~

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

@@ -91,6 +91,7 @@ features:
     - 'Non-binary decoding algorithm for CSS-type QLDPC codes \cite{doi:10.1109/ACCESS.2015.2503267}.'
     - '2D geometrically local syndrome extraction circuits with bounded depth using order \(O(n^2)\) ancilla qubits \cite{arxiv:2109.14599}. For CSS codes, syndrome extraction can be implemented in constant depth \cite{arxiv:2109.14609}.'
     - 'Soft (i.e., analog) syndrome iterative belief propagation for CSS-type QLDPC codes, utilizing the continuous signal obtained in the physical implementation of the stabilizer measurement (as opposed to discretizing the signal into a syndrome bit) \cite{arxiv:2205.02341}.'
+    - 'The MWPM decoder for surface codes may be generalizable to QLDPC codes \cite{arxiv:2207.06428}.'
     - 'Extensions of the union-find decoder for qubit QLDPC codes \cite{arxiv:2209.01180,arxiv:2407.15988}.'
     - 'Sliding-window decoding \cite{arxiv:2311.03307}.'
     - 'Closed-branch decoder \cite{arxiv:2402.01532}.'

codes/quantum/qubits/qubits_into_qubits.yml

@@ -50,7 +50,7 @@ protection: |
 
   \subsection{Noise channels}
 
-  A quantum channel whose Kraus operators are Pauli strings is called a \textit{Pauli channel}, and such channels are typically more tractable than general, non-Pauli channels.
+  A quantum channel that admits a set of Pauli strings as its Kraus operators is called a \textit{Pauli channel}, and such channels are typically more tractable than the more general, non-Pauli channels.
   Relevant Pauli channels include dephasing noise and depolarizing noise (a.k.a. Werner-Holevo channel \cite{arxiv:quant-ph/0203003}).
   Relevant non-Pauli channels are \hyperref[topic:ad]{AD} noise, erasure (which maps all qubit states into a third state \(|e\rangle\) outside of the qubit Hilbert space), and biased erasure (in which case only the \(|1\rangle\) qubit state is mapped to \(|e\rangle\)).
   Noise can be correlated in space or in time, with the latter being an example of a non-Markovian phenomenon \cite{arxiv:quant-ph/0505153,arxiv:2012.01894}.
@@ -111,8 +111,7 @@ features:
     - 'Arbitrary \(n\)-qubit circuits can be implemented fault-tolerantly in a 3D architecture using \(O(n^{3/2}\log^3 n)\) qubits, and in a 2D architecture using only \(O(n^2 \log^3 n)\) qubits \cite{arxiv:2402.13863}.'
   decoders:
     - 'Incorporating faulty syndrome measurements can be done using the \textit{phenomenological noise model}, which simulates errors during syndrome extraction by flipping some of the bits of the measured syndrome bit string. In the more involved \textit{circuit-level noise model}, every component of the syndrome extraction circuit can be faulty.'
-    - '\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 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.'
+    - '\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 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 \textit{flag qubits} (see \cite{preset:GottesmanBook}) to detect hook errors may be necessary to yield fault-tolerant decoders.'
     - 'The decoder determining the most likely error given a noise channel is called the \textit{maximum probability error} (MPE) decoder. For few-qubit codes (\(n\) is small), MPE 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.'
   fault_tolerance:

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

@@ -64,7 +64,7 @@ features:
 
 realizations:
   - 'Used to obtain explicit lower bounds in the sum-of-squares game \cite{arxiv:2204.11469}.'
-  - 'States that, on average, achieve small violations of check operators for quantum Tanner codes require a circuit of non-constant depth to make. They are used in the proof \cite{arxiv:2206.13228} of the \textit{No low-energy trivial states} (NLTS) conjecture \cite{arxiv:1301.1363}.'
+  - 'States that, on average, achieve small violations of check operators for quantum Tanner codes require a circuit of non-constant depth to make. They are used in the proof \cite{arxiv:2206.13228} of the NLTS conjecture \cite{arxiv:1301.1363}.'
 
 notes:
   - 'For details, see talk by \href{https://www.youtube.com/watch?v=5GO3BtJuo3I}{A. Leverrier}.'