LAST QCV ADDON

codes/quantum/oscillators/coherent_state/cat_concatenated.yml

@@ -10,24 +10,28 @@ name: 'Concatenated cat code'
 introduced: '\cite{arxiv:1409.6759}'
 
 description: |
-  A concatenated code whose outer code is a cat code.
+  A concatenated code whose outer code is a cat code. Most examples encode physical qubits of an inner stabilizer codes into the two-component cat code.
 
 protection: |
-  The cat code suppressed dephasing errors exponentially with the size of the coherent states, so the inner code (e.g., a quantum repetition code \cite{arxiv:1904.09474,arxiv:2009.10756,arxiv:2212.11927}) can be highly biased toward one type of noise while still ensuring good performance.
+  The cat code suppressed dephasing errors exponentially with the size of the coherent states, so the inner code (e.g., a quantum repetition code \cite{arxiv:1904.09474,arxiv:1905.00450,arxiv:2009.10756,arxiv:2212.11927}) can be highly biased toward one type of noise while still ensuring good performance.
 
 
 relations:
   parents:
     - code_id: qsc
   cousins:
     - code_id: quantum_repetition
-      detail: 'Cat codes have been concatenated with quantum repetition codes \cite{arxiv:1904.09474,arxiv:2009.10756,arxiv:2012.04108,arxiv:2212.11927}.'
+      detail: 'Cat codes have been concatenated with quantum repetition codes \cite{arxiv:1904.09474,arxiv:1905.00450,arxiv:2009.10756,arxiv:2012.04108,arxiv:2212.11927}.'
     - code_id: rotated_surface
       detail: 'Cat codes have been concatenated with rotated surface codes \cite{arxiv:2012.04108}.'
     - code_id: ldpc
-      detail: 'Cat codes have been concatenated with LDPC codes (which are treated as qubit stabilizer codes) \cite{arxiv:2401.09541}.'
-
-
+      detail: 'Cat codes have been concatenated with LDPC codes (treated as qubit stabilizer codes) \cite{arxiv:2401.09541}.'
+    - code_id: lhz
+      detail: 'LHZ parity-codes have been concatenated with cat codes \cite{arxiv:2404.11332}.'
+    - code_id: steane
+      detail: 'Steane codes have been concatenated with cat codes \cite{arxiv:0707.0327}.'
+    - code_id: qubit_golay
+      detail: 'Quantum Golay codes have been concatenated with cat codes \cite{arxiv:0707.0327}.'
 
 
 

codes/quantum/oscillators/fock_state/constant_excitation/dual_rail.yml

@@ -51,7 +51,7 @@ relations:
     - code_id: one_hot_quantum
   cousins:
     - code_id: oscillators_concatenated
-      detail: 'The KLM protocol, one of the first protocols for fault-tolerant quantum computation, utilizes concatenations of the dual-rail with a stabilizer code \cite{doi:10.1038/35051009}. Concatenating the dual-rail code with an \([[n,k,d]]\) stabilizer code yields an \([[2n,k,d]]\) constant-excitation code \cite{arxiv:2010.00538} that protects against \(d-1\) \hyperref[topic:ad]{AD} errors \cite{arxiv:1001.2356}. Concatenating the outer dual-rail code with an inner single-mode bosonic code yields several gates that are independent of the inner code \cite{arxiv:1605.09278}.'
+      detail: 'The KLM protocol, one of the first protocols for fault-tolerant quantum computation, utilizes concatenations of the dual-rail code with a stabilizer code \cite{doi:10.1038/35051009}. Concatenating the dual-rail code with an \([[n,k,d]]\) stabilizer code yields an \([[2n,k,d]]\) constant-excitation code \cite{arxiv:2010.00538} that protects against \(d-1\) \hyperref[topic:ad]{AD} errors \cite{arxiv:1001.2356}. Concatenating the outer dual-rail code with an inner single-mode bosonic code yields several gates that are independent of the inner code \cite{arxiv:1605.09278}.'
     - code_id: single-mode
       detail: 'Concatenating the outer dual-rail code with an inner single-mode bosonic code yields several gates that are independent of the inner code \cite{arxiv:1605.09278}.'
     - code_id: ampdamp

codes/quantum/oscillators/hybrid/hybrid_qudit_oscillator.yml

@@ -14,7 +14,7 @@ description: |
   Encodes a \(K\)-dimensional logical Hilbert space into \(n_1\) modular qudits of dimension \(q\) and \(n_2 \neq 0\) oscillators, i.e., the Hilbert space of \(\ell^2\)-normalizable functions on \(\mathbb{Z}_q^{n_1} \times \mathbb{R}^{n_2}\).
 
 notes:
-  - 'See reviews \cite{arxiv:1409.3719,arxiv:2407.10381} for introductions to hybrid qudit-oscillator platforms.'
+  - 'See reviews \cite{arxiv:1409.3719,doi:10.1002/9783527635283,arxiv:2407.10381} for introductions to hybrid qudit-oscillator platforms.'
 
 relations:
   parents:

codes/quantum/oscillators/oscillators.yml

@@ -16,11 +16,12 @@ alternative_names:
 
 description: |
   Encodes logical Hilbert space, finite- or infinite-dimensional, into a physical Hilbert space that contains at least one \textit{oscillator} (a.k.a. \textit{bosonic mode} or \textit{qumode}).
+
   States of a single oscillator correspond to \(\ell^2\)-normalizable functions on \(\mathbb{R}\) that have finite energy, finite variance, and finite values of all other moments (where the energy operator is defined to be the harmonic oscillator Hamiltonian); such functions form \textit{Schwartz space}, a subspace of Hilbert space \cite{arxiv:2211.05714}.
   Ideal codewords may not be normalizable because the space is infinite-dimensional, so approximate versions have to be constructed in practice.
 
-protection: |
 
+protection: |
   \subsection{Displacement error basis}
 
   An error set relevant to \hyperref[code:oscillator_stabilizer]{bosonic stabilizer} codes is the set of \textit{displacement operators}, a bosonic analogue of the Pauli string basis for \hyperref[code:qubits_into_qubits]{qubit} codes.
@@ -61,13 +62,8 @@ features:
   These are examples of Gaussian channels, i.e., channels that map Gaussian states to Gaussian states \cite{doi:10.1016/0034-4877(79)90049-1,arxiv:quant-ph/0505151,arxiv:0707.0604,arxiv:0804.0511,arxiv:1004.0196,arxiv:1009.1108,arxiv:1012.4266}.'
 
   general_gates:
-    - 'Displacement operations form a group called the Heisenberg-Weyl group, the oscillator analogue to the Pauli group.
-    Analogues of (non-Pauli) Clifford-group transformations are the \textit{Gaussian unitary transformations} (a.k.a. symplectic, Bogoliubov-Valatin, or linear canonical transformations) \cite{doi:10.1063/1.1665805,arxiv:1110.3234,manual:{Wagner, M. Unitary transformations in solid state physics. Netherlands.}}, which are unitaries generated by quadratic polynomials in positions and momenta.
-    The Gaussian unitary transformation group permutes displacement operators amognst themselves, and, up to any phases, is equivalent to the symplectic group \(Sp(2n,\mathbb{R})\).'
-    - 'Computing using Gaussian states and Gaussian unitaries only can be efficiently simulated on a classical computer \cite{arxiv:1210.1783,arxiv:1208.3660}.
-    This remains true even if superpositions of Gaussian states are considered \cite{arxiv:2010.14363,arxiv:2403.19059}, but is no longer the case when the number of modes scales exponentially \cite{arxiv:2407.06290}.
-    A cubic phase gate is required to make a universal gate set on the oscillator \cite{arxiv:quant-ph/0410100}; other gates are possible, but higher-order squeezing is not well-defined \cite{doi:10.1103/PhysRevD.29.1107}.
-    More generally, controllability has been proven when the normalizable state space is restricted to Shwartz space, the space of states with bounded moments of position and momentum \cite{arxiv:quant-ph/0505063}.'
+    - 'Displacement operations form a group called the Heisenberg-Weyl group, the oscillator analogue to the Pauli group. Analogues of (non-Pauli) Clifford-group transformations are the \textit{Gaussian unitary transformations} (a.k.a. symplectic, Bogoliubov-Valatin, or linear canonical transformations) \cite{doi:10.1063/1.1665805,arxiv:1110.3234,manual:{Wagner, M. Unitary transformations in solid state physics. Netherlands.}}, which are unitaries generated by quadratic polynomials in positions and momenta. The Gaussian unitary transformation group permutes displacement operators amognst themselves, and, up to any phases, is equivalent to the symplectic group \(Sp(2n,\mathbb{R})\).'
+    - 'Computing using Gaussian states and Gaussian unitaries only can be efficiently simulated on a classical computer \cite{arxiv:quant-ph/0109047,arxiv:1210.1783,arxiv:1208.3660}. This remains true even if superpositions of Gaussian states are considered \cite{arxiv:2010.14363,arxiv:2403.19059}, but is no longer the case when the number of modes scales exponentially \cite{arxiv:2407.06290}. A cubic phase gate is required to make a universal gate set on the oscillator \cite{arxiv:quant-ph/9810082,arxiv:quant-ph/0410100}; other gates are possible, but quartic or higher versions of squeezing are not well defined \cite{doi:10.1103/PhysRevD.29.1107}. More generally, controllability has been proven when the normalizable state space is restricted to Schwartz space \cite{arxiv:quant-ph/0505063}.'
     - 'Measurements can be performed by homodyne and generalized homodyne measurements \cite{arxiv:quant-ph/0511044}.'
     - '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}.

codes/quantum/oscillators/stabilizer/hyperplane/cv_cluster_state.yml

@@ -43,6 +43,12 @@ features:
 
 realizations:
   - 'Analog cluster states on a number of modes ranging from tens to millions \cite{arxiv:1306.3366,arxiv:1311.2957,arxiv:1606.06688} have been synthesized in photonic degrees of freedom.'
+  - 'Required primitives for Gaussian gates have been realized \cite{arxiv:0906.3141}.'
+
+notes:
+  - 'See Ref. \cite{doi:10.1002/9783527635283} for a review of analog cluster states and their applications.'
+
+
 
 relations:
   parents:

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

@@ -23,7 +23,7 @@ relations:
     - code_id: qudits_into_oscillators
   cousins:
     - code_id: dfour
-    - code_id: oscillators_concatenated
+    - code_id: gkp_concatenated
       detail: 'The \(D_4\) hyper-diamond GKP code can be seen as a concatenation of a rotated square-lattice GKP code with a repetition code \cite{arxiv:2201.12337}. This is related to the fact that the four-bit repetition code yields the \(D_4\) hyper-diamond lattice code via \term{Construction A}.'
     - code_id: quantum_repetition
       detail: 'The \(D_4\) hyper-diamond GKP code can be seen as a concatenation of a rotated square-lattice GKP code with a repetition code \cite{arxiv:2201.12337}. This is related to the fact that the four-bit repetition code yields the \(D_4\) hyper-diamond lattice code via \term{Construction A}.'

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

@@ -39,7 +39,7 @@ relations:
       detail: 'Oscillator-into-oscillator GKP codes are \(n\)-mode quantum lattice codes with less than \(2n\) stabilizers, i.e., constructed using a degenerate lattice (see Appx. A of Ref. \cite{arxiv:2109.14645}).'
     - code_id: oscillators_into_oscillators
   cousins:
-    - code_id: oscillators_concatenated
+    - code_id: gkp_concatenated
       detail: 'Oscillator-into-oscillator GKP codes concantenated with qubit-into-oscillator GKP codes can outperform more conventional concatenations of qubit-into-oscillator GKP codes with qubit stabilizer codes \cite{arxiv:2209.04573}.'
     - code_id: dfour_gkp
       detail: '\(D_4\) hyper-diamond GKP codes may be optimal for GKP stabilizer codes utilizing two ancilla modes \cite{arxiv:2212.11970}.'

codes/quantum/properties/block/block_quantum.yml

@@ -12,14 +12,16 @@ description: |
   For finite dimensional codes, the dimension of the underlying subsystem is denoted by \(q\).
 
 protection: |
-  Block codes protect from errors acting on a few of the \(n\) subsystems. A block code with \textit{distance} \(d\) detects errors acting on up to \(d-1\) subsystems, and corrects erasure errors on up to \(d-1\) subsystems.
+  Block codes protect from erasures or, more generally, errors acting on a few of the \(n\) subsystems. A block code with \textit{distance} \(d\) detects errors acting on up to \(d-1\) subsystems, and corrects erasure errors on up to \(d-1\) subsystems.
 
   The \textit{weight} of an operator on a tensor-product Hilbert space is the number of subsystems on which the operator acts non-trivially.
   For example, an operator acting on two subsystem is called a weight-two operator or a two-body operator.
 
-  Noise models for block codes include \textit{stochastic noise}, in which every possible error is assigned a probability.
+  General noise models for block codes include \textit{stochastic noise}, in which every possible error is assigned a probability.
   In the case of \textit{local stochastic noise}, the probability decreases rapidly (typically, exponentially) with the number of subsystems that an error acts on.
   On the other hand, the \textit{adversarial noise} model consists of errors acting on at most a fixed number of subsystems.
+  Errors acting on subsystems in a geometrically local region are called \textit{burst errors} \cite{doi:10.1143/jpsj.69.3540,doi:10.1109/18.771250}.
+
 
 features:
   transversal_gates:

codes/quantum/properties/qecc.yml

@@ -56,7 +56,7 @@ features:
   rate: 'The quantum channel capacity, i.e., the regularized coherent information, is the highest rate of quantum information transmission through a quantum channel with arbitrarily small error rate \cite{arxiv:quant-ph/9604015,preset:ShorMSRI,arxiv:quant-ph/0304127}. See \cite[Ch. 24]{arxiv:1106.1445} for definitions and a history.'
 
 notes:
-  - 'See Refs. \cite{doi:10.1090/gsm/047,doi:10.1017/CBO9780511976667,arxiv:0905.2794,arxiv:1302.3428,doi:10.1103/RevModPhys.88.041001,doi:10.1002/9783527805785.ch1,arxiv:1907.11157,preset:PreskillNotes,arxiv:1910.03672,doi:10.1002/9781119790327.ch10} for overviews of quantum error correction.'
+  - 'See Refs. \cite{arxiv:quant-ph/9712048,doi:10.1090/gsm/047,doi:10.1017/CBO9780511976667,arxiv:0905.2794,arxiv:1302.3428,doi:10.1103/RevModPhys.88.041001,doi:10.1002/9783527805785.ch1,arxiv:1907.11157,preset:PreskillNotes,arxiv:1910.03672,doi:10.1002/9781119790327.ch10} for overviews of quantum error correction.'
   - 'See Refs. \cite{doi:10.1017/CBO9781139034807,doi:10.1201/b15868,preset:GottesmanBook} for books on quantum error correction.'
   - 'See video tutorials by \href{https://www.youtube.com/watch?v=_ls3KczZL2c}{V. V. Albert}, \href{https://www.youtube.com/watch?v=uD69GCYF9Zg}{S. M. Girvin}, \href{https://www.youtube.com/watch?v=buIbd_aXAHw}{P. Shor}, \href{https://www.youtube.com/watch?v=Je7sVJGKMgU}{B. Terhal}, and \href{https://www.youtube.com/watch?v=mcwpe8iJ5uo}{J. Wright}.'
   - 'Quantum error correction was initially claimed not to be theoretically possible \cite{arxiv:hep-th/9406058,doi:10.1098/rsta.1995.0106}.'

codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml

@@ -86,7 +86,7 @@ realizations:
   - 'Quantum compututation with cluster states has been realized in the polarizations of photons \cite{arxiv:quant-ph/0503126,arxiv:0906.2233}.'
 
 notes:
-  - 'See Ref. \cite{arxiv:quant-ph/0602096} for a review of cluster states and their applications.'
+  - 'See Refs. \cite{arxiv:quant-ph/0602096,doi:10.1002/9783527635283} for a review of cluster states and their applications.'
 
 
 relations:

codes/quantum/qubits/stabilizer/quantum_tensor_product.yml

@@ -13,6 +13,9 @@ introduced: '\cite{arxiv:quant-ph/0703181,arxiv:1605.09598}'
 description: |
   CSS code constructed from a tensor code. In some cases, only one of the classical codes forming the tensor code needs to be self-orthogonal. 
 
+protection: |
+  If one of the classical codes forming the tensor code protects against burst errors, the resulting quantum code does also \cite{arxiv:1605.09598}.
+
 relations:
   parents:
     - code_id: qubit_css