refs, edits

Author: valbert4

codes/classical/analog/sphere_packing/lattice/bw/leech.yml

@@ -34,7 +34,7 @@ relations:
     - code_id: golay
       detail: 'The Leech lattice can be obtained by lifting the Golay code to \(\mathbb{Z}_4\) \cite{doi:10.1109/18.312154}, appending a parity check, and applying \term{Construction \(A_4\)} \cite{doi:10.1007/3-540-57843-9_20} (see also \cite{doi:10.1098/rspa.1982.0071,doi:10.1007/978-1-4757-6568-7}). Half of the lattice can be obtained in a different construction \cite[Exam. 10.7.3]{preset:EricZin}.'
     - code_id: ternary_golay
-      detail: 'The Leech lattice can be obtained by from the ternary Golay code \cite{doi:10.1098/rspa.1982.0071}.'
+      detail: 'A 12-dimensional complex version of the Leech lattice can be obtained from the ternary Golay code \cite{doi:10.1016/0021-8693(83)90074-1,doi:10.1098/rspa.1982.0071}\cite[pg. 200]{doi:10.1007/978-1-4757-6568-7}.'
     - code_id: sharp_config
       detail: 'Several spherical sharp configrations are derived from the Leech lattice \cite{arxiv:math/0607446}.'
     - code_id: octacode

codes/quantum/oscillators/stabilizer/lattice/quantum_lattice.yml

@@ -32,7 +32,7 @@ description: |
   The \(m=2n\) case yields multimode GKP codes encoding a finite-dimensional logical subspace, while removing some displacements yields oscillator-into-oscillator GKP codes encoding an infinite-dimensional logical subspace. Codes defined on a hyper-rectangular lattice are \textit{CSS GKP} codes, and more general lattices, obtained by Gaussian transformations, yield non-CSS codes.
 
 notes:
-  - 'Quantum lattice states are featured in the proof of hardness of LWE \cite[pg. 12]{doi:10.1145/1568318.1568324}.'
+  - 'Quantum lattice states are featured in the proof of hardness of LWE \cite[pg. 12]{doi:10.1145/1568318.1568324} and the hidden subgroup problem over the reals \cite{doi:10.1145/2591796.2591860}.'
   - 'Single-mode quantum lattice states on a square lattice, otherwise known as square-lattice GKP states, are relevant to signal processing and condensed-matter physics; see the corresponding \hyperref[code:gkp]{code entry} for details.'
 
 

codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml

@@ -148,6 +148,9 @@ relations:
       detail: 'Kerdock codes correspond to cluster states, and the corresponding Clifford-group automorphisms of this set form a particular group \cite{doi:10.1112/S0024611597000403} that is a unitary 2-design on \(U(2^n)\) \cite{arxiv:1904.07842}. As such, cluster states form complex projective 2-designs on \(\mathbb{C}P^{2^n}\). These are useful in matrix-vector multiplication \cite{arxiv:2105.05879}.'
     - code_id: complex_projective
       detail: 'Kerdock codes correspond to cluster states, and the corresponding Clifford-group automorphisms of this set form a particular group \cite{doi:10.1112/S0024611597000403} that is a unitary 2-design on \(U(2^n)\) \cite{arxiv:1904.07842}. As such, cluster states form complex projective 2-designs on \(\mathbb{C}P^{2^n}\). These are useful in matrix-vector multiplication \cite{arxiv:2105.05879}.'
+    - code_id: surface
+      detail: 'Foliating the surface code yields a cluster state on the Lieb lattice \cite{arxiv:quant-ph/9707021,arxiv:1508.03468,arXiv:2211.01376,arXiv:2310.16032}.'
+    # Kitaev writes about the larger lattice but doesn't call it Lieb lattice
 
 
 # In 1D, cluster states are examples of SPT phases with global symmetries and allow MBQC on a single qubit. In 2D, cluster states with subsystem symmetries are universal resources for MBQC. In 3D, cluster states with higher-form symmetries enable universal fault-tolerant MBQC.

codes/quantum/qudits/small/three_qutrit_permutation_invariant.yml

@@ -5,12 +5,18 @@
 
 code_id: three_qutrit_permutation_invariant
 
-name: '\(((3,3,2))_{3}\) Three-qutrit single-deletion code'
+name: '\(((3,2,2))_3\) Three-qutrit single-deletion code'
 introduced: '\cite{arxiv:2509.20545}'
 
 description: |
   Three-qutrit PI code that is the smallest qutrit PI code to correct one deletion error.
 
+  The code admits the following logical codewords:
+  \begin{align}
+    |\overline{0}\rangle\propto&|000\rangle+|111\rangle+|222\rangle\\
+    |\overline{1}\rangle\propto&|012\rangle+|021\rangle+|102\rangle+|120\rangle+|201\rangle+|210\rangle~.
+  \end{align}
+
 protection: |
   The smallest qutrit PI code to correct one deletion error.