refs

codes/quantum/oscillators/oscillators.yml

@@ -22,10 +22,12 @@ description: |
 
   States can be represented by a series via a basis expansion, such as that in the countable basis of Fock states \(|n\rangle\) with \(n\geq 0\).
   Alternatively, states can be represented as functions over the reals by expanding in a continuous "basis" (more technically, set of tempered distributions in the space dual to Schwartz space), such as the position "basis" \(|y\rangle\) with \(y\in\mathbb{R}\) or the momentum "basis" \(|p\rangle\) with \(p\in\mathbb{R}\).
+  A third option is to use coherent states \(|\alpha\rangle\) with \(\alpha\in\mathbb{C}\), which are eigenstates of the annihilation operator, which correspond to classical electromagnetic signals, and which resolve the identity \cite{arxiv:math-ph/0210005,arxiv:10.1016/0034-4877(71)90006-1,arxiv:10.1103/PhysRevB.12.1118,arxiv:10.1103/PhysRevB.18.6744}.
   States can further be represented as functions over the joint position-momentum phase space in the Wigner function formalism \cite{doi:10.1103/PhysRev.40.749,doi:10.1103/PhysRevA.15.449}.
 
   An important subset of states is formed by the \textit{Gaussian states}, which are in one-to-one correspondence with a (displacement) vector and covariance matrix \cite{arxiv:quant-ph/0410100,arxiv:0801.4604,arxiv:1110.3234,arxiv:2010.15518,arxiv:2409.11628}.
   Pure Gaussian states can be obtained from the \textit{vacuum Fock state} \(|n=0\rangle\) via a Gaussian unitary transformation (defined below). 
+  Any coherent state can be obtained from the vacuum Fock state, itself a coherent state, by a displacement.
 
 protection: |
   \subsection{Displacement error basis}

codes/quantum/qubits/stabilizer/topological/surface/higher_d/higher_dimensional_toric.yml

@@ -16,6 +16,8 @@ description: |
   Picking a hypercubic lattice yields the ordinary \(D\)-dimensional toric code.
   It is conjectured that appropriate twisted boundary conditions yield multi-dimensional toric code families with linear distance and logarithmic-weight stabilizer generators \cite{arxiv:1608.05089}.
 
+protection: |
+  Some higher-dimensional toric codes protect against burst errors \cite{arxiv:2205.13582}.
 
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