~

Author: Tamara

codes/classical/spherical/polytope/8d/witting_polytope.yml

@@ -23,7 +23,7 @@ description: |
   See \cite[pg. 132]{preset:coxeterComplex} for a complex representation.
 
 protection: |
-  Code yields an optimal solution to the kissing problem in 4D \cite{preset:Schlafli1901,arxiv:math/0309430} and saturates the Levenshtein bound \cite{doi:10.1016/0097-3165(79)90074-8}.
+  Code yields an optimal solution to the kissing problem in 8D \cite{preset:Schlafli1901,arxiv:math/0309430} and saturates the Levenshtein bound \cite{doi:10.1016/0097-3165(79)90074-8}.
 
 notes:
   - 'The Witting polytope yields 40 states of a qudit of dimension 4 and a non-probabilistic version of Bell''s theorem \cite{manual:{R. Penrose, "On Bell non-locality without probabilities: some curious geometry." Quantum Reflections (2000): 1-27.},doi:10.1016/0039-3681(93)90061-N,doi:10.1119/1.19336,arxiv:1701.06512}.'

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

@@ -29,7 +29,7 @@ description: |
   This operator elongates the vacuum state along direction \(\theta\) in phase space.
 
 protection: |
-  In Fock space, the logical states occupy photon numbers \(n \equiv 2k \pmod{2m}\) for \(k \in \{0, m/2\}\), yielding natural number distributions that are interleaved by \(\Delta n = m\). 
+  In Fock space, the logical states occupy photon numbers in distinct congruence classes \(n \equiv 0 \pmod{2m}\) and \(n \equiv m \pmod{2m}\), yielding photon-number distributions that are interleaved by \(\Delta n = m\). 
   The code distance against single-photon loss is \(d = m\), where \(m\) is the number of legs (squeezed vacuum states in superposition). 
   The code provides protection against both photon loss and dephasing noise, with a fundamental trade-off: increasing \(m\) improves loss tolerance at the cost of higher dephasing sensitivity.
 
@@ -63,7 +63,7 @@ features:
     - 'Logical operations within a single mode can be performed using Gaussian operations (displacement, rotation, squeezing) combined with conditional control from an ancilla qubit.'
 
   decoders:
-    - 'The interleaved photon-number structure, \(n \equiv 2k \pmod{2m}\), enables photon-number-resolving measurements to identify single-photon loss events, which can then be corrected.'
+    - 'The interleaved photon-number structure, with support on distinct classes modulo \(2m\), enables photon-number-resolving measurements to identify single-photon loss events, which can then be corrected.'
 
 
 # Circuit QED: Recent proposals demonstrate controlled-squeezing gates using driven

codes/quantum/qubits/stabilizer/css/quantum_parity.yml

@@ -15,7 +15,7 @@ alternative_names:
   - 'Subspace Shor code'
 
 description: |
-  A \([[m_1 m_2,1,\min(m_1,m_2)]]\) CSS code family obtained from concatenating an \(m_1\)-qubit phase-flip repetition code with an \(m_2\)-qubit bit-flip repetition code.
+  A \([[m_1 m_2,1,\min(m_1,m_2)]]\) CSS code family obtained from concatenating an \(m_1\)-qubit bit-flip repetition code with an \(m_2\)-qubit phase-flip repetition code.
 
   Logical codewords are
   \begin{align}
@@ -54,7 +54,7 @@ realizations:
   - 'QPCs have been discussed independently in the context of superconducting circuits \cite[Eq. (1)]{arxiv:cond-mat/0403712}\cite[Eqs. (8-10)]{doi:10.1088/0034-4885/75/7/072001}, and aspects of such designs have been realized in experiments \cite{arxiv:0802.2295}.'
 
 notes:
-  - 'Non-determinisitic linear-optical encoding \cite{arxiv:quant-ph/0501184} whose success probability \(P_{E}\) is determined by the efficiency \(\eta\) of the photonic encoding circuit. A threshold \(\eta > 0.82 \) exists for the efficiency, above which \(P_{E}\to 1\) as \(m_1\to\infty\) given particular \(m_2\).'
+  - 'Non-deterministic linear-optical encoding \cite{arxiv:quant-ph/0501184} whose success probability \(P_{E}\) is determined by the efficiency \(\eta\) of the photonic encoding circuit. A threshold \(\eta > 0.82 \) exists for the efficiency, above which \(P_{E}\to 1\) as \(m_1\to\infty\) given particular \(m_2\).'
 
 relations:
   parents:
@@ -67,7 +67,7 @@ relations:
     - code_id: bacon_shor
       detail: 'Bacon-Shor codes reduce to QPCs when all \(X\)-type gauge generators are fixed \cite[pg. 6]{arxiv:1809.01193}.'
     - code_id: majorana_stab
-      detail: 'QPCs for \(m_1=m_2\) can be conveniantly expressed in terms of mutually commuting Majorana operators \cite{arxiv:quant-ph/0003137}.'
+      detail: 'QPCs for \(m_1=m_2\) can be conveniently expressed in terms of mutually commuting Majorana operators \cite{arxiv:quant-ph/0003137}.'
     - code_id: constant_excitation
       detail: 'QPCs for even \(m_1\) can be made into CE codes by a Pauli transformation (e.g., \(XIXI\cdots XI\)) applied to each block of \(m_1\) qubits.'
     - code_id: ampdamp