penrose, 833, refs

codelists/descendants/quantum/list_quantum_mds.yml

@@ -5,7 +5,7 @@ title: |
   Quantum MDS codes
 
 intro: |
-  Here is a list of code families which contain \hyperref[code:quantum_mds]{quantum MDS codes}.
+  Here is a list of code families which contain \hyperref[code:quantum_mds]{quantum MDS codes} or \hyperref[code:ea_mds]{entanglement-assisted MDS codes}.
 
 
 display:
@@ -38,3 +38,5 @@ codes:
   select:
     - descendant_of: quantum_mds
     - cousin_of: quantum_mds
+    - descendant_of: ea_mds
+    - cousin_of: ea_mds

codes/classical/q-ary_digits/easy/dodecacode.yml

@@ -27,7 +27,7 @@ relations:
       detail: 'The dodecacode is trace-Hermitian self-dual additive.'
   cousins:
     - code_id: combinatorial_design
-      detail: 'There exists a \(5-(12, 6, 3)\) design in the dodecacode, and a \(3-(11, 5, 4)\) design in the shortened dodecacode.'
+      detail: 'There exists a \(5-(12, 6, 3)\) design in the dodecacode, and a \(3-(11, 5, 4)\) design in the shortened dodecacode \cite{doi:10.1023/A:1025484821641}.'
     - code_id: stab_11_1_5
       detail: 'Applying the \hyperref[code:stabilizer_over_gf4]{Hermitian} construction to the dodecacode yields a \([[12,0,6]]\) quantum code \cite{arXiv:quant-ph/9608006}.
       The \([[11,1,5]]\) quantum dodecacode code can be obtained by applying the \hyperref[code:stabilizer_over_gf4]{Hermitian} construction to the shortened dodecacode \cite{doi:10.1007/s11128-005-0002-1}.

codes/quantum/oscillators/fock_state/rotation/bosonic_rotation.yml

@@ -44,6 +44,9 @@ relations:
     - code_id: fock_state
       detail: 'Single-mode Fock-state codes are typically rotationally invariant.'
     - code_id: single-mode
+  cousins:
+    - code_id: quantum_random
+      detail: 'Random bosonic rotation codes can outperform cat and binomial codes when loss rate is large relative to dephasing rate \cite{arxiv:2311.16089}.'
 
 
 # Begin Entry Meta Information

codes/quantum/oscillators/penrose.yml

@@ -0,0 +1,36 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: oscillators
+physical: oscillators
+
+name: 'Penrose tiling code'
+introduced: '\cite{arxiv:2311.13040}'
+
+description: |
+  Encodes quantum information into superpositions of rotated and translated versions of different Penrose tilings of \(\mathbb{R}^n\).
+
+  Letting \(|T\rangle\) be a Penrose tiling, the codeword corresponding to this tiling is a superposition of all points in the tiling's orbit under all Euclidean transformations,
+  \begin{align}
+    |\overline{T}\rangle=\int dg|gT\rangle~,
+  \end{align}
+  where \(g\) is a Euclidean transformation.
+
+protection: |
+  Properties of Pensrose tilings such as local indistinguishability and local recoverability ensure that Penrose tiling codes can correct erasures of any finite region of space.
+
+
+relations:
+  parents:
+    - code_id: oscillators
+      detail: 'Penrose tiling codes encode information into Penrose tilings, which are non-periodic tilings of \(\mathbb{R}^n\).'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2022-11-28'

codes/quantum/properties/block/quantum_perfect.yml

@@ -27,7 +27,7 @@ description: |
   A quantum Hamming-like bound exists for degenerate qubit stabilizer codes \cite{arxiv:2306.00048}.
 
 protection: |
-  Perfect codes have been classified. For qubits (\(q=2\)), the only codes are the stabilizer code family \([[(4^r-1)/3, (4^r-1)/3 - 2r, 3]]\) for \(r \geq 2\) \cite{arxiv:quant-ph/9607027,arxiv:quant-ph/9608006}. For qudits, the family is parameterized by \(K=q^{n-2r}\) for \(n=\frac{q^{2r}-1}{q^{2}-1}\) and \(r \geq 2\); all codes correct a single error (\(t=1\)) \cite{arxiv:0907.0049,doi:10.1002/(SICI)1520-6610(2000)8:3<174::AID-JCD3>3.0.CO;2-T}. The trivial code (\(k=n\)) is also perfect.
+  Perfect codes have been classified. For qubits (\(q=2\)), the only codes are the stabilizer code family \([[(4^r-1)/3, (4^r-1)/3 - 2r, 3]]\) for \(r \geq 2\), obtained from Hamming codes over \(GF(4)\) via the Hermitian construction \cite{arxiv:quant-ph/9607027,arxiv:quant-ph/9608006}. For qudits, the family is parameterized by \(K=q^{n-2r}\) for \(n=\frac{q^{2r}-1}{q^{2}-1}\) and \(r \geq 2\); all codes correct a single error (\(t=1\)) \cite{arxiv:0907.0049,doi:10.1002/(SICI)1520-6610(2000)8:3<174::AID-JCD3>3.0.CO;2-T}. The trivial code (\(k=n\)) is also perfect.
 
 features:
   rate: '\(k/n\to 1\) asymptotically with \(n\).'
@@ -43,6 +43,8 @@ relations:
   cousins:
     - code_id: perfect
       detail: 'A classical (quantum) perfect code saturates the classical (quantum) Hamming bound.'
+    - code_id: stabilizer_over_gf4
+      detail: 'The only perfect qubit codes are the stabilizer code family \([[(4^r-1)/3, (4^r-1)/3 - 2r, 3]]\) for \(r \geq 2\), obtained from Hamming codes over \(GF(4)\) via the Hermitian construction \cite{arxiv:quant-ph/9607027,arxiv:quant-ph/9608006}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/small_distance/small/stab_8_3_3.yml

@@ -0,0 +1,31 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: stab_8_3_3
+physical: qubits
+logical: qubits
+
+name: '\([[8, 3, 3]]\) code'
+short_name: '\([[8, 3, 3]]\)'
+introduced: '\cite{arXiv:quant-ph/9604038,arxiv:quant-ph/9605005,arxiv:quant-ph/9605021}'
+
+description: |
+  Eight-qubit code obtained from the CSS construction using a first-order \([8,4,4]\) RM code and a \([8,7,2]\) even-weight code \cite{arxiv:quant-ph/9605021}.
+
+  See \cite[Table 3.3]{arxiv:quant-ph/9705052} for its stabilizer generator matrix.
+  The code's automorphism group is \(\text{A}\Gamma\text{L}(1,8)\) \cite{arxiv:2109.12735}.
+
+
+relations:
+  parents:
+    - code_id: quantum_hamming
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2023-11-28'

codes/quantum/qubits/small_distance/stab_11_1_5.yml

@@ -14,7 +14,7 @@ introduced: '\cite{arXiv:quant-ph/9608006}'
 description: |
   Eleven-qubit pure stabilizer code that is the smallest qubit stabilizer code to correct two-qubit errors.
 
-  See \cite[Table 8.5]{arxiv:quant-ph/9705052} for its stabilizer generators.
+  See \cite[Table 8.5]{arxiv:quant-ph/9705052}\cite{arxiv:quant-ph/0406063} for its stabilizer generator matrix.
 
 protection: 'Smallest stabilizer code that protects against errors on any two qubits. Detects four-qubit errors.'
 

codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface/surface.yml

@@ -114,7 +114,7 @@ features:
     - 'Renormalization group (RG) \cite{arXiv:0911.0581,arXiv:1304.6100,arXiv:1411.3028}.'
     - 'Markov-chain Monte Carlo \cite{arXiv:1302.2669}.'
     - 'Cellular automaton \cite{doi:10.7907/AHMQ-EG82,arXiv:1511.05579}.'
-    - 'Neural network \cite{arXiv:1610.04238,arXiv:1802.06441,arXiv:1810.07207,arxiv:2208.05758} and reinforcement learning \cite{arxiv:2212.11890}.'
+    - 'Neural network \cite{arXiv:1610.04238,arXiv:1802.06441,arXiv:1810.07207,arxiv:2208.05758}, reinforcement learning \cite{arxiv:2212.11890}, and transformer-based \cite{arxiv:2311.16082} decoders.'
     - 'Decoders can be augmented with a pre-decoder \cite{arXiv:2001.11427,arXiv:2208.04660}, which can allow for some processing to be done inside the cryogenic environment of the quantum system \cite{arxiv:2208.08547}.'
     - 'Sliding-window \cite{arxiv:2209.09219,arxiv:2209.08552} and parallel-window \cite{arxiv:2209.09219} parallelizable decoders, designed to overcome the backlog problem, can be combined with many inner decoders, such as MWPM or union-find.'
     - 'Generalized belief propagation (GBP) \cite{arxiv:2212.03214} based on a classical version \cite{manual:{J. S. Yedidia, W. T. Freeman, and Y. Weiss, Generalized belief propagation, in NIPS, Vol. 13 (2000) pp. 689–695.}}.

codes/quantum/qubits/subsystem/topological/heavy_hex.yml

@@ -31,7 +31,8 @@ features:
 
   decoders:
     - 'Any graph-based decoder can be used, such as MWPM and Union Find. However, edge weights must be dynamically renormalized using flag-qubit measurement outcomes after each syndrome measurement round.'
-    - 'Machine-learning decoder \cite{arxiv:2210.09730}.'
+    - 'Machine-learning \cite{arxiv:2210.09730} and neural-network \cite{arxiv:2311.15146} decoders.'
+
 
   fault_tolerance:
     - 'All logical gates can be fault-tolerantly implemented using lattice surgery and magic state injection.'

codes/quantum/qudits/topological/double_semion.yml

@@ -14,6 +14,10 @@ description: |
   Modular-qudit stabilizer code with qudit dimension \(q=4\) that is characterized by the double semion topological phase. The code can be obtained from the \(\mathbb{Z}_4\) surface code by \hyperref[topic:code-switching]{condensing} the anyon \(e^2 m^2\) \cite{arxiv:2211.03798}.
   Originally formulated as a non-stabilizer qubit code \cite{arXiv:cond-mat/0404617}.
 
+  This stabilizer code family is inequivalent to a CSS code via a Clifford circuit whose depth does not scale with \(n\) \cite[Thm. 1.1]{arxiv:1506.08883}.
+  This is because the double semion phase has a sign problem \cite{arxiv:1506.08883,arxiv:2005.05343}, and existence of such a Clifford circuit would allow one to construct a code Hamiltonian that is free of such a problem.
+
+
 relations:
   parents:
     - code_id: tqd_abelian
@@ -29,5 +33,9 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2023-11-28'
+    - user_id: nathanan
+      date: '2023-11-28'
     - user_id: VictorVAlbert
       date: '2021-12-29'

codes/quantum/qudits_galois/subsystem/galois_subsystem_css.yml

@@ -8,7 +8,7 @@ physical: galois
 logical: galois
 
 name: 'Subsystem Galois-qudit CSS code'
-introduced: '\cite{arxiv:quant-ph/0604161,arxiv:quant-ph/0610153,arxiv:0811.1570}'
+introduced: '\cite{arxiv:quant-ph/0610153,arxiv:0811.1570}'
 
 alternative_names:
   - 'Euclidean construction subsystem code'

codes/quantum/qudits_galois/subsystem/galois_subsystem_stabilizer.yml

@@ -8,7 +8,7 @@ physical: galois
 logical: galois
 
 name: 'Subsystem Galois-qudit stabilizer code'
-# introduced: '\cite{arXiv:quant-ph/0508131}'
+introduced: '\cite{arxiv:quant-ph/0604161}'
 
 description: |
   Galois-qudit generalization of a subsystem qubit stabilizer code.