From 30e8b5068bb39b4d2b84af47796968fd631ac93a Mon Sep 17 00:00:00 2001 From: "Victor V. Albert" Date: Wed, 22 Nov 2023 22:11:30 -0500 Subject: [PATCH] small_distance --- .../descendants/classical/list_small.yml | 31 +++++++++++++++++++ ...list_single.yml => list_small_quantum.yml} | 6 ++-- codes/classical/bits/cyclic/gold.yml | 2 +- codes/classical/bits/cyclic/melas.yml | 1 + .../bits/easy/hamming/extended_hamming.yml | 1 + codes/classical/bits/nonlinear/preparata.yml | 3 +- .../bits/nonlinear/sphere_packing/best.yml | 1 + .../sphere_packing/sloane_whitehead.yml | 2 +- codes/classical/bits/nonlinear/vasilyev.yml | 2 +- .../properties/block/small_distance.yml | 27 ++++++++++++++++ .../classical/q-ary_digits/easy/hexacode.yml | 1 + .../q-ary_digits/easy/q-ary_hamming.yml | 1 + .../q-ary_digits/easy/q-ary_parity_check.yml | 1 + .../q-ary_digits/easy/ternary_golay.yml | 1 + codes/classical/rings/octacode.yml | 2 +- codes/classical/rings/pentacode.yml | 3 +- codes/quantum/groups/group_4_2_2.yml | 2 +- .../rotors/stabilizer/css/current_mirror.yml | 2 +- .../rotors/stabilizer/css/rotor_3_1_2.yml | 2 +- .../groups/rotors/stabilizer/css/zero_pi.yml | 2 +- .../groups/rotors/stabilizer/rotor_5_1_3.yml | 2 +- .../stabilizer/hyperplane/braunstein.yml | 2 +- .../stabilizer/hyperplane/lloyd_slotine.yml | 2 +- ...istance.yml => quantum_small_distance.yml} | 4 +-- codes/quantum/qubits/fermions/mbq.yml | 2 +- .../binary_dihedral_permutation_invariant.yml | 2 +- .../icosahedral_permutation_invariant.yml | 2 +- codes/quantum/qubits/rm/diagonal_clifford.yml | 2 +- .../qubits/small_distance/h_code_jones.yml | 2 +- .../quantum/qubits/small_distance/iceberg.yml | 2 +- .../qubits/small_distance/quantum_hamming.yml | 2 +- .../small_distance/small/qubit_5_6_2.yml | 2 +- .../small_distance/small/stab_8_3_2.yml | 2 +- codes/quantum/qubits/small_distance/tfim.yml | 2 +- .../non-css/rhombic_dodecahedron_surface.yml | 2 +- .../two_dim/stellated_dodecahedron_css.yml | 2 +- .../surface/two_dim/surface-17.yml | 2 +- codes/quantum/qudits/qudit_hamming_css.yml | 2 +- codes/quantum/qudits/small/qudit_5_1_3.yml | 2 +- codes/quantum/qudits/small/stab_3_1_2.yml | 2 +- codes/quantum/qudits/small/stab_9_1_3.yml | 2 +- .../qudits_galois/small/galois_5_1_3.yml | 2 +- 42 files changed, 103 insertions(+), 36 deletions(-) create mode 100644 codelists/descendants/classical/list_small.yml rename codelists/descendants/quantum/{list_single.yml => list_small_quantum.yml} (84%) create mode 100644 codes/classical/properties/block/small_distance.yml rename codes/quantum/properties/block/{small_distance.yml => quantum_small_distance.yml} (75%) diff --git a/codelists/descendants/classical/list_small.yml b/codelists/descendants/classical/list_small.yml new file mode 100644 index 000000000..e293fef3d --- /dev/null +++ b/codelists/descendants/classical/list_small.yml @@ -0,0 +1,31 @@ + +list_id: 'small' + +title: | + Small-distance classical codes + +intro: | + Here is a list of block codes of length \(n\) that detect or correct an error on at most two coordinates. + + +display: + style: table + options: + cssclass: xtra-xtra-stretch + columns: + - property: name + title: Code + link_to_code: true + cssclass: 'top left' + + - property: description + title: Description + cssclass: 'textit' + first_paragraph_only: true + +sort: + by: name + +codes: + select: + - descendant_of: small_distance diff --git a/codelists/descendants/quantum/list_single.yml b/codelists/descendants/quantum/list_small_quantum.yml similarity index 84% rename from codelists/descendants/quantum/list_single.yml rename to codelists/descendants/quantum/list_small_quantum.yml index e10f97d04..6972cbbd0 100644 --- a/codelists/descendants/quantum/list_single.yml +++ b/codelists/descendants/quantum/list_small_quantum.yml @@ -1,8 +1,8 @@ -list_id: 'single' +list_id: 'small_quantum' title: | - Small-distance codes + Small-distance quantum codes intro: | Here is a list of codes defined on \(n\) identical subsystems (e.g., qubits, modular qudits, or Galois qudits) that detect or correct an error on at most one subsystem. @@ -28,4 +28,4 @@ sort: codes: select: - - descendant_of: small_distance + - descendant_of: small_distance_quantum diff --git a/codes/classical/bits/cyclic/gold.yml b/codes/classical/bits/cyclic/gold.yml index 25cfbc3b0..f8bd64b6b 100644 --- a/codes/classical/bits/cyclic/gold.yml +++ b/codes/classical/bits/cyclic/gold.yml @@ -10,7 +10,7 @@ logical: bits name: 'Gold code' introduced: '\cite{doi:10.1109/TIT.1967.1054048}' -description: 'Member of the family of \([2^r-1, 2r ]\) cyclic binary linear code characterized by the generator polynomial of degree \(r\) of two maximum-period sequences of period \(2^r-1\) with absolute cross-correlation \( \leq 2^{(r+2)/2}\). Gold codewords are generated using \(m\)-sequences \(x\) and \(y\), which are codewords of simplex codes with check polynomials of degree \(r\) \cite{doi:10.1109/TIT.1967.1054048}.' +description: 'Member of the family of \([2^r-1, 2r ]\) cyclic binary linear codes characterized by the generator polynomial of degree \(r\) of two maximum-period sequences of period \(2^r-1\) with absolute cross-correlation \( \leq 2^{(r+2)/2}\). Gold codewords are generated using \(m\)-sequences \(x\) and \(y\), which are codewords of simplex codes with check polynomials of degree \(r\) \cite{doi:10.1109/TIT.1967.1054048}.' features: encoders: diff --git a/codes/classical/bits/cyclic/melas.yml b/codes/classical/bits/cyclic/melas.yml index dcb8f0782..e72ca8f65 100644 --- a/codes/classical/bits/cyclic/melas.yml +++ b/codes/classical/bits/cyclic/melas.yml @@ -20,6 +20,7 @@ relations: parents: - code_id: binary_cyclic - code_id: reversible + - code_id: small_distance # MacWilliams Sloane cousins: - code_id: quaternary_over_z4 diff --git a/codes/classical/bits/easy/hamming/extended_hamming.yml b/codes/classical/bits/easy/hamming/extended_hamming.yml index 742573ee1..ba2996fb1 100644 --- a/codes/classical/bits/easy/hamming/extended_hamming.yml +++ b/codes/classical/bits/easy/hamming/extended_hamming.yml @@ -16,6 +16,7 @@ description: | relations: parents: - code_id: binary_linear + - code_id: small_distance cousins: - code_id: univ_opt_q-ary detail: 'Several extended Hamming codes are LP universally optimal codes \cite{arxiv:1212.1913}.' diff --git a/codes/classical/bits/nonlinear/preparata.yml b/codes/classical/bits/nonlinear/preparata.yml index 2a76be540..adbc70052 100644 --- a/codes/classical/bits/nonlinear/preparata.yml +++ b/codes/classical/bits/nonlinear/preparata.yml @@ -9,7 +9,7 @@ physical: bits logical: bits name: 'Preparata code' -introduced: '\cite{doi:10.1007/0-387-34799-2_39}' +introduced: '\cite{doi:10.1016/S0019-9958(68)90874-7}' description: | A nonlinear binary \((2^{m+1}-1, 2^{m+1}-2m-2, 5)\) code where \(m\) is odd. @@ -36,6 +36,7 @@ relations: parents: - code_id: nearly_perfect detail: 'Preparata codes are uniformly packed and nearly perfect \cite{doi:10.1016/0012-365X(72)90025-8}. For any word \(u\) and Preparata codebook \(C\) with \(d(u, C) > 2\), we have that \(u\) has a distance 2 or 3 to exactly floor((2^{m+1}-1)/3) codewords.' + - code_id: small_distance cousins: - code_id: quaternary_over_z4 detail: 'Preparata codes can be seen, via the Gray map, as linear codes over \(\mathbb{Z}_4\) \cite{doi:10.1109/18.312154,arxiv:math/0207208}.' diff --git a/codes/classical/bits/nonlinear/sphere_packing/best.yml b/codes/classical/bits/nonlinear/sphere_packing/best.yml index 083623bde..68de792a7 100644 --- a/codes/classical/bits/nonlinear/sphere_packing/best.yml +++ b/codes/classical/bits/nonlinear/sphere_packing/best.yml @@ -19,6 +19,7 @@ description: | relations: parents: - code_id: bits_into_bits + - code_id: small_distance cousins: - code_id: construction_a detail: 'Using Construction \(A\), the Best code yields \(P_{10c}\), a non-lattice sphere packing in 10 dimensions that is the densest known \cite{doi:10.4153/CJM-1971-081-3}\cite[pg. 140]{doi:10.1007/978-1-4757-6568-7}.' diff --git a/codes/classical/bits/nonlinear/sphere_packing/sloane_whitehead.yml b/codes/classical/bits/nonlinear/sphere_packing/sloane_whitehead.yml index 7222e04cc..e5227e3a3 100644 --- a/codes/classical/bits/nonlinear/sphere_packing/sloane_whitehead.yml +++ b/codes/classical/bits/nonlinear/sphere_packing/sloane_whitehead.yml @@ -20,7 +20,7 @@ relations: parents: - code_id: bits_into_bits - code_id: uplusv - + - code_id: small_distance # Begin Entry Meta Information _meta: diff --git a/codes/classical/bits/nonlinear/vasilyev.yml b/codes/classical/bits/nonlinear/vasilyev.yml index 44c591646..c31ffdf00 100644 --- a/codes/classical/bits/nonlinear/vasilyev.yml +++ b/codes/classical/bits/nonlinear/vasilyev.yml @@ -21,7 +21,7 @@ relations: - code_id: uplusv - code_id: perfect_binary detail: 'Vasilyev codes are perfect nonlinear binary codes and are inequivalent to any linear code.' - + - code_id: small_distance # Begin Entry Meta Information _meta: diff --git a/codes/classical/properties/block/small_distance.yml b/codes/classical/properties/block/small_distance.yml new file mode 100644 index 000000000..6e1740a17 --- /dev/null +++ b/codes/classical/properties/block/small_distance.yml @@ -0,0 +1,27 @@ +####################################################### +## This is a code entry in the error correction zoo. ## +## https://github.com/errorcorrectionzoo ## +####################################################### + +code_id: small_distance +# includes Galois, modular, oscillators, and groups + +name: 'Small-distance block code' + +description: | + A block code of length \(n\) that either detects or corrects errors on at most two coordinates, i.e., has distance \(d \leq 5\). + + +relations: + parents: + - code_id: block + cousins: + - code_id: small_distance_quantum + + +# Begin Entry Meta Information +_meta: + # Change log - most recent first + changelog: + - user_id: VictorVAlbert + date: '2023-11-22' diff --git a/codes/classical/q-ary_digits/easy/hexacode.yml b/codes/classical/q-ary_digits/easy/hexacode.yml index 6135677cd..5d5e94138 100644 --- a/codes/classical/q-ary_digits/easy/hexacode.yml +++ b/codes/classical/q-ary_digits/easy/hexacode.yml @@ -51,6 +51,7 @@ relations: detail: 'The hexacode is an MDS code \cite[Exer. 578]{doi:10.1017/CBO9780511807077}.' - code_id: extended_reed_solomon detail: 'The hexacode is an extended RS code \cite[pg. 82]{doi:10.1007/978-1-4757-6568-7}.' + - code_id: small_distance cousins: - code_id: q-ary_hamming detail: 'The hexacode is an extended ternary Hamming code \cite[Exer. 578]{doi:10.1017/CBO9780511807077}.' diff --git a/codes/classical/q-ary_digits/easy/q-ary_hamming.yml b/codes/classical/q-ary_digits/easy/q-ary_hamming.yml index 897b63a29..72a66433f 100644 --- a/codes/classical/q-ary_digits/easy/q-ary_hamming.yml +++ b/codes/classical/q-ary_digits/easy/q-ary_hamming.yml @@ -20,6 +20,7 @@ relations: - code_id: perfect - code_id: univ_opt_q-ary detail: 'Hamming codes and their punctured and shortened versions are LP universally optimal codes \cite{arxiv:1212.1913}.' + - code_id: small_distance cousins: - code_id: incidence_matrix detail: 'Columns of a Hamming parity-check matrix correspond to one-dimensional subspaces of \(GF(q)^n\).' diff --git a/codes/classical/q-ary_digits/easy/q-ary_parity_check.yml b/codes/classical/q-ary_digits/easy/q-ary_parity_check.yml index 673986831..099173ef5 100644 --- a/codes/classical/q-ary_digits/easy/q-ary_parity_check.yml +++ b/codes/classical/q-ary_digits/easy/q-ary_parity_check.yml @@ -18,6 +18,7 @@ relations: - code_id: q-ary_cyclic detail: 'Since permutations coordinate sums, the cyclic permutation of an SPC codeword is another codeword. The generator polynomial of the code is \(x-1\).' - code_id: mds + - code_id: small_distance cousins: - code_id: q-ary_ldgm detail: 'Concatenated \(q\)-ary parity-check codes are LDGM \cite{doi:10.1109/20.917609}.' diff --git a/codes/classical/q-ary_digits/easy/ternary_golay.yml b/codes/classical/q-ary_digits/easy/ternary_golay.yml index cca7edc3b..8fb1abcc3 100644 --- a/codes/classical/q-ary_digits/easy/ternary_golay.yml +++ b/codes/classical/q-ary_digits/easy/ternary_golay.yml @@ -55,6 +55,7 @@ relations: detail: 'The ternary Golay code is perfect.' - code_id: delsarte_optimal_q-ary detail: 'The ternary Golay code and one of its shortened versions are \(q\)-ary sharp configurations \cite[Table 12.1]{preset:HKSbounds}.' + - code_id: small_distance cousins: - code_id: golay - code_id: self_dual diff --git a/codes/classical/rings/octacode.yml b/codes/classical/rings/octacode.yml index 0e943f4a2..dea25b362 100644 --- a/codes/classical/rings/octacode.yml +++ b/codes/classical/rings/octacode.yml @@ -11,7 +11,7 @@ name: 'Octacode' introduced: '\cite{doi:10.1016/0097-3165(93)90070-O,doi:10.1007/978-1-4757-6568-7,arXiv:math/0208001}' description: | - The unique self-dual linear code of length 8 over \(\mathbb{Z}_4\) with generator matrix + The unique self-dual linear code of length 8 and Lee distance 6 over \(\mathbb{Z}_4\) with generator matrix \begin{align} \begin{pmatrix} 3 & 3 & 2 & 3 & 1 & 0 & 0 & 0\\ diff --git a/codes/classical/rings/pentacode.yml b/codes/classical/rings/pentacode.yml index 8f46e6ddc..e6f22044b 100644 --- a/codes/classical/rings/pentacode.yml +++ b/codes/classical/rings/pentacode.yml @@ -11,12 +11,13 @@ name: 'Pentacode' introduced: '\cite{doi:10.1007/bf01388558}' description: | - Nonlinear code over \(\mathbb{Z}_4\) whose codewords are all cyclic permutations and negations of the strings \(01112\), \(03110\), \(21310\), and \(21132\). + Nonlinear \((5,40,4)_{\mathbb{Z}_4}\) code over \(\mathbb{Z}_4\) whose codewords are all cyclic permutations and negations of the strings \(01112\), \(03110\), \(21310\), and \(21132\). relations: parents: - code_id: rings_into_rings + - code_id: small_distance cousins: - code_id: best detail: 'Codewords of the Best code can be obtained by applying the Gray map to the pentacode \cite[Sec. 2]{doi:10.1007/BF01388558}.' diff --git a/codes/quantum/groups/group_4_2_2.yml b/codes/quantum/groups/group_4_2_2.yml index e2a0d7f9f..8a4923e61 100644 --- a/codes/quantum/groups/group_4_2_2.yml +++ b/codes/quantum/groups/group_4_2_2.yml @@ -22,7 +22,7 @@ relations: detail: 'The four group-qudit code is the smallest quantum double code.' - code_id: covariant detail: 'The four group-qudit code is \(G\)-covariant.' - - code_id: small_distance + - code_id: small_distance_quantum cousins: - code_id: iceberg detail: 'The four group-qudit code can be extended to the \([[2m,2m-2,2]]_{G}\) group-qudit code \cite[Sec. VIII]{arxiv:1902.07714}. The latter reduces to the \([[2m,2m-2,2]]\) error-detecting code for \(G=\mathbb{Z}_2\).' diff --git a/codes/quantum/groups/rotors/stabilizer/css/current_mirror.yml b/codes/quantum/groups/rotors/stabilizer/css/current_mirror.yml index 856b76958..b60ade6c1 100644 --- a/codes/quantum/groups/rotors/stabilizer/css/current_mirror.yml +++ b/codes/quantum/groups/rotors/stabilizer/css/current_mirror.yml @@ -33,7 +33,7 @@ features: relations: parents: - code_id: homological_rotor - - code_id: small_distance + - code_id: small_distance_quantum cousins: - code_id: gkp detail: 'Current-mirror code phase gates utilize ancillary osillators in square-lattice GKP states \cite{arXiv:cond-mat/0609441,arxiv:1302.4122}.' diff --git a/codes/quantum/groups/rotors/stabilizer/css/rotor_3_1_2.yml b/codes/quantum/groups/rotors/stabilizer/css/rotor_3_1_2.yml index 180801989..661f15ba2 100644 --- a/codes/quantum/groups/rotors/stabilizer/css/rotor_3_1_2.yml +++ b/codes/quantum/groups/rotors/stabilizer/css/rotor_3_1_2.yml @@ -26,7 +26,7 @@ relations: detail: 'Taking \(H_X=\begin{pmatrix}-3 & 1 & 2\end{pmatrix}\) and \(H_Z=\begin{pmatrix}4&6&3\end{pmatrix}\) yields the three-rotor code.' - code_id: covariant detail: 'The three-rotor code is \(U(1)\)-covariant.' - - code_id: small_distance + - code_id: small_distance_quantum cousins: - code_id: stab_3_1_2 diff --git a/codes/quantum/groups/rotors/stabilizer/css/zero_pi.yml b/codes/quantum/groups/rotors/stabilizer/css/zero_pi.yml index 8618900fb..599910a67 100644 --- a/codes/quantum/groups/rotors/stabilizer/css/zero_pi.yml +++ b/codes/quantum/groups/rotors/stabilizer/css/zero_pi.yml @@ -47,7 +47,7 @@ notes: relations: parents: - code_id: homological_rotor - - code_id: small_distance + - code_id: small_distance_quantum cousins: - code_id: gkp detail: 'Zero-pi code phase gates utilize ancillary osillators in square-lattice GKP states \cite{arXiv:cond-mat/0609441,arxiv:1302.4122}.' diff --git a/codes/quantum/groups/rotors/stabilizer/rotor_5_1_3.yml b/codes/quantum/groups/rotors/stabilizer/rotor_5_1_3.yml index f2e293b46..254a91d90 100644 --- a/codes/quantum/groups/rotors/stabilizer/rotor_5_1_3.yml +++ b/codes/quantum/groups/rotors/stabilizer/rotor_5_1_3.yml @@ -22,7 +22,7 @@ relations: - code_id: covariant detail: 'The five-rotor code is \(U(1)\)-covariant.' - code_id: quantum_cyclic - - code_id: small_distance + - code_id: small_distance_quantum cousins: - code_id: qudit_5_1_3 detail: 'The five-rotor code is a rotor analogue of the five-qudit code.' diff --git a/codes/quantum/oscillators/stabilizer/hyperplane/braunstein.yml b/codes/quantum/oscillators/stabilizer/hyperplane/braunstein.yml index 8cfe02345..0c4c7aad9 100644 --- a/codes/quantum/oscillators/stabilizer/hyperplane/braunstein.yml +++ b/codes/quantum/oscillators/stabilizer/hyperplane/braunstein.yml @@ -21,7 +21,7 @@ relations: parents: - code_id: analog_stabilizer - code_id: quantum_cyclic - - code_id: small_distance + - code_id: small_distance_quantum cousins: - code_id: qudit_5_1_3 detail: 'The Braunstein five-mode code is a bosonic analogue of the five-qudit code.' diff --git a/codes/quantum/oscillators/stabilizer/hyperplane/lloyd_slotine.yml b/codes/quantum/oscillators/stabilizer/hyperplane/lloyd_slotine.yml index 2531cae57..0050fab22 100644 --- a/codes/quantum/oscillators/stabilizer/hyperplane/lloyd_slotine.yml +++ b/codes/quantum/oscillators/stabilizer/hyperplane/lloyd_slotine.yml @@ -35,7 +35,7 @@ realizations: relations: parents: - code_id: analog_stabilizer - - code_id: small_distance + - code_id: small_distance_quantum cousins: - code_id: shor_nine detail: 'The Lloyd-Slotine nine-mode code is a bosonic analogue of Shor''s code.' diff --git a/codes/quantum/properties/block/small_distance.yml b/codes/quantum/properties/block/quantum_small_distance.yml similarity index 75% rename from codes/quantum/properties/block/small_distance.yml rename to codes/quantum/properties/block/quantum_small_distance.yml index e1ac077bb..a27320285 100644 --- a/codes/quantum/properties/block/small_distance.yml +++ b/codes/quantum/properties/block/quantum_small_distance.yml @@ -3,13 +3,13 @@ ## https://github.com/errorcorrectionzoo ## ####################################################### -code_id: small_distance +code_id: small_distance_quantum # includes Galois, modular, oscillators, and groups name: 'Small-distance block quantum code' description: | - A block code on \(n\) subsystems that either detects or corrects errors on only a single subsystem. These two cases correspond to distance \(d=2\) or \(d=3\) block quantum codes, respectively. + A block quantum code on \(n\) subsystems that either detects or corrects errors on only a single subsystem. These two cases correspond to distance \(d=2\) or \(d=3\) block quantum codes, respectively. All single error-correcting qubit stabilizer codes have been classified \cite{arxiv:0901.1968}. See Ref. \cite{arxiv:quant-ph/9704043} for single error-detecting qubit stabilizer codes. diff --git a/codes/quantum/qubits/fermions/mbq.yml b/codes/quantum/qubits/fermions/mbq.yml index 2716a7ecb..72d85582b 100644 --- a/codes/quantum/qubits/fermions/mbq.yml +++ b/codes/quantum/qubits/fermions/mbq.yml @@ -29,7 +29,7 @@ features: relations: parents: - code_id: majorana_stab - - code_id: small_distance + - code_id: small_distance_quantum - code_id: topological_abelian detail: 'When treated as ground states of the code Hamiltonian, surface codewords realize, codewords of a single Kitaev chain realize \(\mathbb{Z}_2\) fermionic topological order. The MZMs used to define the tetron code act as Ising anyons, which are non-Abelian.' diff --git a/codes/quantum/qubits/nonstabilizer/permutation_invariant/binary_dihedral_permutation_invariant.yml b/codes/quantum/qubits/nonstabilizer/permutation_invariant/binary_dihedral_permutation_invariant.yml index 30ce4ebf3..b6338c741 100644 --- a/codes/quantum/qubits/nonstabilizer/permutation_invariant/binary_dihedral_permutation_invariant.yml +++ b/codes/quantum/qubits/nonstabilizer/permutation_invariant/binary_dihedral_permutation_invariant.yml @@ -30,7 +30,7 @@ relations: - code_id: j_gross detail: 'Binary dihedral permutation-invariant codes can be interpreted as Clifford single-spin codes.' cousins: - - code_id: small_distance + - code_id: small_distance_quantum detail: 'The first and second families of binary dihedral permutation-invariant codes have distance three.' - code_id: xp_stabilizer detail: 'Binary dihedral permutation invariant codewords form error spaces of XP stabilizer codes.' diff --git a/codes/quantum/qubits/nonstabilizer/permutation_invariant/icosahedral_permutation_invariant.yml b/codes/quantum/qubits/nonstabilizer/permutation_invariant/icosahedral_permutation_invariant.yml index f50f1a3dc..052dfbdf9 100644 --- a/codes/quantum/qubits/nonstabilizer/permutation_invariant/icosahedral_permutation_invariant.yml +++ b/codes/quantum/qubits/nonstabilizer/permutation_invariant/icosahedral_permutation_invariant.yml @@ -31,7 +31,7 @@ relations: - code_id: qubits_into_qubits - code_id: j_gross detail: 'The \(((7,2,3))\) permutation-invariant code can be interpreted as a spin-\(7/2\) Clifford code \cite{arXiv:2005.10910}.' - - code_id: small_distance + - code_id: small_distance_quantum # Begin Entry Meta Information diff --git a/codes/quantum/qubits/rm/diagonal_clifford.yml b/codes/quantum/qubits/rm/diagonal_clifford.yml index bb60ecf8a..20cbe8a0f 100644 --- a/codes/quantum/qubits/rm/diagonal_clifford.yml +++ b/codes/quantum/qubits/rm/diagonal_clifford.yml @@ -21,7 +21,7 @@ features: relations: parents: - code_id: quantum_reed_muller - - code_id: small_distance + - code_id: small_distance_quantum # Begin Entry Meta Information _meta: diff --git a/codes/quantum/qubits/small_distance/h_code_jones.yml b/codes/quantum/qubits/small_distance/h_code_jones.yml index 03d5c4dea..74d61f302 100644 --- a/codes/quantum/qubits/small_distance/h_code_jones.yml +++ b/codes/quantum/qubits/small_distance/h_code_jones.yml @@ -28,7 +28,7 @@ features: relations: parents: - code_id: qubit_css - - code_id: small_distance + - code_id: small_distance_quantum # Begin Entry Meta Information diff --git a/codes/quantum/qubits/small_distance/iceberg.yml b/codes/quantum/qubits/small_distance/iceberg.yml index b68c960d7..c362199b2 100644 --- a/codes/quantum/qubits/small_distance/iceberg.yml +++ b/codes/quantum/qubits/small_distance/iceberg.yml @@ -44,7 +44,7 @@ relations: - code_id: qubit_css - code_id: quantum_mds detail: 'The \([[2m,2m-2,2]]\) error-detecting code is one of the two qubit quantum MDS codes \cite{arxiv:quant-ph/0312164}.' - - code_id: small_distance + - code_id: small_distance_quantum # Begin Entry Meta Information diff --git a/codes/quantum/qubits/small_distance/quantum_hamming.yml b/codes/quantum/qubits/small_distance/quantum_hamming.yml index e26f4a07f..e40955e6d 100644 --- a/codes/quantum/qubits/small_distance/quantum_hamming.yml +++ b/codes/quantum/qubits/small_distance/quantum_hamming.yml @@ -19,7 +19,7 @@ protection: 'Protects against any single qubit error.' relations: parents: - code_id: qubit_stabilizer - - code_id: small_distance + - code_id: small_distance_quantum cousins: - code_id: quantum_perfect detail: 'Quantum Hamming codes saturate the asymptotic quantum Hamming bound.' diff --git a/codes/quantum/qubits/small_distance/small/qubit_5_6_2.yml b/codes/quantum/qubits/small_distance/small/qubit_5_6_2.yml index 5fc40b838..5f73a8020 100644 --- a/codes/quantum/qubits/small_distance/small/qubit_5_6_2.yml +++ b/codes/quantum/qubits/small_distance/small/qubit_5_6_2.yml @@ -18,7 +18,7 @@ relations: - code_id: quantum_cyclic - code_id: non_stabilizer detail: 'The six-qubit CWS code is a non-stabilizer qubit code \cite{arxiv:quant-ph/0210097}.' - - code_id: small_distance + - code_id: small_distance_quantum # Begin Entry Meta Information diff --git a/codes/quantum/qubits/small_distance/small/stab_8_3_2.yml b/codes/quantum/qubits/small_distance/small/stab_8_3_2.yml index e6a07456b..9f675190f 100644 --- a/codes/quantum/qubits/small_distance/small/stab_8_3_2.yml +++ b/codes/quantum/qubits/small_distance/small/stab_8_3_2.yml @@ -33,7 +33,7 @@ relations: parents: - code_id: 3d_color detail: 'The \([[8,3,2]]\) code is the smallest non-trivial 3D color code.' - - code_id: small_distance + - code_id: small_distance_quantum cousins: - code_id: stab_15_1_3 detail: 'The \([[8,3,2]]\) code can be obtained from a subset of physical qubits of the \([[15,1,3]]\) code \cite{arxiv:2112.01446}.' diff --git a/codes/quantum/qubits/small_distance/tfim.yml b/codes/quantum/qubits/small_distance/tfim.yml index 3e9cc0e47..af2cf2c5d 100644 --- a/codes/quantum/qubits/small_distance/tfim.yml +++ b/codes/quantum/qubits/small_distance/tfim.yml @@ -23,7 +23,7 @@ relations: parents: - code_id: qubit_stabilizer - code_id: translationally_invariant_stabilizer - - code_id: small_distance + - code_id: small_distance_quantum cousins: - code_id: majorana_stab detail: 'The TFIM code stabilizers can be expressed in terms of Majorana operators.' diff --git a/codes/quantum/qubits/stabilizer/topological/surface/non-css/rhombic_dodecahedron_surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/non-css/rhombic_dodecahedron_surface.yml index 677990e68..ec111b9c1 100644 --- a/codes/quantum/qubits/stabilizer/topological/surface/non-css/rhombic_dodecahedron_surface.yml +++ b/codes/quantum/qubits/stabilizer/topological/surface/non-css/rhombic_dodecahedron_surface.yml @@ -16,7 +16,7 @@ description: | relations: parents: - code_id: clifford-deformed_surface - - code_id: small_distance + - code_id: small_distance_quantum cousins: - code_id: polytope detail: 'The rhombic dodecahedron surface code arranges qubits and stabilizer generators on polytopes.' diff --git a/codes/quantum/qubits/stabilizer/topological/surface/two_dim/stellated_dodecahedron_css.yml b/codes/quantum/qubits/stabilizer/topological/surface/two_dim/stellated_dodecahedron_css.yml index af491bc64..6f7d1cf71 100644 --- a/codes/quantum/qubits/stabilizer/topological/surface/two_dim/stellated_dodecahedron_css.yml +++ b/codes/quantum/qubits/stabilizer/topological/surface/two_dim/stellated_dodecahedron_css.yml @@ -20,7 +20,7 @@ description: | relations: parents: - code_id: two_dimensional_hyperbolic_surface - - code_id: small_distance + - code_id: small_distance_quantum cousins: - code_id: polytope detail: 'Bring''s code and related codes listed in \cite[Table 1]{arXiv:1712.07666} arrange qubits and stabilizer generators on polytopes.' diff --git a/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface-17.yml b/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface-17.yml index 3f5820aa3..a3d36575f 100644 --- a/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface-17.yml +++ b/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface-17.yml @@ -33,7 +33,7 @@ realizations: relations: parents: - code_id: rotated_surface - - code_id: small_distance + - code_id: small_distance_quantum cousins: - code_id: shor_nine detail: 'Both Shor''s code and surface-17 are \([[9,1,3]]\) codes, but they are distinct (e.g., they have different weight enumerators).' diff --git a/codes/quantum/qudits/qudit_hamming_css.yml b/codes/quantum/qudits/qudit_hamming_css.yml index 77907a5f4..bbcfc0c88 100644 --- a/codes/quantum/qudits/qudit_hamming_css.yml +++ b/codes/quantum/qudits/qudit_hamming_css.yml @@ -18,7 +18,7 @@ description: 'A family of CSS codes extending \hyperref[code:quantum_hamming_css relations: parents: - code_id: qudit_css - - code_id: small_distance + - code_id: small_distance_quantum # Begin Entry Meta Information diff --git a/codes/quantum/qudits/small/qudit_5_1_3.yml b/codes/quantum/qudits/small/qudit_5_1_3.yml index 25ed23a15..f156967df 100644 --- a/codes/quantum/qudits/small/qudit_5_1_3.yml +++ b/codes/quantum/qudits/small/qudit_5_1_3.yml @@ -26,7 +26,7 @@ relations: parents: - code_id: qudit_stabilizer - code_id: quantum_cyclic - - code_id: small_distance + - code_id: small_distance_quantum # Begin Entry Meta Information diff --git a/codes/quantum/qudits/small/stab_3_1_2.yml b/codes/quantum/qudits/small/stab_3_1_2.yml index d63d71691..042386953 100644 --- a/codes/quantum/qudits/small/stab_3_1_2.yml +++ b/codes/quantum/qudits/small/stab_3_1_2.yml @@ -52,7 +52,7 @@ relations: detail: 'Three-qutrit code is a minimal model for holography \cite{arxiv:1411.7041,arXiv:1607.03901}.' - code_id: quantum_mds detail: 'The three-qutrit code is the smallest nontrivial quantum MDS code.' - - code_id: small_distance + - code_id: small_distance_quantum cousins: - code_id: quantum_secret_sharing detail: 'Three-qutrit code defines a minimal secret-sharing scheme \cite{arXiv:quant-ph/9901025} that is substantially generalized by approximate secret-sharing codes.' diff --git a/codes/quantum/qudits/small/stab_9_1_3.yml b/codes/quantum/qudits/small/stab_9_1_3.yml index c3969b95c..3caae3fa1 100644 --- a/codes/quantum/qudits/small/stab_9_1_3.yml +++ b/codes/quantum/qudits/small/stab_9_1_3.yml @@ -26,7 +26,7 @@ relations: parents: - code_id: qudit_surface detail: 'The qudit Shor code is a small qudit surface code on a Möbius strip with smooth boundary, which is obtained from removing a face of the tesselation of the projective plane \(\mathbb{R}P^2\) \cite[Fig. 4]{arxiv:quant-ph/9810055}.' - - code_id: small_distance + - code_id: small_distance_quantum cousins: - code_id: real_projective_plane detail: 'The qudit Shor code is a small qudit surface code on a Möbius strip with smooth boundary, which is obtained from removing a face of the tesselation of the projective plane \(\mathbb{R}P^2\) \cite[Fig. 4]{arxiv:quant-ph/9810055}.' diff --git a/codes/quantum/qudits_galois/small/galois_5_1_3.yml b/codes/quantum/qudits_galois/small/galois_5_1_3.yml index 9144189ea..3bcb1b3ef 100644 --- a/codes/quantum/qudits_galois/small/galois_5_1_3.yml +++ b/codes/quantum/qudits_galois/small/galois_5_1_3.yml @@ -20,7 +20,7 @@ relations: parents: - code_id: stabilizer_over_gfqsq - code_id: quantum_cyclic - - code_id: small_distance + - code_id: small_distance_quantum # Begin Entry Meta Information