~

codes/quantum/qubits/nonstabilizer/circuit_to_hamiltonian.yml

@@ -24,15 +24,15 @@ features:
   encoders:
     - 'There exists a circuit of size polynomial in \(n\) whose terms act on at most \(\log (n)+2\) qubits \cite[Thm. 3.3]{arxiv:1811.00277}.'
   decoders:
-    - 'Local detection of Pauli errors can be done using circuits of depth \(\textit{polylog}(n)\) based on exact decoders for the Brown-Fawzi code \cite[Lemma 3.2]{arxiv:1811.00277}.'
+    - 'Local detection of Pauli errors can be done using circuits of depth \(O(\text{polylog}(n))\) based on exact decoders for the Brown-Fawzi code \cite[Lemma 3.2]{arxiv:1811.00277}.'
 
 
 relations:
   parents:
     - code_id: qubits_into_qubits
     - code_id: approximate_qecc
     - code_id: hamiltonian
-      detail: 'Circuit-to-Hamiltonian approximate codes form the ground-state space of a non-commuting projector Hamiltonian whose projectors are constant weight, but such that each physical qubit is acted on by order \(O(\text{polylog}(n)\) projectors.'
+      detail: 'Circuit-to-Hamiltonian approximate codes form the ground-state space of a frustration-free non-commuting projector Hamiltonian whose projectors are constant weight, but such that each physical qubit is acted on by order \(O(\text{polylog}(n))\) projectors.'
   cousins:
     - code_id: qlwc
       detail: 'The circuit-to-Hamiltonian code construction yields approximate codes whose distance and logical-qubit number are both of order \(\Omega(n/\log^5 n)\) \cite[Thm. 3.1]{arxiv:1811.00277}.

codes/quantum/qubits/nonstabilizer/movassagh_ouyang.yml

@@ -26,7 +26,7 @@ relations:
     - code_id: qubits_into_qubits
     - code_id: hamiltonian
       detail: 'Movassagh-Ouyang codes reside in the ground space of a Hamiltonian.
-      Justesen codes can be used to build a family of \(n\)-qudit Movassagh-Ouyang Hamiltonian codes encoding one logical qubit with linear distance.
+      Justesen codes can be used to build a family of \(n\)-qudit Movassagh-Ouyang Hamiltonian spin codes encoding one logical qubit with linear distance.
       These codes form the ground-state subspace of a frustration-free geometrically local Hamiltonian \cite{arxiv:2012.01453}.'
 
   cousins:
@@ -35,7 +35,10 @@ relations:
     - code_id: bits_into_bits
       detail: 'Movassagh-Ouyang codes are constructed from classical binary codes.'
     - code_id: justesen
-      detail: 'Justesen codes can be used to build a family of \(n\)-qudit Movassagh-Ouyang Hamiltonian codes encoding one logical qubit with linear distance.
+      detail: 'Justesen codes can be used to build a family of \(n\)-qudit Movassagh-Ouyang Hamiltonian spin codes encoding one logical qubit with linear distance.
+      These codes form the ground-state subspace of a frustration-free geometrically local Hamiltonian \cite{arxiv:2012.01453}.'
+    - code_id: spins_into_spins
+      detail: 'Justesen codes can be used to build a family of \(n\)-qudit Movassagh-Ouyang Hamiltonian spin codes encoding one logical qubit with linear distance.
       These codes form the ground-state subspace of a frustration-free geometrically local Hamiltonian \cite{arxiv:2012.01453}.'
 
 

codes/quantum/qudits/nonstabilizer/vbs.yml → codes/quantum/spins/vbs.yml

@@ -4,15 +4,14 @@
 #######################################################
 
 code_id: vbs
-physical: qudits
-logical: qudits
+physical: spins
 
 name: 'Valence-bond-solid (VBS) code'
 short_name: 'VBS'
 introduced: '\cite{arxiv:1910.00038,arxiv:2105.14777}'
 
 description: |
-  An \(n\)-qubit approximate \(q\)-dimensional qudit code family whose codespace is described in terms of \(SU(q)\) valence-bond-solid (VBS) \cite{doi:10.1007/978-3-662-06390-3_18} matrix product states with various boundary conditions.
+  An \(n\)-qubit approximate \(q\)-dimensional spin code family whose codespace is described in terms of \(SU(q)\) valence-bond-solid (VBS) \cite{doi:10.1007/978-3-662-06390-3_18} matrix product states with various boundary conditions.
   The codes become exact when either \(n\) or \(q\) go to infinity.
 
 features:
@@ -21,7 +20,7 @@ features:
 
 relations:
   parents:
-    - code_id: qudits_into_qudits
+    - code_id: spins_into_spins
     - code_id: hamiltonian
       detail: 'VBS codewords are eigenstates of the frustration-free VBS Hamiltonian \cite{arxiv:1910.00038,arxiv:2105.14777}.'
     - code_id: approximate_qecc