diff --git a/codes/classical/bits/cyclic/binary_quad_residue.yml b/codes/classical/bits/cyclic/binary_quad_residue.yml index fb1743745..07705aee5 100644 --- a/codes/classical/bits/cyclic/binary_quad_residue.yml +++ b/codes/classical/bits/cyclic/binary_quad_residue.yml @@ -35,6 +35,9 @@ relations: detail: 'Extended binary quadratic residue codes of length \(8m\) are self-dual doubly even codes \cite[pg. 82]{doi:10.1007/978-1-4757-6568-7}.' - code_id: lexicographic detail: 'The \([18,9,6]\) binary QR code is a lexicode \cite{doi:10.1109/TIT.1986.1057187}.' + - code_id: quasi_cyclic + detail: 'Binary QR codes are equivalent to double circulant codes for all \(n<200\) except 89 and 167 \cite{manual:{Beenker, G. J. M. "On double circulant codes." (1980).}}.' + # Begin Entry Meta Information diff --git a/codes/classical/q-ary_digits/group/cyclic/q-ary_quad_residue.yml b/codes/classical/q-ary_digits/group/cyclic/q-ary_quad_residue.yml index d06551111..bfc0f1966 100644 --- a/codes/classical/q-ary_digits/group/cyclic/q-ary_quad_residue.yml +++ b/codes/classical/q-ary_digits/group/cyclic/q-ary_quad_residue.yml @@ -7,8 +7,8 @@ code_id: q-ary_quad_residue physical: q-ary_digits logical: q-ary_digits -name: '\(q\)-ary quadratic-residue (QR) code' -short_name: '\(q\)-ary QR' +name: 'Quadratic-residue (QR) code' +short_name: 'QR' #introduced: '' description: | diff --git a/codes/quantum/qubits/qubits_into_qubits.yml b/codes/quantum/qubits/qubits_into_qubits.yml index 7cd658416..601d97393 100644 --- a/codes/quantum/qubits/qubits_into_qubits.yml +++ b/codes/quantum/qubits/qubits_into_qubits.yml @@ -133,6 +133,7 @@ features: C_k = \{ U | U P U^{\dagger} \in C_{k-1} \}~, \end{align} where \(P\) is any Pauli matrix, where \(C_1\) is the \hyperref[topic:pauli]{Pauli group}, and where \(C_2\) is the \hyperref[topic:clifford]{Clifford group}. + Gates for one qubit have been classified \cite{arxiv:2501.07939}. \end{defterm}' - 'Arbitrary \(n\)-qubit circuits can be implemented fault-tolerantly in a 3D architecture using \(O(n^{3/2}\log^3 n)\) qubits, and in a 2D architecture using only \(O(n^2 \log^3 n)\) qubits \cite{arxiv:2402.13863}.' - 'Fault-tolerant gates can be done for any code supporting a transversal implementation of Pauli gates using generalized gate teleportation \cite{arxiv:2409.11616}.' diff --git a/codes/quantum/qudits/qudits_into_qudits.yml b/codes/quantum/qudits/qudits_into_qudits.yml index 2edec2411..b85276902 100644 --- a/codes/quantum/qudits/qudits_into_qudits.yml +++ b/codes/quantum/qudits/qudits_into_qudits.yml @@ -56,6 +56,7 @@ features: C_k = \{ U | U P U^{\dagger} \in C_{k-1} \}~, \end{align} where \(P\) is any modular-qudit Pauli matrix, and \(C_1\) is the \hyperref[topic:qudit-pauli]{modular-qudit Pauli group}. + Gates for one prime-dimensional qudit have been classified \cite{arxiv:2501.07939}. \end{defterm}' decoders: - 'For few-qudit codes (\(n\) is small), decoding can be based on a lookup table. For infinite code families, the size of such a table scales exponentially with \(n\), so approximate decoding algorithms scaling polynomially with \(n\) have to be used. The decoder determining the most likely error given a noise channel is called the \textit{maximum-likelihood} (ML) decoder.' @@ -65,6 +66,7 @@ features: notes: - 'Weight distribution of a code depends on the average entanglement of codewords \cite{arxiv:quant-ph/0310137,arxiv:2209.07607}.' + - 'Qudit Cirq library \cite{arxiv:2501.07812}.' relations: