refs

codes/classical/spherical/polytope/infinite/hypercube.yml

@@ -28,7 +28,9 @@ relations:
     - code_id: hypercubic
       detail: 'Hypercube codewords form the minimal lattice shell code of the \(\mathbb{Z}^n\) hypercubic lattice when the lattice is shifted such that the center of a hypercube is at the origin.'
     - code_id: binary_antipodal
-      detail: 'Binary antipodal codes are subcodes of a hypercube code since the hypercube code corresponds to the Hamming \(n\)-cube embedded into the unit \(n\)-sphere.'
+      detail: 'Binary antipodal codes are subcodes of a hypercube code since the hypercube code corresponds to the Hamming \(n\)-cube (a.k.a. Boolean hypercube) embedded into the unit \(n\)-sphere.'
+    - code_id: bits_into_bits
+      detail: 'Binary strings are elements of the Hamming \(n\)-cube (a.k.a. Boolean hypercube).'
 
 
 # Begin Entry Meta Information

codes/quantum/oscillators/oscillators.yml

@@ -76,6 +76,7 @@ features:
     - 'The number-phase interpretation allows for the mapping of rotor Clifford gates into the oscillator, some of which become non-unitary (e.g., conditional occupation number addition) \cite{arxiv:2311.07679}.'
     - 'ZX calculus has been extended to bosonic codes for both Gaussian operators \cite{arxiv:2405.07246} and Fock-state based operators \cite{arxiv:2406.02905}.
     An earlier graphical calculus exists for Gaussian pure states \cite{arxiv:1007.0725}.'
+    - 'Circuits can be decomposed into a series of primitives such as quantum lattice gates \cite{arxiv:2410.17069}.'
 
 
 notes:

codes/quantum/oscillators/single-mode.yml

@@ -11,6 +11,7 @@ name: 'Single-mode bosonic code'
 
 description: 'Encodes \(K\)-dimensional Hilbert space into a single bosonic mode. A trivial single-mode code encoding a qubit into the first two Fock states \(\{|0\rangle,|1\rangle\}\) is called the \textit{single-rail} encoding \cite{arxiv:quant-ph/0007106,arxiv:quant-ph/0205044}.'
 
+
 relations:
   parents:
     - code_id: qudits_into_oscillators

codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml

@@ -23,6 +23,7 @@ protection: 'Detects errors on \(d-1\) qubits, corrects errors on \(\left\lfloor
 
 features:
   transversal_gates:
+    - 'Stabilizer generators are Pauli strings can be defined as acting on subsets of qubits corresponding to subcubes of the Hamming \(n\)-cube (a.k.a. Boolean hypercube) \cite{arxiv:2410.07595}. Transversal \(Z\)-rotations by angles \(\pi/2^k\) acting on subcubes can implement logical multi-controlled-\(Z\) gates \cite{arxiv:2410.07595}.'
     - 'The \([[2^m,{m \choose r}, 2^{\min(r,m-r)}]]\) family, where \(r\) divides \(m\), admits diagonal gates in the form of \(Z\)-rotations by angle \(\pi/2^{m/r}\) \cite[Exam. 8 and Thm. 19]{arxiv:1910.09333}\cite{arxiv:1606.01904,arxiv:1606.01906,arxiv:1709.02832}.'
     - 'The family constructed out of shortened RM codes
     with parameters \([[\sum_{i=w+1}^m \binom{m}{i}, \sum_{i=0}^{w} \binom{m}{i}, \sum_{i=w+1}^{r+1} \binom{r+1}{i}]]\) for integers \(m > 2r\) and \(r > w \geq 0\) admits a transversal gate at the \(\nu\)th level in the hierarchy whenever \(m > \nu r\) \cite[Thm. 1]{arxiv:1709.03543}.'