Merge branch 'main' of https://github.com/errorcorrectionzoo/eczoo_data…

… into main

codes/classical/analog/lattice/root/hexagonal.yml

@@ -11,8 +11,8 @@ name: '\(A_2\) hexagonal lattice'
 
 description: |
     Two-dimensional lattice that exhibits optimal packing, solving the packing, kissing, covering and quantization problems.
-    Its dual is the \textit{honeycomb lattice}.
-    The \textit{ruby lattice} is a fattened honeycomb lattice interpolating between the honeycomb and hexagonal lattices. 
+    Its dual is the \textit{honeycomb tiling}, which is not a lattice (since the points do not form a group under addition) but which consists of two hexagonal lattices.
+    The \textit{ruby lattice} is a fattened honeycomb tiling interpolating between the honeycomb tiling and hexagonal lattice. 
 
     It's generator matrix is
     \begin{align}

codes/quantum/categories/string_net/fibonacci.yml

@@ -18,7 +18,7 @@ description: |
 
   The second type of encoding is into the degenerate fusion space of a number of anyonic quasiparticle excitations of the Levin-Wen model. This can equivalently constructed by braiding holes in a spherical geometry \cite[Sec. 5]{arxiv:1002.2816}.
 
-protection: When defined on a \(L \times L\) tailed honeycomb lattice on a torus, the code distance for ground-state encoding is \(L\).
+protection: When defined on a \(L \times L\) tailed honeycomb tiling on a torus, the code distance for ground-state encoding is \(L\).
 
 features:
 #  rate: Rate of \(n = k d^2\) for the ground-state encoding.

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

@@ -33,7 +33,7 @@ protection: |
 features:
 
   decoders:
-    - 'Modular phase measurement done in the logical \(X\), or dual, basis has zero uncertainty in the case of ideal number phase codes. This is equivalent to a quantum measurement of the spectrum of the Susskind–Glogower phase operator. Approximate number-phase codes are characterized by vanishing phase uncertainty. Such measurements can be utilized for Knill error correction (a.k.a. telecorrection \cite{arxiv:quant-ph/0601066}), which is based on teleportation \cite{arxiv:quant-ph/0410199,arxiv:quant-ph/0312190}. This type of error correction avoids the complicated correction procedures typical in Fock-state codes, but requires a supply of clean codewords \cite{arxiv:1901.08071}. Performance of this method was analyzed in Ref. \cite{arxiv:2108.01009}.'
+    - 'Modular phase measurement done in the logical \(X\), or dual, basis has zero uncertainty in the case of ideal number phase codes. This is equivalent to a quantum measurement of the spectrum of the Susskind–Glogower phase operator. Approximate number-phase codes are characterized by vanishing phase uncertainty. Such measurements can be utilized for Knill error correction (a.k.a. telecorrection \cite{arxiv:quant-ph/0601066}), which is based on teleportation \cite{arxiv:quant-ph/0410199,arxiv:quant-ph/0312190}. This type of error correction avoids the complicated correction procedures typical in Fock-state codes, but requires a supply of clean codewords \cite{arxiv:1901.08071}. Performance of this method was analyzed in Ref. \cite{arxiv:2108.01009}, and it was extended in Ref. \cite{arxiv:2412.15134}.'
     - 'Number measurement can be done by extracting modular number information using a CROT gate \(\mathrm{e}^{(2\pi \mathrm{i} / NM) \hat n \otimes \hat n}\) and performing phase measurements \cite{preset:Helstrom,doi:10.1007/978-88-7642-378-9} on an ancillary mode. See Section 4.B.1 of Ref. \cite{arxiv:1901.08071}.'
 
   fault_tolerance:

codes/quantum/qubits/dynamic/floquet/honeycomb.yml

@@ -73,7 +73,7 @@ relations:
     - code_id: kitaev_honeycomb
       detail: 'The Kitaev honeycomb model Hamiltonian is a sum of checks of the honeycomb Floquet code \cite{arxiv:2107.02194}.'
     - code_id: hexagonal
-      detail: 'The honeycomb Floquet code is defined on the honeycomb lattice.'
+      detail: 'The honeycomb Floquet code is defined on the honeycomb tiling.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/stabilizer/qldpc/homological/balanced_product/quantum_expander.yml

@@ -41,6 +41,8 @@ relations:
       detail: 'Quantum expander codes are single-shot \cite{arxiv:1808.03821}.'
   cousins:
     - code_id: expander
+    - code_id: topological
+      detail: 'Quantum expander codes realize topological quantum spin glass order \cite{arxiv:2412.13248}.'
     #      detail: 'Quantum expander codes are constructed from classical expander codes.'
 
 

codes/quantum/qubits/stabilizer/qldpc/homological/dlv.yml

@@ -26,6 +26,8 @@ relations:
     - code_id: qltc
       detail: 'DLV codes have linear dimension and inverse poly-logarithmic relative distance and soundness, assuming a conjecture about random linear maps \cite{arxiv:2402.07476}.
       Applying distance amplification and soundness amplification yields asymptotically constant soundness, \hyperref[topic:asymptotics]{order} \(\Theta(n)\) distance, \hyperref[topic:asymptotics]{order} \(\Theta(n)\) dimension, but poly-logarithmic locality \cite[Table 4]{arxiv:2309.05541}.'
+    - code_id: topological
+      detail: 'DLV codes are expected to realize topological quantum spin glass order \cite{arxiv:2412.13248}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/stabilizer/topological/color/2d_color/2d_color.yml

@@ -33,7 +33,7 @@ description: |
 # They anti-commute when they cross an odd number of times and have a different color and type.
 # \begin{figure}
   #   \includegraphics{colorCodeHoneycombHighlightedChecksAdjColor.svg}
-  #   \caption{Stabilizer generators and string operators of a 2D color code defined on a honeycomb lattice on a torus.
+  #   \caption{Stabilizer generators and string operators of a 2D color code defined on a honeycomb tiling on a torus.
   #   The plaquette operators generate the stabilizer group of the toric code where each face corresponds to an X or Z plaquette operator.  The string operators
   #   are pairs of X and Z logical operators that wrap around the torus. There are only four independent string operators, so there are two independent colors for the string operators \cite{arxiv:1311.0277}.}
   #   \label{figure:toric-code-operators}

codes/quantum/qubits/stabilizer/topological/color/2d_color/488_color/488_color.yml

@@ -60,6 +60,9 @@ features:
     - 'Phenomenological noise: \(3.05(4)\%\) under IP decoder \cite[Table I]{arxiv:1108.5738} and \(2.08(1)\%\) under projection decoder \cite{arxiv:1402.3037}.'
     - 'Circuit-level noise: \(0.082(3)\%\) under IP decoder, \(0.143(1)\%\) under projection decoder \cite{arxiv:1402.3037}, \(0.143\%\) under matching decoder \cite{arxiv:1407.5103}, and an analytic lower bound of \(\approx 0.1\%\) \cite{arxiv:0907.1708} (see \cite[Table I]{arxiv:1108.5738}).'
 
+realizations:
+  - 'Rydberg atomic devices: logical magic-state distillation using distance-three and five 4.8.8 color codes, observing an improvement in logical fidelity on a device by Quera \cite{arxiv:2412.15165}.'
+
 
 relations:
   parents:
@@ -68,7 +71,7 @@ relations:
     - code_id: triangular_color
       detail: 'Lattice surgery scheme for a hybrid 6.6.6-4.8.8 layout yields lower resource overhead when compared to analogous surface code scheme \cite{arxiv:2201.07806}.'
     - code_id: hypercubic
-      detail: 'The 4.8.8 (square-octagon) tiling is obtained by applying a fattening procedure to the honeycomb lattice \cite{arxiv:cond-mat/0607736}.'
+      detail: 'The 4.8.8 (square-octagon) tiling is obtained by applying a fattening procedure to the honeycomb tiling \cite{arxiv:cond-mat/0607736}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/stabilizer/topological/color/2d_color/triangular_color/triangular_color.yml

@@ -50,6 +50,9 @@ features:
     - 'Möbius matching decoder gives low logical failure rate \cite{arxiv:2108.11395} and has an open-source implementation called Chromöbius \cite{arxiv:2312.08813}.'
     - 'AMBP4, a quaternary version \cite{arxiv:2202.06612} of the MBP decoder \cite{arxiv:2104.13659}.'
     - 'MaxSAT-based decoder \cite{arxiv:2303.14237}.'
+    - 'Most likely error (MLE) decoder \cite{arxiv:2412.14256}.'
+    - 'Neural network decoder \cite{arxiv:2412.14256}.'
+
 
   fault_tolerance:
     - 'Fault-tolerant syndrome extraction circuits using flag qubits \cite{arxiv:1708.02246,arxiv:1911.00355}.'
@@ -68,12 +71,15 @@ features:
     - 'A \hyperref[topic:measurement-threshold]{measurement threshold} of one \cite{arxiv:2402.00145}.'
 
 
+realizations:
+  - 'Superconducting qubits: transversal Clifford gates, randomized logical benchmarking, and magic-state injection demonstrated on distance-three and five triangular color codes on the Willow device by Google Quantum AI \cite{arxiv:2412.14256}. Logical state teleportation using lattice surgery performed between two distance-three color codes.'
+
 relations:
   parents:
     - code_id: 2d_color
   cousins:
     - code_id: hexagonal
-      detail: 'The triangular color code is defined on a trivalent lattice such as the honeycomb lattice.'
+      detail: 'The triangular color code is defined on the honeycomb tiling.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/stabilizer/topological/color/color.yml

@@ -20,7 +20,7 @@ description: |
   See also a construction based on the more general quantum pin codes \cite{arxiv:1906.11394}.
 
 
-# For 2-dimensional color code, the lattice must be such that it is 3-valent and has 3-colorable faces, such as a honeycomb lattice.
+# For 2-dimensional color code, the lattice must be such that it is 3-valent and has 3-colorable faces, such as a honeycomb tiling.
 # The qubits are placed on the vertices and two stabilizer generators are placed on each face \cite{arxiv:1311.0277}.
 
 

codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface.yml

@@ -88,13 +88,13 @@ features:
     - 'Magic-state distillation protocols \cite{arxiv:1208.0928,arxiv:1209.0510,arxiv:2212.00813,arxiv:2403.03991} leading up to magic-state cultivation \cite{arxiv:2409.17595}.'
     - 'Framework of fault tolerance utilizing ZX calculus \cite{doi:10.1007/978-3-540-70583-3_25,arxiv:0906.4725} that is applicable to MBQC, FBQC, and conventional computation versions of the surface code \cite{arxiv:2303.08829}.'
     - 'Single-shot state preparation \cite{arxiv:1904.01502} and MWPM decoding \cite{arxiv:2209.09774}.'
-    - 'Syndrome extraction circuits consisting of CNOT gates and ancillary measurements \cite{arxiv:1208.0928}. Measurement schedules can be optimized using spacetime circuit codes to yield what is know as the \textit{3CX surface code} \cite{arxiv:2302.02192}. Schedules can also be optimized via ZX calculus \cite{doi:10.1007/978-3-540-70583-3_25,arxiv:0906.4725}. Inspired by the honeycomb Floquet code, various weight-two measurement schemes have been designed \cite{arxiv:2007.00307,arxiv:2206.12780,arxiv:2310.12981}, with the scheme in Ref. \cite{arxiv:2206.12780} being a special case of DWR.'
+    - 'Syndrome extraction circuits consisting of CNOT gates and ancillary measurements \cite{arxiv:1208.0928}. Measurement schedules can be optimized using spacetime circuit codes to yield what is known as the \textit{3CX surface code} \cite{arxiv:2302.02192}. Schedules can also be optimized via ZX calculus \cite{doi:10.1007/978-3-540-70583-3_25,arxiv:0906.4725}. Inspired by the honeycomb Floquet code, various weight-two measurement schemes have been designed \cite{arxiv:2007.00307,arxiv:2206.12780,arxiv:2310.12981}, with the scheme in Ref. \cite{arxiv:2206.12780} being a special case of DWR.'
 
   decoders:
     - 'Using data from multiple syndrome measurements prior to decoding allows for correcting syndrome measurement errors.
     The surface code requires \hyperref[topic:asymptotics]{order} \(O(d)\) extraction rounds in order to gain a reliable estimate.
     Syndrome measurements are \hyperref[topic:effective-distance]{distance-preserving} because syndrome extraction circuits can be designed to avoid \hyperref[topic:effective-distance]{hook errors} \cite{arxiv:quant-ph/0110143}.'
-    - 'Syndrome extraction circuits consist of CNOT gates and ancillary measurements since this is a stabilizer code \cite{arxiv:1208.0928}. Measurement schedules can be optimized using spacetime circuit codes to yield the \textit{3CX surface code} \cite{arxiv:2302.02192}. Schedules can also be optimized via ZX calculus \cite{doi:10.1007/978-3-540-70583-3_25,arxiv:0906.4725}. Inspired by the honeycomb Floquet code, various weight-two measurement schemes have been designed \cite{arxiv:2007.00307,arxiv:2206.12780,arxiv:2310.12981}, with the scheme in Ref. \cite{arxiv:2206.12780} being a special case of DWR.'
+    - 'Syndrome extraction circuits consist of CNOT gates and ancillary measurements since this is a stabilizer code \cite{arxiv:1208.0928}. Measurement schedules can be optimized using spacetime circuit codes to yield what is known as the \textit{3CX surface code} \cite{arxiv:2302.02192}. Schedules can also be optimized via ZX calculus \cite{doi:10.1007/978-3-540-70583-3_25,arxiv:0906.4725}. Inspired by the honeycomb Floquet code, various weight-two measurement schemes have been designed \cite{arxiv:2007.00307,arxiv:2206.12780,arxiv:2310.12981}, with the scheme in Ref. \cite{arxiv:2206.12780} being a special case of DWR.'
     - 'Expanding diamonds decoder correcting errors of some maximum fractal dimension \cite{manual:{Andrew Landahl, private communication, 2023}}.
     The sub-threshold failure probability scales as \((p/p_{\text{th}})^{d^\beta}\), where \(p_{\text{th}}\) is the threshold and \(\beta = \log_3 2\).'
     - 'Minimum weight perfect-matching (MWPM) \cite{arxiv:quant-ph/0110143,arxiv:1307.1740} (based on work by Edmonds on finding a matching in a graph \cite{doi:10.4153/CJM-1965-045-4,doi:10.6028/jres.069B.013}), which takes time up to polynomial in \(n\) for the surface code.
@@ -141,6 +141,7 @@ features:
 realizations:
   - |
     Signatures of corresponding topological phase of matter detected in superconducting circuits \cite{arxiv:2104.01180} and two-dimensional Rydberg atomic arrays \cite{arxiv:2104.04119}.
+  - 'Measurement schedules associated with the 3CX surface code realized in superconducting qubits on the Willow device by Google Quantum AI \cite{arxiv:2412.14360}.'
 
 notes:
   - 'Introduction to computation with the surface code \cite{doi:10.21468/SciPostPhysLectNotes.49,arxiv:1504.01444}.'

codes/quantum/qubits/subsystem/qldpc/bbs/bacon_shor/bacon_shor.yml

@@ -41,6 +41,7 @@ features:
   general_gates:
     - 'Piecably fault-tolerant circuits can be employed to construct non-transversal gates effectively \cite{manual:{Yoder, Theodore., \emph{DSpace@MIT} Practical Fault-Tolerant Quantum Computation (2018)}}.'
     - 'Subsystem lattice surgery \cite{arxiv:1609.08062}.'
+    - 'Measurement-free deformation protocol realizing the \(CCZ\) gate \cite{arxiv:2412.15187}.'
   fault_tolerance:
     - 'Fault-tolerant teleportation-based computation scheme for asymmetric Bacon-Shor codes that is effective against highly biased noise \cite{arxiv:1211.1400}.'
     - 'Pieceably fault-tolerant circuits can be employed to construct non-transversal gates effectively \cite{manual:{Yoder, Theodore., \emph{DSpace@MIT} Practical Fault-Tolerant Quantum Computation (2018)}}.'

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

@@ -47,7 +47,7 @@ relations:
       This code can be obtained from the square-lattice surface code by \hyperref[topic:gauging-out]{gauging out} the anyon \(em\) \cite[Sec. 7.3]{arxiv:2211.03798}.
       During this process, the square lattice is effectively expanded to a hexagonal lattice \cite[Fig. 12]{arxiv:2211.03798}.'
     - code_id: hexagonal
-      detail: 'The Kitaev honeycomb model is defined on the honeycomb lattice.'
+      detail: 'The Kitaev honeycomb model is defined on the honeycomb tiling.'
     - code_id: topological
       detail: 'The Kitaev honeycomb model realizes all anyon theories of the 16-fold way, i.e., all minimal modular extensions of the \(\mathbb{Z}_2^{(1)}\) anyon theory \cite{arxiv:cond-mat/0506438}\cite[Footnote 25]{arxiv:2211.03798}. This includes the (non-Abelian) Ising-anyon topological order \cite{arxiv:cond-mat/0506438} (a.k.a. \(p+ip\) superconducting phase \cite{arxiv:1104.5485}) as well as Abelian \(\mathbb{Z}_2\) topological order.'
 

codes/quantum/qudits/nonstabilizer/qudit_3_6_2.yml

@@ -12,7 +12,7 @@ introduced: '\cite{arxiv:2104.05122}'
 # Qudits labeled by Z_6
 
 description: |
-  Six-qudit error-detecting code with logical dimension \(K=6\) that is obtained from a particular \hyperref[topic:ame]{AME state} that serves as a solution to the 36 officers of Euler problem.
+  Three-qudit error-detecting code with logical dimension \(K=6\) that is obtained from a particular \hyperref[topic:ame]{AME state} that serves as a solution to the 36 officers of Euler problem.
   The code is obtained from a \(((4,1,3))_{\mathbb{Z}_6}\) code.
 
 relations:

codes/quantum/qudits_galois/stabilizer/qldpc/balanced_product/lp/matrix/expander_lifted_product.yml

@@ -45,6 +45,8 @@ relations:
       detail: 'Expander lifted-product codes are products of regular \(q\)-ary Tanner codes defined on expander graphs \cite{doi:10.1090/S0273-0979-06-01126-8}.'
     - code_id: random
       detail: 'Expander lifted-product codes are quantum CSS codes that utilize short classical codes in their construction which need to satisfy some properties (Ref. \cite{arxiv:2111.03654}, Lemma 10). It is shown that such codes exist, but they are not explicitly constructed. Such codes can be obtained by repeated random sampling or by performing a search of all codes of desired length. Nevertheless, since the length of the desired short codes does not scale with \(n\), this construction is effectively explicit.'
+    - code_id: topological
+      detail: 'Expander lifted-product codes are expected to realize topological quantum spin glass order \cite{arxiv:2412.13248}.'
 
 
 # Begin Entry Meta Information