bacon_shor_9

codes/classical/spherical/spherical.yml

@@ -66,6 +66,10 @@ notes:
   - 'See \cite{preset:EricZin,manual:{Sloane, N. J. A., R. H. Hardin, and W. D. Smith. "Tables of spherical codes." collaboration with RH Hardin, WD Smith and others. Published electronically at https://neilsloane.com/packings/ (2004).}} for more details and tables of optimal codes.'
   - 'See article \cite{doi:10.1007/BF03024331} for relations of spherical codes to other fields.'
 
+realizations:
+  - 'Spherical codes are relevant to modern Hopfield networks \cite{arxiv:2410.23126,arxiv:2402.13725}'
+
+
 relations:
   parents:
     - code_id: points_into_spheres

codes/quantum/qubits/small_distance/small/4/stab_4_2_2.yml

@@ -71,7 +71,7 @@ realizations:
   - 'Logical Clifford gates for a twist-defect surface code that is single-qubit Clifford equivalent to a \([[4,1,2]]\) realized in a trapped ion device by Quantinuum \cite{arxiv:2406.09951}.'
   - 'CPC gadgets for the \([[4,2,2]]\) code have been implemented on the IBM 5Q superconducting device \cite{arxiv:1709.01866}.'
   - 'An FPGA implementation of the collision clustering decoder \cite{arxiv:2309.05558} realized on a Rigetti supercondutcing device \cite{arxiv:2410.05202}.'
-  - 'Rydberg atomic devices: error detection, erasure correction, and post-selected fault-tolerant circuits demonstrated on 24 logical qubits on a 256-qubit device by Atom Computing, with each qubit encoded in the \([[4,2,2]]\) code \cite{arxiv:2411.11822}. '
+  - 'Rydberg atomic devices: error detection, erasure correction, and post-selected fault-tolerant circuits demonstrated on 24 logical qubits on a 256-qubit device by Atom Computing, with each qubit encoded in the \([[4,2,2]]\) code \cite{arxiv:2411.11822}. The device also ran the Bernstein-Vazirani algorithm on up to 28 logical qubits encoded in a \([[4,1,2]]\) subcode.'
 
 
 relations:

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

@@ -12,7 +12,7 @@ short_name: 'Carbon'
 introduced: '\cite{arxiv:2404.02280}'
 
 description: |
-  Self-dual twelve-qubit CSS code.
+  Twelve-qubit CSS code for which \(H_X\) and \(H_Z\) are equal up to qubit permutations.
 
 features:
   transversal_gates:

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

@@ -75,7 +75,6 @@ features:
 realizations:
   - 'Trapped-ion qubits: state preparation with 98.8(1)\% and 98.5(1)\% fidelity for state \(|\overline{0}\rangle\) and \(|\overline{1}\rangle\), respectively, by N. Linke group \cite{arxiv:2104.01205}. Variants of the code to handle coherent noise studied and realized by K. Brown and C. Monroe groups \cite{arxiv:2105.05068}.'
   - 'Optical systems: quantum teleportation of information implemented by J.-W. Pan group on maximally entangled pair of one physical and one logical qubit with fidelity rate of up to 78.6\% \cite{arxiv:2009.06242}. All-photonic quantum repeater architecture tested on the same code \cite{arxiv:2203.07979}.'
-  - 'Rydberg atomic devices: repeated error correction demonstrated on a device by Atom Computing \cite{arxiv:2411.11822}. '
 
 relations:
   parents:
@@ -90,7 +89,7 @@ relations:
       detail: 'The Shor code is a concatenation of a three-qubit bit-flip with a three-qubit phase-flip repetition code.'
     - code_id: qubit_concatenated
       detail: 'The Shor code is a concatenation of a three-qubit bit-flip with a three-qubit phase-flip repetition code.'
-    - code_id: bacon_shor
+    - code_id: bacon_shor_9
       detail: 'The \([[9,1,3,3]]\) Bacon-Shor code reduces to the \hyperref[code:shor_nine]{Shor code} for a particular gauge configuration.'
     - code_id: qecc
       detail: 'The Shor code is the first quantum error-correcting code.'

codes/quantum/qubits/stabilizer/topological/color/stab_16_6_4.yml

@@ -11,7 +11,8 @@ name: '\([[16,6,4]]\) Tesseract color code'
 introduced: '\cite{arxiv:2008.05051,arxiv:2112.03785}'
 
 description: |
-  A 4D color code defined on a tesseract, with stabilizer generators of both types supported on each cube. 
+  A (self-dual CSS) 4D color code defined on a tesseract, with stabilizer generators of both types supported on each cube. 
+  A \([[16,4,2,4]]\) tesseract subsystem code can be obtained from this code by using two logical qubits as gauge qubits \cite{arxiv:2409.04628}.
 
 
 features:
@@ -21,7 +22,8 @@ features:
     - 'Post-selected fault-tolerant syndrome extraction \cite{arxiv:2008.05051,arxiv:2112.03785}.'
 
 realizations:
-  - 'Trapped-ion devices: logical graph and GHZ states of up to 12 logical qubits constructed using three copies of the tesseract color code, along with five rounds of post-selected fault-tolerant error correction in a device by Quantinuum \cite{arxiv:2409.04628}.'
+  - 'Trapped-ion devices: logical graph and GHZ states of up to 12 logical qubits constructed using three copies of the \([[16,4,2,4]]\) tesseract subsystem code, along with five rounds of post-selected fault-tolerant error correction in a device by Quantinuum \cite{arxiv:2409.04628}.'
+
 
 relations:
   parents:
@@ -30,6 +32,8 @@ relations:
   cousins:
     - code_id: stab_15_7_3
       detail: 'The \([[15,7,3]]\) quantum Hamming code can be obtained by puncturing the tesseract color code \cite{arxiv:2008.05051}.'
+    - code_id: hypercube
+      detail: 'Stabilizer generators of both types of the tesseract color code are supported on each cube of a tesseract \cite{arxiv:2008.05051,arxiv:2112.03785}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface-17.yml

@@ -10,6 +10,9 @@ logical: qubits
 name: 'Surface-17 code'
 introduced: '\cite{arxiv:1404.3747}'
 
+alternative_names:
+  - '\([[9,1,3]]\) rotated surface code'
+
 description: |
   A \([[9,1,3]]\) rotated surface code named for the sum of its 9 data qubits and 8 syndrome qubits.
   It uses the smallest number of qubits to perform fault-tolerant error correction on a surface code with parallel syndrome extraction.

codes/quantum/qubits/stabilizer/topological/surface/non-css/xzzx/xzzx.yml

@@ -53,7 +53,7 @@ features:
 realizations:
   - |
     Superconducting circuits: Distance-five 25-qubit code implemented on a superconducting quantum processor by Google Quantum AI \cite{arxiv:2207.06431}.
-    This code outperformed the average of several instances of the smaller distance-three 9-qubit \(XZZX\) variant of the \hyperref[code:surface-17]{surface-17} code realized on the same device, both in terms of logical error probability over 25 cycles and in terms of logical error per cycle.
+    This code outperformed the average of several instances of the smaller distance-three nine-qubit \(XZZX\) variant of the \hyperref[code:surface-17]{surface-17} code realized on the same device, both in terms of logical error probability over 25 cycles and in terms of logical error per cycle.
     This increase in error-correcting capabilities while using more physical qubits supports the notion of an error threshold.
     Braiding of defects has been demonstrated for the distance-five code \cite{arxiv:2210.10255}. Leakage errors have been handled in a separate work in a distance-three code \cite{arxiv:2211.04728}.
     Google Quantum AI follow-up experiment realizing distance-5 and distance-7 codes with 100 rounds of correction using the Libra and transformer-based decoders. The logical error rate is suppressed by a factor of \(\approx 2\), demonstrating beyond-break-even error correction with a block quantum code \cite{arxiv:2408.13687}.

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

@@ -27,29 +27,6 @@ description: |
   \end{align}
   Syndrome extraction can be done by measuring these gauge operators, which are on fewer qubits and local.
 
-  The shortest error-correcting Bacon-Shor code is \([[9,1,3,3]]\), with four stabilizer generators
-  \begin{align}
-    \begin{array}{ccccccccc}
-      X & X & X & X & X & X & I & I & I\\
-      I & I & I & X & X & X & X & X & X\\
-      Z & Z & I & Z & Z & I & Z & Z & I\\
-      I & Z & Z & I & Z & Z & I & Z & Z
-    \end{array}~,
-  \end{align}
-  which generate the gauge group with the help of eight additional generators
-  \begin{align}
-    \begin{array}{ccccccccc}
-    X & I & I & X & I & I & I & I & I\\
-    I & X & I & I & X & I & I & I & I\\
-    I & I & I & X & I & I & X & I & I\\
-    I & I & I & I & X & I & I & X & I\\
-    Z & Z & I & I & I & I & I & I & I\\
-    I & I & I & Z & Z & I & I & I & I\\
-    I & Z & Z & I & I & I & I & I & I\\
-    I & I & I & I & Z & Z & I & I & I
-    \end{array}~.
-  \end{align}
-  If the physical qubits are arranged in a three-by-three square, the \(Z\)-type (\(X\)-type) gauge operators are supported on qubits in the same row (column). The code reduces to the \hyperref[code:shor_nine]{Shor code} for a particular gauge configuration.
 
 protection: |
   The \([[m_1 m_2,1,min(m_1,m_2)]]\) variant has distance \(d=min(m_1,m_2)\).
@@ -72,20 +49,16 @@ features:
     However, a threshold can be obtained from concatenated Bacon-Shor codes that are further restricted to planar geometries, whose recovery circuit is a subset of a circuit used by a larger bona-fide Bacon-Shor code \cite{arxiv:2305.12046}.
     This threshold differs from a \hyperref[topic:computational-threshold]{concatenated threshold} in that there are no long-range connectivity requirements.'
     - 'Lower bounds for the \hyperref[topic:computational-threshold]{concatenated threshold} of various small Bacon-Shor codes are tabulated in \cite[Table I]{arxiv:quant-ph/0610063}.'
-    - '\(2.02 \times 10^{-5}\) \hyperref[topic:computational-threshold]{concatenated threshold} for the concatenated \([[9,1,3,3]]\) Bacon-Shor code \cite{arxiv:0805.4213}.'
   threshold:
     - 'Numerical study of \hyperref[topic:computational-threshold]{concatenated thresholds} of logical CNOT gates for various codes against depolarizing noise \cite{arxiv:0711.1556}.'
     - 'The Bacon-Shor code has a \hyperref[topic:measurement-threshold]{measurement threshold} of zero \cite{arxiv:2402.00145}.'
   decoders:
-    - 'Message passing for \([[9,1,3,3]]\) Bacon-Shor code \cite{arxiv:0806.2188}.'
     - 'Both Steane error correction and Shor error correction can be used for syndrome extraction, with the former outperforming the latter \cite{arxiv:2403.01659}.'
     - 'Utilizing the mapping of the effect of the noise to a statistical mechanical model \cite{arxiv:quant-ph/0110143,arxiv:2002.11733} yields several copies of the 1D Ising model \cite[Sec. V.B]{arxiv:0908.4246}.'
     - 'While check operators are few-body, stabilizer weights scale with the number of qubits, and stabilizer expectation values are obtained by taking products of gauge-operator expectation values.
     It is thus not clear how to extract stabilizer values in a fault-tolerant manner \cite{arxiv:2009.03921,arxiv:2107.02194}.'
     - 'Continuous-time QEC \cite{arxiv:1212.3564}.'
 
-realizations:
-  - 'Trapped-ion qubits: state preparation, logical measurement, and syndrome extraction (deferred to the end) for nine-qubit Bacon-Shor code demonstrated on a 13-qubit device by M. Cetina and C. Monroe groups \cite{arxiv:2009.11482}.'
 
 notes:
   - 'See \cite[Sec. III.C1]{arxiv:1302.3428} for an exposition.'

codes/quantum/qubits/subsystem/qldpc/bacon_shor/bacon_shor_9.yml

@@ -0,0 +1,65 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: bacon_shor_9
+physical: qubits
+logical: qubits
+
+name: '\([[9,1,3,3]]\) Nine-qubit Bacon-Shor code'
+short_name: 'Nine-qubit Bacon-Shor'
+introduced: '\cite{doi:10.1103/PhysRevA.52.R2493,arxiv:quant-ph/0506023}'
+
+description: |
+  Error-correcting nine-qubit subsystem stabilizer code encoding one logical qubit and three gauge qubits.
+
+  Admits the following stabilizers,
+  \begin{align}
+    \begin{array}{ccccccccc}
+      X & X & X & X & X & X & I & I & I\\
+      I & I & I & X & X & X & X & X & X\\
+      Z & Z & I & Z & Z & I & Z & Z & I\\
+      I & Z & Z & I & Z & Z & I & Z & Z
+    \end{array}~,
+  \end{align}
+  which generate the gauge group with the help of eight additional gauge-group generators
+  \begin{align}
+    \begin{array}{ccccccccc}
+    X & I & I & X & I & I & I & I & I\\
+    I & X & I & I & X & I & I & I & I\\
+    I & I & I & X & I & I & X & I & I\\
+    I & I & I & I & X & I & I & X & I\\
+    Z & Z & I & I & I & I & I & I & I\\
+    I & I & I & Z & Z & I & I & I & I\\
+    I & Z & Z & I & I & I & I & I & I\\
+    I & I & I & I & Z & Z & I & I & I
+    \end{array}~.
+  \end{align}
+  If the physical qubits are arranged in a three-by-three square, the \(Z\)-type (\(X\)-type) gauge operators are supported on qubits in the same row (column). 
+  The code reduces to the \hyperref[code:shor_nine]{Shor code} for a particular gauge configuration.
+
+features:
+  decoders:
+    - 'Message passing for \([[9,1,3,3]]\) Bacon-Shor code \cite{arxiv:0806.2188}.'
+  code_capacity_threshold:
+    - '\(2.02 \times 10^{-5}\) \hyperref[topic:computational-threshold]{concatenated threshold} for the recursively concatenated code \cite{arxiv:0805.4213}.'
+
+
+realization: 
+  - 'Trapped-ion qubits: state preparation, logical measurement, and syndrome extraction (deferred to the end)  demonstrated on a 13-qubit device by M. Cetina and C. Monroe groups \cite{arxiv:2009.11482}.'
+  - 'Rydberg atomic devices: repeated error correction demonstrated on a device by Atom Computing \cite{arxiv:2411.11822}. '
+
+
+relations:
+  parents:
+    - code_id: bacon_shor
+      detail: 'The nine-qubit Bacon-Shor code is the shortest error-correcting Bacon-Shor code.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-12-12'