qec2023

codes/quantum/properties/block/single_shot.yml

@@ -16,7 +16,7 @@ description: |
   The property is sufficient (but not necessary \cite{arxiv:2002.05180}) to reduce the number of error-correction rounds required for fault-tolerant error correction.
 
   In the loosest form of the single-shot property for qubit, modular qudit, or Galois qudit codes, given some data error \(e\), ideal data error syndrome \(s\), and measurement error \(m\), there exists an error-correction protocol that outputs a correction \(f\) such that the Hamming weight of the \textit{residual error} \(e-f\) is \textit{polynomial} in the weight of \(m\).
-  Note that the \textit{stabilizer-reduced weight} \cite{arxiv:1805.09271} of \(e\) is often used instead of the weight of \(e\), with the justification that many decoders are desgined to obtain the minimum-weight error representative.
+  Note that the \textit{stabilizer-reduced weight} \cite{arxiv:1805.09271} of \(e\) is often used instead of the weight of \(e\), with the justification that many decoders are designed to obtain the minimum-weight error representative.
 
 #  Single-shot codes admit a threshold after only one round of noisy syndrome measurements.
 

codes/quantum/properties/stabilizer/qldpc/qldpc.yml

@@ -100,6 +100,8 @@ relations:
       This opens up the possibility that some QLDPC codes, despite not being \textit{geometrically} local, can in fact be associated with a geometrically local theory described by a category.'
     - code_id: dynamic_gen
       detail: 'QLDPC codes can arise from a dynamical process \cite{arxiv:2004.09560}.'
+    - code_id: hamiltonian
+      detail: 'QLDPC code Hamiltonians can be simulated by two-dimensional Hamiltonians with non-commuting terms whose interactions scale with \(n\) \cite{arxiv:2308.13277}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/qubits_into_qubits.yml

@@ -39,6 +39,8 @@ features:
   decoders:
     - 'The decoder determining the most likely error given a noise channel is called the \textit{maximum-likelihood decoder}. For few-qubit codes (\(n\) is small), maximum-likelihood decoding can be based by creating a lookup table. For infinite code families, the size of such a table scales exponentially with \(n\), so approximate decoding algorithms scaling polynomially with \(n\) have to be used.'
     - 'Decoders are characterized by an \textit{effective distance} or \textit{circuit-level distance}, the minimum number of faulty operations during syndrome measurement that is required to make an undetectable error. A code is \textit{distance-preserving} if it admits a decoder whose circuit-level distance is equal to the code distance.'
+    - '\textit{Hook errors} are syndrome measurement circuit faults that cause more than one data-qubit error \cite{arxiv:quant-ph/0110143} and significantly decrease the effective distance.
+    Hook errors occur at specific places in a syndrome extraction circuit and can sometimes be removed by re-ordering the gates of the circuit. If not, the use of flag qubits to detect hook errors may be necessary to yield fault-tolerant decoders.'
   fault_tolerance:
     - 'There are lower bounds on the overhead of fault-tolerant QEC in terms of the capacity of the noise channel \cite{arxiv:2202.00119}. A more stringent bound applies to geometrically local QEC due to the fact that locality constrains the growth of the entanglement that is needed for protection \cite{arxiv:2302.04317}.'
 

codes/quantum/qubits/stabilizer/qldpc/hierarchical.yml

@@ -3,9 +3,9 @@
 ##       https://github.com/errorcorrectionzoo       ##
 #######################################################
 
-code_id: 'hierarchical'
-physical: 'qubits'
-logical: 'qubits'
+code_id: hierarchical
+physical: qubits
+logical: qubits
 
 name: 'Hierarchical code'
 introduced: '\cite{arxiv:2303.04798}'
@@ -19,7 +19,9 @@ features:
   rate: 'Rate vanishes as \(\Omega(1/\log(n)^2)\).'
 
   decoders:
-    - 'Decoding is performed as in a standard \hyperref[code:quantum_concatenated]{concatenated code} using a decoder for the inner code and outer code.'
+    - 'Decoding is performed as in a standard \hyperref[code:quantum_concatenated]{concatenated code} using a decoder for the inner code and outer code.
+    The syndrome extraction circuit depth for the outer code is optimized using a permutation routing algorithm \cite{doi:10.1145/97444.97707}.
+    The bilayer architecture allows for logical entangling gates between logical surface-code patches.'
 
   threshold:
     - 'Threshold exists for the locally decaying error model; see \cite[Thm. 1.3]{arxiv:2303.04798}.

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

@@ -37,7 +37,7 @@ features:
     - '2D geometrically local syndrome extraction circuits with depth order \(O(\sqrt{n})\) using order \(O(n)\) ancilla qubits \cite{arxiv:2109.14599}.'
     - 'Improved BP-OSD decoder \cite{arxiv:2206.03122}.'
     - 'Erasure-correction can be implemented approximately with \(O(n^2)\) operations with quantum generalizations \cite{arxiv:2208.01002} of the peeling and pruned peeling decoders \cite{doi:10.1109/18.910575}, with a probabilistic version running in \(O(n^{1.5})\) operations.'
-    - 'Syndrome measurements are distance-preserving \cite{arxiv:2308.15520}.'
+    - 'Syndrome measurements are distance-preserving because syndrome extraction circuits can be designed to avoid hook errors \cite{arxiv:2308.15520}.'
   general_gates:
     - 'Code deformation techniques yield Clifford gates \cite{arXiv:1909.07424}.'
   code_capacity_threshold:

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

@@ -21,7 +21,8 @@ features:
     - 'Small set-flip linear-time decoder, which corrects \(\Omega(n^{1/2})\) adversarial errors \cite{arXiv:1504.00822}.'
     - 'Log-time decoder \cite{arxiv:1808.03821}.'
     - 'Constant-time decoder \cite{manual:{A. Grospellier. Constant time decoding of quantum expander codes and application to fault-tolerant quantum computation. PhD thesis, Inria Paris (2019).}}.'
-    - '2D geometrically local syndrome extraction circuits acting on a patch of \(N\) physical qubits have to be of depth at least \(\Omega(n/\sqrt{N})\) \cite{arxiv:2109.14599}.'
+    - '2D geometrically local syndrome extraction circuits acting on a patch of \(N\) physical qubits have to be of depth at least \(\Omega(n/\sqrt{N})\). More generally, there is a tradeoff between the depth \(D\) and width \(W\) of a syndrome extraction circuit, namely, \(D \geq n/\sqrt{W}\) \cite{arxiv:2109.14599}.'
+'
   fault_tolerance:
     - 'Fault-tolerance with constant overhead can be achieved \cite{arXiv:1808.03821}.'
 

codes/quantum/qubits/stabilizer/qubit_stabilizer.yml

@@ -53,8 +53,6 @@ features:
 
   fault_tolerance:
     - 'Logical Bell measurements can be done transversally, and thus fault tolerantly, by performing bitwise Bell measurements for each pair of qubits (with each member of the pair taken from one of the two code blocks) and processing the result.'
-    - '\textit{Hook errors} are syndrome measurement circuit faults that cause more than one data-qubit error \cite{arxiv:quant-ph/0110143}.
-    Hook errors occur at only specific places in a syndrome extraction circuits and can sometimes be removed by re-ordering the gates of the circuit. If not, the use of flag qubits to detect hook errors may be necessary to yield fault-tolerant decoders.'
     - 'With pieceable fault-tolerance, any nondegenerate stabilizer code with a complete set of fault-tolerant single-qubit Clifford gates has a universal set of non-transversal fault-tolerant gates \cite{arXiv:1603.03948}.'
     - 'Fault-tolerant error correction scheme by Shor \cite{arXiv:quant-ph/9605011}, which is based on repeated measurements. A modification uses adaptive measurements \cite{arxiv:2208.05601}.'
     - 'Generalization of Steane error correction stabilizer codes \cite[Sec. 3.6]{manual:{Yoder, Theodore., \emph{DSpace@MIT} Practical Fault-Tolerant Quantum Computation (2018)}}.'

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

@@ -102,7 +102,7 @@ features:
     Circuits can be optimized to specific architectures \cite{arxiv:2302.02192} using spacetime circuit codes and ZX calculus \cite{doi:10.1007/978-3-540-70583-3_25,arxiv:0906.4725}.'
 
   decoders:
-    - 'Syndrome measurements are distance-preserving \cite{arxiv:quant-ph/0110143}.'
+    - 'Syndrome measurements are distance-preserving because syndrome extraction circuits can be designed to avoid hook errors \cite{arxiv:quant-ph/0110143}.'
     - 'Degenerate maximum-likelihood (ML) \cite{arxiv:quant-ph/0110143}, which takes time of order \(O(n^2)\) under independent \(X,Z\) noise for the surface code \cite{arxiv:1405.4883}.'
     - '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.
     For the case of the surface code, minimum-weight decoding reduces to MWPM \cite{arxiv:quant-ph/0110143,doi:10.4153/CJM-1965-045-4,doi:10.1088/0305-4470/15/2/033}.'