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errorcorrectionzoo · Sep 6, 2023 · 535b53b · 535b53b
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diff --git a/codes/classical/analog/lattice/root/eeight.yml b/codes/classical/analog/lattice/root/eeight.yml
@@ -12,7 +12,8 @@ short_name: '\(E_8\)'
 introduced: '\cite{manual:{Gosset, Thorold. "On the regular and semi-regular figures in space of n dimensions." Messenger of Mathematics 29 (1900): 43-48.}}'
 
 description: |
-  BW lattice in dimension \(8\), which is the lattice corresponding to the \([8,4,4]\) Hamming code via the mod-two lattice construction.
+  Unimodular even BW lattice in dimension \(8\), consisting of the Cayley integral octonions rescaled by \(\sqrt{2}\).
+  The lattice corresponds to the \([8,4,4]\) Hamming code via the mod-two lattice construction.
 
 protection: |
   The \(E_8\) lattice has a nominal coding gain of \(2\).

diff --git a/codes/quantum/oscillators/stabilizer/lattice/gkp.yml b/codes/quantum/oscillators/stabilizer/lattice/gkp.yml
@@ -53,6 +53,7 @@ notes:
 realizations:
   - 'Motional degree of freedom of a trapped ion: square-lattice GKP encoding realized with the help of post-selection \cite{arxiv:1807.01033,arXiv:1907.06478}, followed by realization of reduced form of GKP error correction, where displacement error syndromes are measured to one bit of precision using an ion electronic state \cite{arxiv:2010.09681}.'
   - 'Microwave cavity coupled to superconducting circuits: reduced form of square-lattice GKP error correction, where displacement error syndromes are measured to one bit of precision using an ancillary transmon \cite{arxiv:1907.12487}. Subsequent paper \cite{arxiv:2211.09116} uses reinforcement learning for error-correction cycle design and is the first to go beyond break-even error-correction, with the lifetime of a logical qubit exceeding the cavity lifetime by about a factor of two (see also \cite{arxiv:2211.09319}).'
+  - 'GKP states and homodyne measurements have been realized in propagating telecom light by the Furusawa group \cite{arxiv:2309.02306}.'
   - 'Single-qubit \(Z\)-gate has been demonstrated in the single-photon subspace of an infinite-mode space \cite{arxiv:1904.01351}, in which time and frequency become bosonic conjugate variables of a single effective bosonic mode.'
   - 'In signal processing, GKP state position-state wavefunctions are related to Dirac combs \cite{doi:10.1007/978-1-4612-2016-9}.'