ref

codes/quantum/qubits/majorana/fermions.yml

@@ -11,14 +11,20 @@ name: 'Fermion code'
 #introduced: ''
 
 description: |
-  Finite-dimensional quantum error-correcting code encoding a logical (qudit or fermionic) Hilbert space into a physical Fock space of fermionic modes.
+  Finite-dimensional quantum error-correcting code encoding a logical qudit or fermionic Hilbert space into a physical Fock space of fermionic modes.
   Codes are typically described using Majorana operators, which are linear combinations of fermionic creation and annihilation operators \cite{arxiv:quant-ph/0003137}.
 
-  Admissible codewords are called fermionic states, a subset of which is the Gaussian fermionic states \cite{arxiv:quant-ph/0108033,arxiv:quant-ph/0108010,arxiv:quant-ph/0404180,arxiv:2010.15518,arxiv:2409.11628}.
+  Admissible codewords include fermionic states, a subset of which is the Gaussian fermionic states \cite{arxiv:quant-ph/0108033,arxiv:quant-ph/0108010,arxiv:quant-ph/0404180,arxiv:2010.15518,arxiv:2409.11628}.
 
 features:
+  encodings:
+    - '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}.'
+
   general_gates:
     - 'Clifford operations on fermionic codes can often 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:2010.15518,arxiv:2409.11628}. The structure of the Majorana Clifford group has been studied \cite{arxiv:2407.11319}.'
+    - 'General gates include include qubit-like \(S\), \(T\), and \(CZ\) gates acting on either logical qubit or logical fermionic encodings. Fermionic gates include braiding gates which correspond to exchanging Majorana modes. Hybrid gates include \(CZ_{qf}\) gates between a logical qubit and a logical fermion. The braiding, \(CZ_{f}\), \(CZ_{qf}\), Hadamard, \(S\), and \(T\) gates are universal \cite{arxiv:2411.08955}.'
+    - 'Logical-fermion circuits constructed out of certain transversal gates do not admit a lower \(T\) gate count than logical-qubit circuits \cite{arxiv:2411.08955}.'
+    - '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}.'
 
 notes:
   - 'See Ref. \cite{arxiv:1404.0897} for an introduction into Majorana-based qubits.'
@@ -32,9 +38,12 @@ relations:
     - code_id: oscillators
       detail: 'Bosonic (fermionic) codes are associated with bosonic (fermionic) degrees of freedom.'
     - code_id: fermions_into_qubits
-      detail: 'Fermion (fermion-into-qubit) codes encode logical information into a physical space of fermionic modes (qubits).
-      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}.'
+      detail: |
+        Fermion (fermion-into-qubit) codes encode logical information into a physical space of fermionic modes (qubits).
+        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}.
+
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/majorana/kitaev_chain.yml

@@ -10,9 +10,14 @@ logical: qubits
 name: 'Kitaev chain code'
 introduced: '\cite{arxiv:cond-mat/0010440}'
 
+alternative_names:
+  - 'Majorana repetition code'
+# 2411.08955
+
 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}.
 
   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.
@@ -23,6 +28,13 @@ protection: |
   However, the distance is one because the code does not protect against single Majorana operators, which do not commute with the parity symmetry.
   Disorder may help with protection \cite{arxiv:1108.3845}.
 
+features:
+  general_gates:
+    - 'Braiding gates, fermionic \(S\) gates, braid-based fermionic \(T\) gates, and fermion and hybrid qubit-fermion \(CZ\) gates \cite{arxiv:2411.08955}.'
+  decoders:
+    - 'Syndrome extraction can be performed by interfacing with a qubit ancilla and a hybrid qubit-fermion gate \cite{arxiv:2411.08955}.'
+
+
 realizations:
   - 'Photonic systems: braiding of defects has been simulated in a device that has a different notion of locality than a bona-fide fermionic system \cite{arxiv:1411.7751}.'
   - 'Superconducting circuits: initialization \cite{arxiv:2206.00563}, braiding \cite{arxiv:2203.15083} and detection \cite{arxiv:2203.15083,arxiv:2204.11372} of defects has been simulated in devices that have a different notion of locality than a bona-fide fermionic system.'
@@ -36,6 +48,10 @@ relations:
   parents:
     - code_id: mbq
       detail: 'Kitaev chain codewords can be obtained by restricting to only one Kitaev chain out of the two chains that define the tetron Majorana code.'
+  cousins:
+    - code_id: quantum_repetition
+      detail: 'The Kitaev chain code can be thought of as the Majorana stabilizer analogue of the quantum repetition code \cite{arxiv:2411.08955}.'
+
 
 # Begin Entry Meta Information
 _meta:

codes/quantum/qubits/stabilizer/topological/color/2d_color/2d_color.yml

@@ -19,6 +19,7 @@ description: |
 
   Most translation-invariant color codes are defined in trivalent planar graphs with three-colorable faces.
   The three admissible uniform tilings are the 6.6.6 (honeycomb) tiling, the 4.8.8 (square octagon) tiling, and the 4.6.12 tiling \cite[Fig. 1]{arxiv:1108.5738}.
+  Non-uniform tilings include the [4.6.8, 6.8.8] and [4.6.8, 4.8.12] tilings \cite{arxiv:1801.08143}.
   More general admissible tilings can be obtained via a fattening procedure \cite{arxiv:cond-mat/0607736}; see also a construction based on the  more general quantum pin codes \cite{arxiv:1906.11394}.
 
   Logical dimension is determined by the genus of the underlying surface (for closed surfaces) and the types of boundaries (for open surfaces).