diff --git a/codes/quantum/qudits/qudits_into_qudits.yml b/codes/quantum/qudits/qudits_into_qudits.yml index 5abadb7df..e97deb0fd 100644 --- a/codes/quantum/qudits/qudits_into_qudits.yml +++ b/codes/quantum/qudits/qudits_into_qudits.yml @@ -29,10 +29,10 @@ protection: | features: general_gates: - - 'Universal computing can be achieved using qudit Clifford gates \cite{arxiv:quant-ph/9802007,arxiv:quant-ph/0408190,arxiv:2008.00959} and a single type of non-Clifford gate, such as the \(T\) gate \cite{arxiv:1503.08800}.' + - 'Universal computing can be achieved using qudit Clifford gates \cite{arxiv:quant-ph/9802007,arxiv:quant-ph/0408190,arxiv:quant-ph/0512155,arxiv:2008.00959} and a single type of non-Clifford gate, such as the \(T\) gate \cite{arxiv:1503.08800}.' - '\begin{defterm}{Qudit Clifford hierarchy} \label{topic:qudit-clifford-hierarchy} - The modular-qudit Clifford hierarchy \cite{arXiv:quant-ph/9908010,arxiv:1608.06596} is a tower of gate sets which includes modular-qudit Pauli and modular-qudit Clifford gates at its first two levels, and non-Clifford qudit gates at higher levels. + The modular-qudit Clifford hierarchy \cite{arXiv:quant-ph/9908010,arxiv:1206.1598,arxiv:1408.1720,arxiv:1608.06596} is a tower of gate sets which includes modular-qudit Pauli and modular-qudit Clifford gates at its first two levels, and non-Clifford qudit gates at higher levels. The \(k\)th level is defined recursively by \begin{align} C_k = \{ U | U P U^{\dagger} \in C_{k-1} \}~, @@ -41,10 +41,6 @@ features: \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.' -# CITE qudit Clifford. Gottesman, Chaos, Solitons & Fractals 10, 1749 - 1758 (1999) + S. Clark, J. Phys. A-Math. Gen. 39, 2701 (2006) for qudit Clifford -# CITE for qudit Clifford hierarchy -# F. Pastawski and B. Yoshida, Phys. Rev. A 91 012305 (2015). -# M. Howard and J. Vala, Phys. Rev. A 86, 022316 (2012 notes: - 'Weight distribution of a code depends on the average entanglement of codewords \cite{arXiv:quant-ph/0310137,arxiv:2209.07607}.' diff --git a/codes/quantum/qudits/topological/qudit_surface.yml b/codes/quantum/qudits/topological/qudit_surface.yml index 281502294..9707b7437 100644 --- a/codes/quantum/qudits/topological/qudit_surface.yml +++ b/codes/quantum/qudits/topological/qudit_surface.yml @@ -26,8 +26,6 @@ description: | features: decoders: - 'Renormalization-group decoder \cite{arxiv:1311.4895,arxiv:1411.3028}.' -# More on RG: CITE H. Anwar, B.J. Brown, E.T. Campbell and D.E. Browne, New J. Phys. 16, 063038 (2014) -# RG: CITE G. Duclos-Cianci and D. Poulin, Quant. Inf. Comp. 9&10, 0721 (2014). notes: - 'The simplest \href{https://citizensciencegames.com/games/decodoku/}{Decodoku game} is based on the qudit surface code with \( q=10\). See related \href{https://github.com/quantumjim/qec_lectures}{Qiskit tutorial}.' diff --git a/codes/quantum/qudits_galois/qldpc/galois_topological.yml b/codes/quantum/qudits_galois/qldpc/galois_topological.yml index 6fedaaca3..d1d7c9308 100644 --- a/codes/quantum/qudits_galois/qldpc/galois_topological.yml +++ b/codes/quantum/qudits_galois/qldpc/galois_topological.yml @@ -9,13 +9,12 @@ logical: galois name: 'Galois-qudit topological code' introduced: '\cite{arxiv:quant-ph/0609070,doi:10.1109/CIG.2010.5592860,arxiv:1202.3338}' -# CITE P. Sarvepalli, IEEE ITW 1–5 (2010). Galois color? Has this been cited already? alternative_names: - '\(\mathbb{F}_q\)-qudit topological code' description: | - Abelian topological code, such as a surface \cite{arxiv:quant-ph/0609070,arxiv:1202.3338} or color \cite{doi:10.1109/CIG.2010.5592860} code, constructed on lattices of Galois qudits. + Abelian topological code, such as a 2D surface \cite{arxiv:quant-ph/0609070,arxiv:1202.3338} or 2D color \cite{doi:10.1109/CIG.2010.5592860} code, constructed on lattices of Galois qudits. relations: parents: