perm invariant gnu

codes/quantum/qubits/nonstabilizer/cws.yml

@@ -16,8 +16,7 @@ description: |
 
   There is an alternative description to the one above that is locally Clifford-equivalent. In particular, we can describe CWS codes as \( \mathcal{Q} = (S,\mathcal{W})\) where \(S\) is a stabilizer group and \( \mathcal{W} = \{ w_\ell \}_{\ell = 1}^K \) is a family of \(K\) \(n\)-qubit Pauli strings. We then form CWS codeswords as \( | i \rangle = w_i | S \rangle \), where \( | S \rangle \) is the (unique) stabilizer state of \(S\).
 
-  The term CWS was coined in Ref. \cite{arxiv:0708.1021}, and their approach is equivalent to another approach \cite{arXiv:cs/0610159} based on Boolean functions.
-# , as shown in Ref. \cite{doi:1721.1/53235}.
+  The term CWS was coined in Ref. \cite{arxiv:0708.1021}, and their approach is equivalent to another approach \cite{arXiv:cs/0610159} based on Boolean functions (see Ref. \cite{manual:{Zeng, Bei. Quantum operations and codes beyond the Stabilizer-Clifford framework. Diss. Massachusetts Institute of Technology, 2009.}}).
 
 
 protection: 'Code distance \(\mathcal{Q} = ( \mathcal{G},\mathcal{C}) \) is upper bounded by the distance of the classical code \(\mathcal{C} \). The \hyperref[code:qubits_into_qubits]{diagonal distance} is upper bounded by \(\delta + 1\), where \(\delta\) is the minimum degree of \(\mathcal{G}\). Computing the distance is generally \(NP\)-complete, and is \(NP\)-hard for non-degenerate codes \cite{arXiv:2203.04262}.'

codes/quantum/spins/single_spin/single_spin.yml → codes/quantum/spins/single_spin.yml

@@ -31,6 +31,9 @@ relations:
       A single-spin code correcting spherical tensors can be mapped into a permutation-invariant code with an analogous distance \cite[Thm. 1]{arxiv:2310.17652}.'
     - code_id: single_subsystem
     - code_id: qecc_finite
+  cousins:
+    - code_id: qubits_into_qubits
+      detail: 'Certain single-spin codes yield permutation-invariant qubit codes with non-trivial distance \cite{arxiv:2304.08611} when the single spin is treated as a collective spin of several qubits.'
 
 
 # Begin Entry Meta Information

codes/quantum/spins/transversal/j_gross.yml → codes/quantum/spins/single_spin/j_gross.yml

@@ -38,9 +38,6 @@ features:
 relations:
   parents:
     - code_id: single_spin
-  cousins:
-    - code_id: qubits_into_qubits
-      detail: 'Certain Clifford codes yield permutation-invariant qubit codes with non-trivial distance \cite{arxiv:2304.08611} when the single spin is treated as a collective spin of several qubits.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/nonstabilizer/permutation_invariant/binary_dihedral_permutation_invariant.yml → codes/quantum/spins/transversal/binary_dihedral_permutation_invariant.yml

@@ -26,7 +26,6 @@ features:
 
 relations:
   parents:
-    - code_id: qubits_into_qubits
     - code_id: j_gross
       detail: 'Binary dihedral permutation-invariant codes can be interpreted as Clifford single-spin codes.'
   cousins:

codes/quantum/spins/transversal/gnu_permutation_invariant.yml

@@ -9,16 +9,17 @@ logical: qubits
 
 name: 'GNU permutation-invariant code'
 short_name: 'GNU'
-introduced: '\cite{arXiv:1302.3247}'
+introduced: '\cite{arXiv:1302.3247,arxiv:1512.02469}'
 
 description: |
   Permutation-invariant code whose codewords can be expressed as superpositions of \hyperref[topic:dicke]{Dicke states} with coefficients are square-roots of the binomial distribution.
 
-  The logical states are
+  Logical codewords for codes encoding a single qubit \cite{arXiv:1302.3247} are
   \begin{align}
   |\overline{\pm}\rangle = \sum_{\ell=0}^{n} \frac{(\pm 1)^\ell}{\sqrt{2^n}} \sqrt{n \choose \ell} |D^m_{g \ell}\rangle~.
   \end{align}
   Here, \(m\) is the number of particles used for encoding \(1\) qubit, and \(g, n \leq m\) are arbitrary positive integers.
+  Codes with higher logical dimension are developed in Ref. \cite{arxiv:1512.02469}.
 
 
 protection: 'Depends on the family. One family which is completely symmetrized versions of Bacon-Shor codes (parameterized by \(t\)) protects against arbitrary weight-\(t\) spin errors. Additionally, codes with large enough length \((t+1)(3t+1)+t\) can approximately correct \(t\) spontaneous decay errors.'
@@ -30,8 +31,7 @@ features:
 
 relations:
   parents:
-    - code_id: spins_into_spins
-    - code_id: permutation_invariant
+    - code_id: qudit_gnu_permutation_invariant
   cousins:
     - code_id: bacon_shor
       detail: 'GNU codes of length \((2t+1)^2\) result from projecting Bacon-Shor codes into the permutation-invariant qubit subspace \cite{arXiv:1302.3247}.'

codes/quantum/qubits/nonstabilizer/permutation_invariant/icosahedral_permutation_invariant.yml → codes/quantum/spins/transversal/icosahedral_permutation_invariant.yml

@@ -31,7 +31,6 @@ features:
 
 relations:
   parents:
-    - code_id: qubits_into_qubits
     - code_id: j_gross
       detail: 'The \(((7,2,3))\) permutation-invariant code can be interpreted as a spin-\(7/2\) Clifford code \cite{arXiv:2005.10910}.'
     - code_id: small_distance_quantum

codes/quantum/spins/transversal/qudit_gnu_permutation_invariant.yml

@@ -0,0 +1,30 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: qudit_gnu_permutation_invariant
+physical: spins
+logical: qudits
+
+name: 'Qudit GNU permutation-invariant code'
+short_name: 'Qudit GNU'
+introduced: '\cite{arXiv:1604.07925}'
+
+description: |
+  Extension of the GNU permutation-invariant codes to those encoding logical qudits.
+  Codewords can be expressed as superpositions of \hyperref[topic:dicke]{Dicke states} with coefficients are square-roots of polynomial coefficients, with the case of binomial coefficients reducing to the GNU permutation-invariant codes.
+
+
+relations:
+  parents:
+    - code_id: spins_into_spins
+    - code_id: permutation_invariant
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-02-12'

codes/quantum/spins/transversal/ruskai.yml

@@ -27,7 +27,6 @@ protection: |
 
 relations:
   parents:
-    - code_id: qubits_into_qubits
     - code_id: gnu_permutation_invariant
       detail: 'The \(((9,2,3))\) Ruskai code is a GNU permutation-invariant code \cite{arXiv:1302.3247}.'
     - code_id: small_distance_quantum

codes/quantum/qudits/small/su3_sigma360.yml → codes/quantum/spins/transversal/su3_sigma360.yml

@@ -19,7 +19,6 @@ features:
 
 relations:
   parents:
-    - code_id: qudits_into_qudits
     - code_id: su3_spin
       detail: '\(\Sigma(360\phi)\) spin codes can be interpreted as \(SU(3)\) single-spin codes.'
   cousins: