syk codes

codes/quantum/oscillators/fock_state/matrix_qm.yml

@@ -8,20 +8,20 @@ physical: oscillators
 logical: qudits
 
 name: 'Matrix-model code'
-introduced: '\cite{arxiv:2211.08448}'
+introduced: '\cite{arxiv:2008.12869,arxiv:2211.08448}'
 
 description: |
   Multimode-mode Fock-state bosonic approximate code derived from a matrix model, i.e., a non-Abelian bosonic gauge theory with a large gauge group.
   The model's degrees of freedom are matrix-valued bosons \(a\), each consisting of \(N^2\) harmonic oscillator modes and subject to an \(SU(N)\) gauge symmetry.
 
-  A simple matrix-model code consists of two spatially separated bosons with codewords
+  A simple matrix-model code \cite{arxiv:2211.08448} consists of two spatially separated bosons with codewords
   \begin{align}
       |\mathcal{I}\rangle :=\prod_{(m,n)\in \mathcal{I} } \frac{\text{Tr}(a_1^{\dagger m}a_2^{\dagger n})}{N^{\frac{m+n}{2}}}|0\rangle_{12}~,
   \end{align}
   where \(\cal I\) is some set of integer two-tuples, and \(n,m\geq 0\).
 
   Gauge symmetry is assumed to be enforced in the above model.
-  In other variants, gauge symmetry is enforced energetically, requiring a parameter to scale as \(\log(N)\) for polynomial memory lifetime. This translates to the bath coupling being suppressed as \(1/N\).
+  In other variants \cite{arxiv:2211.08448}, gauge symmetry is enforced energetically, requiring a parameter to scale as \(\log(N)\) for polynomial memory lifetime. This translates to the bath coupling being suppressed as \(1/N\).
 
 protection: |
   For the spatially separated boson code, logical errors stemming from gauge-invariant physical errors are suppressed polynomially with the number of modes \(N\), as shown per the error-correction conditions.
@@ -36,9 +36,9 @@ relations:
       detail: 'Matrix-model codes approximately protect against gauge-invariant errors in the large-mode limit.'
     - code_id: hamiltonian
       detail: 'Matrix-model codewords for simple codes are eigenstates of a matrix-model Hamiltonian.'
-  cousins:
     - code_id: holographic
       detail: 'Matrix-model codes are motivated by the Ads/CFT correspondence because it is manifest in continuous non-Abelian gauge theories with large gauge groups \cite{arxiv:2211.08448}.'
+  cousins:
     - code_id: self_correct
       detail: 'Matrix-model codes are similar to self-correcting memories in the sense that memory time becomes infinite in the thermodynamic limit, but with corrections being polynomial in \(N\).'
 

codes/quantum/properties/block/tensor_network/holographic.yml

@@ -9,8 +9,9 @@ name: 'Holographic code'
 introduced: '\cite{arxiv:1503.06237}'
 
 description: |
-  Block quantum code whose encoding isometry serves to model aspects of the AdS/CFT holographic duality.
-  Encoding map models radial time evolution for a fixed time slice in Anti de Sitter (AdS) space, mapping operators in the bulk of AdS, represented by logical qudits, onto operators on the boundary of the corresponding Conformal Field Theory (CFT), represented by physical qudits.
+  Block quantum code whose features (typically, the encoding isometry) serve to model aspects of the AdS/CFT holographic duality.
+
+  The encoding map often models radial time evolution for a fixed time slice in Anti de Sitter (AdS) space, mapping operators in the bulk of AdS, represented by logical qudits, onto operators on the boundary of the corresponding Conformal Field Theory (CFT), represented by physical qudits.
   Encoding can often be represented by a tensor network associated with a tiling of hyperbolic space. See Defn 4.3 of Ref. \cite{arxiv:2108.11402} for a technical formulation.
 
   Typically, the encoding isometry \(U\) obeys the \textit{entanglement-wedge reconstruction condition}, which states that for any boundary region \(R\), any bulk operator \(O\) localized to the entanglement wedge of \(R\) must be implementable by some boundary operator \(\tilde{O}\) localized to \(R\). Formally, \(UO = \tilde{O}U\) and \([\tilde{O},UU^\dagger] = 0\). The entanglement wedge is the space enclosed within the Ryu–Takayanagi surface in the bulk (minimal surface) with boundary \(R\).
@@ -30,13 +31,15 @@ features:
 notes:
   - 'All Boundary global symmetries must be dual to bulk gauge symmetries, and vice versa \cite{arxiv:1810.05338}.'
 
+# SYK codes do not seem to be related to Lego, so parent is block quantum
 relations:
   parents:
+    - code_id: block_quantum
+  cousins:
     - code_id: quantum_lego
       detail: 'Quantum Lego codes codes whose encoders are tensor networks discretizing hyperbolic space can be thought of as holographic codes.
       More generally, tensor-network codes are types of LEGO codes made from stabilizer codes where logical and physical legs are pre-assigned and logical legs are not contracted.
       In other words, logical legs resulting from the conversion of codes to tensors must remain logical in the final tensor network, and the same for physical. Contracting logical legs is another word for gluing two logical legs together.'
-  cousins:
     - code_id: approximate_qecc
       detail: 'Universal subspace approximate error correction is used to model black holes \cite{arxiv:1807.06041}.'
     - code_id: approximate_oaecc

codes/quantum/properties/hamiltonian/hamiltonian.yml

@@ -9,7 +9,7 @@ name: 'Hamiltonian-based code'
 #introduced: ''
 
 description: |
-  Encoding corresponds to a set of energy eigenstates of a quantum-mechanical Hamiltonian.
+  Code whose codespace corresponds to a set of energy eigenstates of a quantum-mechanical Hamiltonian.
   The codespace is typically a set of low-energy eigenstates or ground states, but can include subspaces of arbitrarily high energy.
 
   For block quantum codes, the Hamiltonian can be \textit{local}, i.e., consisting of operators acting on a number of subsystems that is independent of the total number of subsystems (e.g., \hyperref[code:qldpc]{QLDPC codes}).

codes/quantum/qubits/fermions/syk.yml

@@ -0,0 +1,35 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: syk
+physical: qubits
+logical: qubits
+
+name: 'SYK code'
+introduced: '\cite{arXiv:2203.05058,arxiv:2310.07770}'
+
+description: |
+  Approximate \(n\)-fermionic code whose codewords are low-energy states of the Sachdev-Ye-Kitaev (SYK) Hamiltonian \cite{arxiv:cond-mat/9212030,manual:{Kitaev, Alexei. "A simple model of quantum holography (part 2)." Entanglement in Strongly-Correlated Quantum Matter (2015): 38.}} or other low-rank SYK models \cite{arxiv:1910.10173,arxiv:2010.10545}.
+
+features:
+  rate: 'SYK codes can have a constant rate and distance scaling as \(n^c\) for some power \(c\) \cite{arxiv:2310.0777}.'
+
+relations:
+  parents:
+    - code_id: fermions
+    - code_id: approximate_qecc
+      detail: 'SYK codes are approximately error correcting in that they satisfy certain error-correction conditions based on mutual information \cite{arxiv:2310.07770}.'
+    - code_id: hamiltonian
+      detail: 'The SYK code Hamiltonian is constructed out of non-commuting few-site terms, and every fermion participates in many interactions.'
+    - code_id: holographic
+      detail: 'In a holographic model \cite{arxiv:2310.07770}, the large distance of these codes can be interpreted as being due to the emergence of a wormhole.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2023-10-16'