refs

codes/quantum/qubits/qubits_into_qubits.yml

@@ -115,7 +115,8 @@ features:
     More generally, the \textit{Solovay-Kitaev} theorem \cite{doi:10.1070/rm1997v052n06abeh002155,doi:10.1090/gsm/047} states that any subset of gates the generates a dense subgroup of the full \(n\)-qubit gate group can be used to construct any gate to arbitrary accuracy (see \cite{arxiv:quant-ph/0505030}\cite[Appx. 3]{doi:10.1017/cbo9780511976667.019}). The task of approximating a desired gate by Clifford gates and a fixed set of non-Clifford gates is called \textit{gate compilation} or \textit{circuit synthesis}.'
     - 'Non-Clifford gates are typically more difficult to implement than Clifford gates and so are treated as a resource. Optimizing T-gate count in circuit synthesis is \(NP\)-hard \cite{arxiv:2310.05958} and can be done using various procedures \cite{arxiv:1303.2042,arxiv:1308.4134,arxiv:1601.07363,arxiv:1710.07345,arxiv:1712.01557,arxiv:2110.10292}, e.g., \textit{ZX calculus} (a.k.a. Penrose spin calculus) \cite{arxiv:1903.10477,arxiv:1911.09039,arxiv:2004.05164,arxiv:2109.01076} or reinforcement learning \cite{arxiv:2402.14396}.
     There is an optimal asymptotic scaling of the number of T gates needed to prepare an arbitrary state \cite{arxiv:1812.00954,arxiv:2411.04790}.
-    Decompositions in terms of Toffoli and Hadamard gates \cite{arxiv:quant-ph/0205115} as well as cosine-sine gates also exist \cite{arxiv:quant-ph/0404089}. Gate errors in circuit synthesis can sometimes add up destructively \cite{arxiv:1612.01011}.'
+    Decompositions in terms of Toffoli and Hadamard gates \cite{arxiv:quant-ph/0205115} as well as cosine-sine gates also exist \cite{arxiv:quant-ph/0404089}. Gate errors in circuit synthesis can sometimes add up destructively \cite{arxiv:1612.01011}.
+    There is a threshold against depolarizing noise for any single-qubit gate that determines if the gate enables universal quantum computation \cite{arxiv:0907.3189}.'
     - '\begin{defterm}{Clifford hierarchy}
       \label{topic:clifford-hierarchy}
       The Clifford hierarchy \cite{arxiv:quant-ph/9908010,arxiv:1608.06596,arxiv:1902.04022,arXiv:2212.05398,arxiv:2410.11818} is a tower of gate sets which includes Pauli and Clifford gates at its first two levels, and non-Clifford gates at higher levels.
@@ -151,6 +152,7 @@ features:
         Subsequently, thresholds were determined for infinite families of lattice stabilizer codes, starting with the toric code \cite{arxiv:quant-ph/0110143}; such a threshold is colloquially called a \textit{topological threshold}.
         Fault-tolerant computations with no notion of locality can be made local on a 2D or 3D geometry with minimal overhead \cite{arxiv:2402.13863}.
         \end{defterm}
+    - 'There is a threshold against depolarizing noise for any single-qubit gate that determines if the gate enables universal quantum computation \cite{arxiv:0907.3189}.'
     - '\begin{defterm}{Measurement threshold}
       \label{topic:measurement-threshold}
       One can derive conditions quantifying how many random single-qubit measurements can be made without destroying the logical information \cite{arxiv:2402.00145}.
@@ -159,6 +161,7 @@ features:
       \end{defterm}'
     - 'There is a dynamical phase transition between a bounded-error and an unbounded-error phase for a model of qubits weakly coupled to a refrigerator \cite{arxiv:2411.12805}.'
 
+
 notes:
   - 'There is a relation between one-way entanglement distillation protocols and QECCs \cite{arxiv:quant-ph/9604024}.'
   - 'See \href{https://github.com/qiskit-community/qiskit-qec}{Qiskit QEC framework} for realizing protocols on IBM machines.'

codes/quantum/qubits/small_distance/small/7/steane/steane.yml

@@ -93,6 +93,9 @@ realizations:
   Rains shadow enumerators have been measured \cite{arxiv:2408.16914}.'
   - 'Rydberg atom arrays: Lukin group \cite{arxiv:2112.03923}; ten logical qubits, transversal CNOT gate performed, logical ten-qubit GHZ state initialized with break-even fidelity, and fault-tolerant logical two-qubit GHZ state initialized \cite{arxiv:2312.03982}.'
 
+notes:
+  - 'The Steane code can be used for entanglement purification \cite{arxiv:0811.2639}.'
+
 
 relations:
   parents:

codes/quantum/qubits/stabilizer/mbqc/rbh.yml

@@ -41,6 +41,7 @@ features:
   threshold:
     - 'Various thresholds for optical quantum computing scheme with RBH codes \cite{arxiv:quant-ph/0509060,arxiv:1005.2915}.'
     - '\(0.75\%\) for preparation, gate, storage, and measurement errors \cite{arxiv:quant-ph/0610082}.'
+    - '\(24.9\%\) under erasure noise \cite{arxiv:1005.2456}.'
     - 'Concatenation of the RBH code with small codes such as the \([[2,1,1]]\) repetition code, \([[4,1,1,2]]\) subsystem code, or Steane code can improve thresholds \cite{arxiv:2209.09390}.'
 
 notes:

codes/quantum/qubits/stabilizer/mbqc/tree_cluster.yml

@@ -8,14 +8,17 @@ physical: qubits
 logical: qubits
 
 name: 'Tree cluster-state code'
-introduced: '\cite{arxiv:quant-ph/0507036,arxiv:1309.7207,arxiv:1603.01353}'
+introduced: '\cite{arxiv:quant-ph/0507036,arxiv:1008.2048,arxiv:1008.3752,arxiv:1309.7207,arxiv:1603.01353}'
 
 description: |
-  Code obtained from a cluster state on a tree graph that has been proposed in the context of quantum repeater and MBQC architectures.
+  Code obtained from a cluster state on a tree graph (e.g., a star graph \cite{arxiv:1008.2048,arxiv:1008.3752}) that has been proposed in the context of quantum repeater and MBQC architectures.
 
 protection: |
   Some tree cluster-state codes have shown good performance over the depolarizing channel \cite{arxiv:1910.00471}.
 
+features:
+  general_gates:
+    - 'Cluster states constructed from star clusters can be used to perform universal MBQC with probabilistic two-qubit gates \cite{arxiv:1008.3752}.'
 
 relations:
   parents:

codes/quantum/qubits/stabilizer/topological/color/2d_color/4612_color/4612_color.yml

@@ -13,7 +13,7 @@ introduced: '\cite{arxiv:1108.5738}'
 
 
 description: |
-  Triangular color code defined on a patch of the 4.6.12 (truncated trihexagonal or square-hexagon-dodecagon) tiling.
+  2D color code defined on a patch of the 4.6.12 (truncated trihexagonal or square-hexagon-dodecagon) tiling.
 
   Stabilizer generators are shown in \ref{figure:4.6.12-operators}.
     \begin{figure}

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

@@ -13,7 +13,7 @@ introduced: '\cite{arxiv:quant-ph/0605138}'
 
 
 description: |
-  Triangular color code defined on a patch of the 4.8.8 (square-octagon) tiling, which itself is obtained by applying a fattening procedure to the  square lattice \cite{arxiv:cond-mat/0607736}.
+  2D color code defined on a patch of the 4.8.8 (square-octagon) tiling, which itself is obtained by applying a fattening procedure to the  square lattice \cite{arxiv:cond-mat/0607736}.
 
   Stabilizer generators are shown in \ref{figure:4.8.8-operators}.
     \begin{figure}

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

@@ -12,7 +12,7 @@ introduced: '\cite{arxiv:0910.0573}'
 
 
 description: |
-  Triangular color code defined on a patch of the Tetrakis square tiling (a.k.a. the Union Jack lattice).
+  2D color code defined on a patch of the Tetrakis square tiling (a.k.a. the Union Jack lattice).
 
 
 features:

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

@@ -12,7 +12,7 @@ short_name: '6.6.6 color'
 introduced: '\cite{arxiv:quant-ph/0605138}'
 
 description: |
-  Triangular color code defined on a patch of the 6.6.6 (honeycomb) tiling.
+  2D color code defined on a patch of the 6.6.6 (honeycomb) tiling.
 
   Stabilizer generators are shown in \ref{figure:6.6.6-operators}.
     \begin{figure}
@@ -64,10 +64,9 @@ features:
     - 'Depolarizing channel: \(12.6\%\) under the restriction decoder \cite{arxiv:1911.00355} and the projection decoder \cite{arxiv:1308.6207}, and \(\approx 14.5\%\) under AMBP4 decoding \cite[Fig. 12]{arxiv:2202.06612}.'
 
 
-# First point is for this code
   threshold:
-    - 'Circuit-level noise: \(0.2\%\) using two flag qubits per stabilizer generator and the restriction decoder \cite{arxiv:1911.00355}, and
-    \(0.46\%\) under concatenated MWPM decoder \cite{arxiv:2404.07482}.'
+    - 'The threshold under ML decoding with measurement errors corresponds to the value of a critical point of a three-dimensional disordered Ising model, estimated to be \(4.8(2)\%\) \cite{arxiv:1005.0777}.'
+    - 'Circuit-level noise: \(0.2\%\) using two flag qubits per stabilizer generator and the restriction decoder \cite{arxiv:1911.00355}, and \(0.46\%\) under concatenated MWPM decoder \cite{arxiv:2404.07482}.'
     - 'A \hyperref[topic:measurement-threshold]{measurement threshold} of one \cite{arxiv:2402.00145}.'
 
 

codes/quantum/qudits/stabilizer/qudit_cluster_state.yml

@@ -24,6 +24,9 @@ description: |
   where the neighborhood \(N(v)\) is the set of vertices which share an edge with \(v\).'
 
 features:
+  encoders:
+    - 'Operators forming the information group can be used to track how logical information is encoded \cite{arxiv:0912.2017}.'
+
   general_gates:
     - '1D modular-qudit cluster states \cite{arxiv:quant-ph/0304054,arxiv:quant-ph/0512155} are resources for universal MBQC.'