diff --git a/codes/classical/bits/combinatorial_design.yml b/codes/classical/bits/combinatorial_design.yml index 4c305db1a..81f1c2bf6 100644 --- a/codes/classical/bits/combinatorial_design.yml +++ b/codes/classical/bits/combinatorial_design.yml @@ -34,7 +34,7 @@ description: | notes: - - 'See \cite{preset:HKSdesigns} for a review on combinatorial designs.' + - 'See \cite{doi:10.1090/surv/175,preset:HKSdesigns} for reviews on combinatorial designs.' - 'See \cite{doi:10.1017/CBO9780511549533,doi:10.1201/9781420010541,doi:10.1017/CBO9780511623714,doi:10.1007/b97564} for books on combinatorial designs.' relations: @@ -77,7 +77,7 @@ relations: detail: 'Some Steiner systems can be used to construct Gallager codes \cite{doi:10.1007/978-1-4613-0165-3_6}.' - code_id: algebraic_ldpc detail: 'Combinatorial designs can be used to construct explicit LDPC codes \cite{doi:10.1109/ITW.2001.955146,doi:10.1109/GLOCOM.2001.965562,doi:10.1109/TCOMM.2003.816946}.' - - code_id: biorthogonal + - code_id: hadamard detail: '\textit{Hadamard designs} form a set of combinatorial designs that are equivalent to Hadamard matrices \cite{doi:10.1002/sapm1933121321}; see Ref. \cite{doi:10.1201/9781420010541}.' diff --git a/codes/classical/bits/easy/dual_hamming/hadamard.yml b/codes/classical/bits/easy/dual_hamming/hadamard.yml index 33364c88b..c8e7a05cf 100644 --- a/codes/classical/bits/easy/dual_hamming/hadamard.yml +++ b/codes/classical/bits/easy/dual_hamming/hadamard.yml @@ -19,6 +19,9 @@ description: | The \([2^m,m+1,2^{m-1}]\) augmented Hadamard code is the first-order RM code (a.k.a. RM\((1,m)\)), while the \([2^m-1,m,2^{m-1}]\) shortened Hadamard code is the simplex code (a.k.a. RM\(^*(1,m)\)). +notes: + - 'Review of Hadamard matrices \cite{doi:10.1214/aos/1176344370}.' + relations: parents: - code_id: binary_ltc diff --git a/codes/classical/spherical/q-ary/complex_hadamard.yml b/codes/classical/spherical/q-ary/complex_hadamard.yml new file mode 100644 index 000000000..4a7f5bb55 --- /dev/null +++ b/codes/classical/spherical/q-ary/complex_hadamard.yml @@ -0,0 +1,36 @@ +####################################################### +## This is a code entry in the error correction zoo. ## +## https://github.com/errorcorrectionzoo ## +####################################################### + +code_id: complex_hadamard +physical: spheres +logical: reals + +name: 'Complex Hadamard spherical code' +introduced: '\cite{arxiv:2311.00354}' + +description: | + A spherical code obtained from particular complex Hadamard matrices \cite{arxiv:2309.07522}. + +protection: | + Covering radius can be bounded in terms of the code's spherical design strength \cite{arxiv:2311.00354}. + + +notes: + - 'Database of complex Hadamard matrices \cite{arXiv:quant-ph/0512154}.' + +relations: + parents: + - code_id: spherical + cousins: + - code_id: stabilizer_over_gfqsq + detail: 'Complex Hadamard matrices can be used to build Hermitian Galois-qudit codes \cite{arxiv:2309.07522}.' + + +# Begin Entry Meta Information +_meta: + # Change log - most recent first + changelog: + - user_id: VictorVAlbert + date: '2024-07-07' diff --git a/codes/quantum/properties/block/tensor_network/holographic_tensor.yml b/codes/quantum/properties/block/tensor_network/holographic_tensor.yml index 5c4e18f78..a0ca9bd35 100644 --- a/codes/quantum/properties/block/tensor_network/holographic_tensor.yml +++ b/codes/quantum/properties/block/tensor_network/holographic_tensor.yml @@ -62,5 +62,7 @@ relations: _meta: # Change log - most recent first changelog: + - user_id: MatthewSteinberg + date: '2024-07-01' - user_id: VictorVAlbert date: '2024-07-01' diff --git a/codes/quantum/qubits/stabilizer/holographic/holographic_steane.yml b/codes/quantum/qubits/stabilizer/holographic/holographic_steane.yml index 345b0e141..e790527ae 100644 --- a/codes/quantum/qubits/stabilizer/holographic/holographic_steane.yml +++ b/codes/quantum/qubits/stabilizer/holographic/holographic_steane.yml @@ -15,14 +15,15 @@ alternative_names: description: | Holographic tensor-network code constructed out of a network of encoding isometries of the Steane code. + Depending on how the isometry tensors are contracted, there is a zero-rate and a finite-rate code family. features: decoders: - 'Optimal erasure decoder \cite{arxiv:1806.06472}.' threshold: - - '\(~33\%\) under erasure noise using optimal erasure decoder \cite{arxiv:1806.06472}.' - - '\(9.4\%\) under depolarizing noise using tensor-network decoder \cite{arxiv:2012.07317}.' + - '\(~33\%\) under erasures using optimal erasure decoder for the finite-rate family, and \(50\%\) for the zero-rate family \cite{arxiv:1806.06472}.' + - 'Depolarizing noise: \(9.4\%\) using tensor-network decoder, and \(\sim 7\%\) using integer optimization decoder \cite{arxiv:2012.07317}.' relations: diff --git a/codes/quantum/qudits_galois/stabilizer/stabilizer_over_gfqsq.yml b/codes/quantum/qudits_galois/stabilizer/stabilizer_over_gfqsq.yml index 8dab4c8e1..d44820aa9 100644 --- a/codes/quantum/qudits_galois/stabilizer/stabilizer_over_gfqsq.yml +++ b/codes/quantum/qudits_galois/stabilizer/stabilizer_over_gfqsq.yml @@ -27,6 +27,7 @@ protection: | There is an isomorphism between the symplectic and \(GF(q^2)\) representations \cite[Thm. 27.3.8]{preset:HKSquantum}. It has also been extended to \(q^{2m}\)-ary Hermitian self-orthogonal linear codes \cite{arxiv:2012.11998}, and similar constructions were formulated in Ref. \cite{arxiv:1002.4088}. + Construction X and XX have also been adapted to yield quantum codes \cite{doi:10.1007/s10623-014-9934-8}. # and later proven via the \hyperref[code:stabilizer_over_gfqsq]{Hermitian construction} (showing self-orthogonality under the trace-alternating inner product; see Ref. \cite[Corr. 19]{arxiv:quant-ph/0508070}, ). diff --git a/users/users_db.yml b/users/users_db.yml index b2943fe9d..4795f2b70 100644 --- a/users/users_db.yml +++ b/users/users_db.yml @@ -34,7 +34,9 @@ # - +- user_id: MatthewSteinberg + name: 'Matthew Steinberg' + gscholaruser: lGZwMRAAAAAJ - user_id: GregKuperberg name: 'Greg Kuperberg'