~

codes/quantum/properties/hamiltonian/constant_excitation.yml

@@ -14,9 +14,10 @@ description: |
   Code whose codewords lie in an excited-state eigenspace of a Hamiltonian governing the total energy or total number of excitations of the underlying quantum system.
   For qubit codes, such a Hamiltonian is often the \textit{total spin Hamiltonian}, \(H=\sum_i Z_i\).
   For spin-\(S\) codes, this generalizes to \(H=\sum_i J_z^{(i)}\), where \(J_z\) is the spin-\(S\) \(Z\)-operator.
-  For bosonic codes, such as Fock-state codes, codewords are often in an eigenspace with eigenvalue \(N>0\) of the \textit{total excitation} or \textit{energy Hamiltonian}, \(H=\sum_i \hat{n}_i\).
+  For bosonic (and, similarly, for fermion) codes, such as Fock-state codes, codewords are often in an eigenspace with eigenvalue \(N>0\) of the \textit{total excitation} or \textit{energy Hamiltonian}, \(H=\sum_i \hat{n}_i\).
 
 protection: |
+  CE codewords have to lie in the same excitation subspace in order to protect against changes in the total excitation number.
   Fock-state CE codes are protected from identical \hyperref[topic:ad]{AD} acting on all modes because the damping acts on all codewords identically \cite{arxiv:quant-ph/9704002,doi:10.1103/PhysRevA.56.1114}.
   The all-zero \hyperref[topic:ad]{AD} Kraus operator acts identically on every state and so can be exactly correctable in the case of Fock-state CE codes.
   For example, this operator's acting on a Fock state \(|\boldsymbol{m}\rangle\) depends only on the total occupation number \(|\boldsymbol{m}|=\sum_j m_j\) and not on the individual occupation numbers \(m_j\),

codes/quantum/qubits/majorana/fermions.yml

@@ -19,7 +19,7 @@ description: |
 
 features:
   encoders:
-    - 'A fermionic code using fermion-number eigenstates as codewords does not admit fermionic logical operators, and the codewords have to lie in the same fermion-number subspace \cite{arxiv:2411.08955}.'
+    - 'A fermionic code using fermion-number eigenstates as codewords does not admit fermionic logical operators \cite{arxiv:2411.08955}.'
 
   general_gates:
     - 'Clifford operations on fermionic codes, shown \cite{arxiv:quant-ph/0108033} to be equivalent to match gates \cite{doi:10.1145/380752.380785}, can be formulated using \textit{Fermionic Linear Optics}, a classically simulable model of computation \cite{arxiv:quant-ph/0108033,arxiv:quant-ph/0108010,arxiv:quant-ph/0404180,arxiv:0804.4050,arxiv:2010.15518,arxiv:2409.11628}. The structure of the Majorana Clifford group has been studied \cite{arxiv:2407.11319}.'
@@ -45,13 +45,20 @@ relations:
         The Majorana operator algebra is isomorphic to the qubit Pauli-operator algebra via various fermion-into-qubit encodings.
         Various conditions on when a fermion code is exactly solvable via a fermion-into-qubit mapping have been formulated \cite{arxiv:2003.05465,arxiv:2012.07857}.
         Using fermion codes with logical fermion encodings and the fermionic fast Fourier transform \cite{arxiv:1706.00023} can yield exponential improvements in circuit depth over fermion-into-qubit encodings \cite{arxiv:2411.08955}.
-
+    - code_id: constant_excitation
+      detail: 'Fermion codewords lying in a fixed fermion-number subspace have to lie in the same subspace in order to protect against changes in fermion number \cite{arxiv:2411.08955}.'
 
 
 # Begin Entry Meta Information
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: MichaelGullans
+      date: '2025-01-12'
+    - user_id: AlexanderSchuckert
+      date: '2025-01-12'
+    - user_id: VictorVAlbert
+      date: '2025-01-12'
     - user_id: VictorVAlbert
       date: '2022-12-04'
     - user_id: VictorVAlbert

codes/quantum/qubits/majorana/kitaev_chain.yml

@@ -17,7 +17,7 @@ alternative_names:
 description: |
   An \([[n,1,1]]_{f}\) Majorana stabilizer code forming the ground-state of the Kitaev Majorana chain (a.k.a. Kitaev Majorana wire) in its fermionic topological phase, which is unitarily equivalent to the 1D quantum Ising model in the symmetry-breaking phase via the Jordan-Wigner transformation.
   The code is usually defined using the algebra of two anti-commuting Majorana operators called \textit{Majorana zero modes (MZMs)} or \textit{Majorana edge modes (MEMs)}.
-  It can be thought of as the Majorana stabilizer analogue of the quantum repetition code \cite{arxiv:2411.08955}.
+  It can be thought of as the Majorana stabilizer analogue of the quantum repetition code, and it encodes a logical fermion because its logical Majorana operator has odd weight \cite{arxiv:2411.08955}.
 
   Codewords have different values of the fermionic parity.
   As a result, this code is considered unphysical because, in the fermionic context, fermion parity conservation prevents one from realizing coherent superpositions between them.