, \frac{\pi j}{m}\right) \ket{0},
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\end{align}
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where \(S(r,\theta) \equiv S(r e^{i\phi(\theta)})\) is the squeezing operator with \(\phi(\theta) = 2\theta + \pi \pmod{2\pi}\), defined as
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\begin{equation}
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- 'Logical operations within a single mode can be performed using Gaussian operations (displacement, rotation, squeezing) combined with conditional control from an ancilla qubit.'
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decoders:
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- 'The interleaved photon-number structure (\(n \equiv 2k \pmod{2m}\)) enables photon-number-resolving measurements to identify single-photon loss events, which can then be corrected.'
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- 'The interleaved photon-number structure, \(n \equiv 2k \pmod{2m}\), enables photon-number-resolving measurements to identify single-photon loss events, which can then be corrected.'
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# Circuit QED: Recent proposals demonstrate controlled-squeezing gates using driven

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