refs

Author: valbert4

codes/quantum/groups/topological/quantum_double.yml

@@ -66,11 +66,14 @@ relations:
       Quantum-double codes for non-Abelian groups \(G\) are dual to Hopf-algebra quantum-double codes for Hopf algebras based on \(\text{Rep}(G)\) under the Tannaka-Krein duality \cite{arxiv:0907.2670}\cite[Fig. 1]{arxiv:1006.5823}.'
   cousins:
     - code_id: hamiltonian
-      detail: 'Quantum double code Hamiltonians can be simulated, with the help of perturbation theory, by two-dimensional two-body Hamiltonians with non-commuting terms \cite{arxiv:1011.1942}.'
+      detail: 'Quantum double code Hamiltonians can be simulated, with the help of perturbation theory and the \([[4,1,1,2]]\) subsystem code, by two-dimensional two-body Hamiltonians with non-commuting terms \cite{arxiv:1011.1942}.'
     - code_id: oecc
       detail: 'Subsystem versions of quantum-double codes have been formulated \cite{doi:10.5446/35287}.'
     - code_id: yetter_gauge_theory
       detail: 'Restricting 2-gauge theory constructions to a 2D manifold and replacing the 2-group with a group reproduces the phase of the Kitaev quantum double model \cite{arxiv:1606.06639}.'
+    - code_id: bacon_shor_4
+      detail: 'Quantum double code Hamiltonians can be simulated, with the help of perturbation theory and the four-qubit subsystem code, by two-dimensional two-body Hamiltonians with non-commuting terms \cite{arxiv:1011.1942}.'
+
 
 # \cite{manual:{Prashant Kumar, Quantum Double Subsystem Codes, Quantum Error Correction conference, University of Southern California, 2011}}'
 # https://qserver.usc.edu/qec11/slides/Kumar_QEC11.pdf

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

@@ -37,6 +37,10 @@ features:
   fault_tolerance:
     - 'Fault-tolerant computation schemes with number-phase codes have been proposed based on concatenation with Bacon-Shor subsystem codes \cite{arxiv:1901.08071}.'
 
+realizations:
+  - 'Motional degree of freedom of a trapped ion: state initialization \cite{arxiv:2412.04865}.'
+
+
 relations:
   parents:
     - code_id: bosonic_rotation

codes/quantum/oscillators/stabilizer/lattice/gkp.yml

@@ -49,7 +49,7 @@ features:
     It has been extended to utilize previously measured syndrome information \cite{arxiv:2312.07391}.'
 
 realizations:
-  - 'Motional degree of freedom of a trapped ion: square-lattice GKP encoding realized with the help of post-selection by Home group \cite{arxiv:1807.01033,arxiv:1907.06478}, followed by realization of reduced form of GKP error correction, where displacement error syndromes are measured to one bit of precision using an ion electronic state \cite{arxiv:2010.09681}. State preparation also realized by Tan group \cite{arxiv:2310.15546}. Universal gate set, including a two-qubit entangling gate, realized by Tan group \cite{arxiv:2409.05455}.'
+  - 'Motional degree of freedom of a trapped ion: square-lattice GKP encoding realized with the help of post-selection by Home group \cite{arxiv:1807.01033,arxiv:1907.06478}, followed by realization of reduced form of GKP error correction, where displacement error syndromes are measured to one bit of precision using an ion electronic state \cite{arxiv:2010.09681}. State preparation also realized by Tan group \cite{arxiv:2310.15546}. Universal gate set, including a two-qubit entangling gate, realized by Tan group \cite{arxiv:2409.05455}. State initialization and application to measuring displacements \cite{arxiv:2412.04865}.'
   - 'Microwave cavity coupled to superconducting circuits: reduced form of square-lattice GKP error correction, where displacement error syndromes are measured to one bit of precision using an ancillary transmon \cite{arxiv:1907.12487}. Subsequent paper by Devoret group \cite{arxiv:2211.09116} uses reinforcement learning for error-correction cycle design and is the first to go beyond break-even error-correction, with the lifetime of a logical qubit exceeding the cavity lifetime by about a factor of two (see also \cite{arxiv:2211.09319}). See Ref. \cite{arxiv:2111.07965} for another experiment. A feed-forward-free, i.e., fully autonomous protocol has also been implemented by Nord Quantique \cite{arxiv:2310.11400}. Qudit encodings with \(q=3,4\) have been realized, with logical error rates also beyond break even \cite{arxiv:2409.15065}.'
   - 'GKP states and homodyne measurements have been realized in propagating telecom light by the Furusawa group \cite{arxiv:2309.02306}.'
   - 'Single-qubit \(Z\)-gate has been demonstrated \cite{arxiv:1904.01351} in the single-photon subspace of an infinite-mode space \cite{arxiv:2310.12618}, in which time and frequency become bosonic conjugate variables of a single effective bosonic mode. In this context, GKP position-state wavefunctions are called Dirac combs or frequency combs.'

codes/quantum/properties/hamiltonian/commuting_projector.yml

@@ -15,8 +15,9 @@ protection: |
   Geometrically local commuting-projector code Hamiltonians on Euclidean manifolds are stable with respect to small perturbations when they satisfy the \hyperref[topic:tqo]{TQO conditions}, meaning that a notion of a phase can be defined \cite{arxiv:1001.4363,arxiv:1001.0344,arxiv:1109.1588,arxiv:1810.02428,arxiv:2010.15337}.
   This notion can be extended to semi-hyperbolic manifolds \cite{arxiv:2405.19412} and non-geometrically local QLDPC codes exhibiting check soundness \cite{arxiv:2411.01002} (see also \cite{arxiv:2411.02384}).
 
-  2D topological order on qubit manifolds requires weight-four Hamiltonian terms, i.e., it cannot be stabilized via weight-two or weight-three terms on nearly Euclidean geometries of qubits or qutrits \cite{arxiv:quant-ph/0308021,arxiv:1102.0770,arxiv:1803.02213}.
-  Hamiltonians with weight-two (two-body) terms cannot be used for suppressing errors \cite{arxiv:1410.5487}.
+  2D topological order on qubit manifolds requires weight-four (four-body) Hamiltonian terms, i.e., it cannot be stabilized via weight-two (two-body) or weight-three (three-body) terms on nearly Euclidean geometries of qubits or qutrits \cite{arxiv:quant-ph/0308021,arxiv:1102.0770,arxiv:1803.02213}.
+
+  Commuting-projector Hamiltonians with weight-two (two-body) terms cannot be used to suppress errors in adiabatic quantum computation \cite{arxiv:1410.5487}, but this can be circumvented with subsystem qubit stabilizer code Hamiltonians \cite{arxiv:1511.01997,arxiv:1606.03795}.
 
 
 relations:
@@ -28,6 +29,8 @@ relations:
     - code_id: topological
       detail: 'Geometrically local commuting-projector code Hamiltonians on Euclidean manifolds are stable with respect to small perturbations when they satisfy the \hyperref[topic:tqo]{TQO conditions}, meaning that a notion of a phase can be defined \cite{arxiv:1001.4363,arxiv:1001.0344,arxiv:1109.1588,arxiv:1810.02428,arxiv:2010.15337}.
       This notion can be extended to semi-hyperbolic manifolds \cite{arxiv:2405.19412} and non-geometrically local QLDPC codes exhibiting check soundness \cite{arxiv:2411.01002} (see also \cite{arxiv:2411.02384}).'
+    - code_id: subsystem_stabilizer
+      detail: 'Commuting-projector Hamiltonians with weight-two (two-body) terms cannot be used to suppress errors in adiabatic quantum computation \cite{arxiv:1410.5487}, but this can be circumvented with subsystem qubit stabilizer code Hamiltonians \cite{arxiv:1511.01997,arxiv:1606.03795}.'
 
 
 # Begin Entry Meta Information

codes/quantum/properties/stabilizer/qldpc/qldpc.yml

@@ -105,6 +105,7 @@ features:
     - 'Performing \(d\) syndrome extraction rounds obtains an \hyperref[topic:effective-distance]{effective distance} of \(d\) for a qubit QLDPC code \cite{arxiv:1310.2984}.'
     - 'Fault-tolerant constant-depth encoder and unencoder \cite{arxiv:2408.06299}.'
     - 'BP plus ordered Tanner forest (BP+OTF) almost-linear time decoder \cite{arxiv:2409.01440}.'
+    - 'Cluster decoder \cite{arxiv:2412.08817}.'
   fault_tolerance:
     - 'Lattice surgery techniques with ancilla qubits \cite{arxiv:2110.10794,arxiv:2308.08648}.
     In one such technique, one first performs a logical measurement by \hyperref[topic:code-switching]{code switching} into a code whose stabilizer group includes the original stabilizers together with the logical Paulis that are to be measured.

codes/quantum/qubits/subsystem/qldpc/bacon_shor/bacon_shor.yml

@@ -71,8 +71,7 @@ relations:
       detail: 'A compass code on a fully non-colored lattice reduces to the Bacon-Shor code.'
   cousins:
     - code_id: hamiltonian
-      detail: 'The 2D Bacon-Shor gauge-group Hamiltonian is the compass model \cite{doi:10.1070/PU1982v025n04ABEH004537,arxiv:cond-mat/0501708,arxiv:1303.5922}.
-      Bacon-Shor code Hamiltonians can be used to suppress errors in adiabatic quantum computation \cite{arxiv:1511.01997}, while subspace-code Hamiltonians with weight-two (two-body) terms cannot \cite{arxiv:1410.5487}.'
+      detail: 'The 2D Bacon-Shor gauge-group Hamiltonian is the compass model \cite{doi:10.1070/PU1982v025n04ABEH004537,arxiv:cond-mat/0501708,arxiv:1303.5922}.'
     - code_id: floquet
       detail: 'The Bacon-Shor code admits a Floquet version with a particular stabilizer measurement schedule \cite{arxiv:2403.03291}.'
     - code_id: hybrid_stabilizer

codes/quantum/qubits/subsystem/subsystem_css.yml

@@ -24,6 +24,12 @@ description: |
   The two matrix blocks, \(G_{Z}\) and \(G_X\), correspond to the parity-check matrices of two \hyperref[code:binary_linear]{binary linear codes}, an \([n,k_X,d_X]\) code \(C_X\) and \([n,k_Z,d_Z]\) code \(C_Z\), respectively.
   Code parameters and basis states can be expressed in terms of only data associated with these two classical codes \cite{arxiv:quant-ph/0610153,arxiv:quant-ph/0604161,arxiv:2311.18003}.
 
+protection: |
+  For any code whose gauge group is generated by \(XX\) and \(ZZ\), the weight of an \(X\)-type (\(Z\)-type) single-qubit bare-logical operator is lower-bounded by the number of \(Z\)-type (\(X\)-type) bare-logical operators acting on its
+  supporting logical qubits \cite{arxiv:1911.01354,manual:{P. Lisonek, A. Roy, and S. Trandafir, private communication, 2019}}.
+
+
+
 features:
   decoders:
     - 'Steane-type decoder utilizing data from the underlying classical codes \cite{arxiv:2311.18003}.'