cft

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

@@ -13,7 +13,7 @@ description: |
   Physical qubits are associated with uncontracted tensor legs at the boundary of the tesselation, while logical qubits are associated with uncontracted legs in the bulk.
   The number of layers emanating form the central point of the tiling is the \textit{radius} of the code.
 
-  The 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.
+  The 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.
   See \cite[Defn. 4.3]{arxiv:2108.11402} for a technical formulation.
 
 protection: |

codes/quantum/qubits/holographic/cft.yml

@@ -0,0 +1,38 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: cft
+physical: qubits
+logical: qubits
+
+name: 'Conformal-field theory (CFT) code'
+short_name: 'CFT'
+introduced: '\cite{arxiv:1611.07528,arxiv:2406.09555}'
+
+description: |
+  Approximate code whose codewords lie in the low-energy subspace of a conformal field theory, e.g., the quantum Ising model at its critical point \cite{arxiv:1611.07528,arxiv:2406.09555}.
+  Its encoding is argued to perform source coding (i.e., compression) as well as channel coding (i.e., error correction) \cite{arxiv:1611.07528}.
+
+protection: |
+  Code performance is quantified by a lower bound on the entanglement fidelity in terms of the conditional mutual information \cite[Eq. (9)]{arxiv:1611.07528}; see also \cite[Appx. A]{arxiv:1801.07271}.
+  The coherent information of the combined noise and recover channel can also be perturbatively expanded \cite{arxiv:2406.09555}.
+
+code_capacity_threshold:
+  - 'Threshold under dephasing depends on the structure of the conformal field theory, with the 1D critical Ising model admitting a finite threshold against certain dephasing noise \cite{arxiv:2406.09555}.'
+
+relations:
+  parents:
+    - code_id: qubits_into_qubits
+    - code_id: hamiltonian
+      detail: 'CFT codewords lie in the low-energy subspace of a conformal field theory (CFT), e.g., the quantum Ising model at its critical point.'
+    - code_id: approximate_qecc
+    - code_id: holographic
+      detail: 'CFT codewords lie in the low-energy subspace of a conformal field theory (CFT), e.g., the quantum Ising model at its critical point.'
+
+
+_meta:
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-07-02'