From d8f6477c03521c2b6590fff1dfdf5c101ad59d71 Mon Sep 17 00:00:00 2001 From: VVA2024 Date: Thu, 1 Aug 2024 20:05:09 -0400 Subject: [PATCH] refs --- codes/quantum/eaqecc.yml | 1 + codes/quantum/properties/block/block_quantum.yml | 2 +- codes/quantum/qubits/ea_qubits_into_qubits.yml | 4 ++++ codes/quantum/qubits/small_distance/small/stab_5_1_3.yml | 2 ++ .../stabilizer/topological/surface/2d_surface/toric/toric.yml | 2 +- .../stabilizer/topological/surface/higher_d/4d_surface.yml | 3 +++ 6 files changed, 12 insertions(+), 2 deletions(-) diff --git a/codes/quantum/eaqecc.yml b/codes/quantum/eaqecc.yml index 4c34a8124..390bf8691 100644 --- a/codes/quantum/eaqecc.yml +++ b/codes/quantum/eaqecc.yml @@ -17,6 +17,7 @@ description: 'QECC whose encoding and decoding utilizes pre-shared entanglement protection: | Pre-shared entanglement can be prepared in a way that is robust to noise \cite{arxiv:0904.1175}. + notes: - 'See Ref. \cite{doi:10.1017/CBO9781139034807.009} for an introduction to EAQECCs.' diff --git a/codes/quantum/properties/block/block_quantum.yml b/codes/quantum/properties/block/block_quantum.yml index b9ea8ff34..6a9647541 100644 --- a/codes/quantum/properties/block/block_quantum.yml +++ b/codes/quantum/properties/block/block_quantum.yml @@ -23,7 +23,7 @@ protection: | 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}. \subsection{Bounds on code parameters} - Bounds on finite dimensional block code performance include the quantum Singleton bound, quantum Hamming bound, \hyperref[topic:quantum-gv-bound]{quantum GV bound}, various quantum linear programming (LP) bounds \cite{arxiv:quant-ph/9611001,arxiv:quant-ph/9709049} (see the book \cite{preset:GottesmanBook}), and other bounds \cite{doi:10.1109/TIT.2005.862086}. + Bounds on finite dimensional block code performance include the quantum Singleton bound, quantum Hamming bound, \hyperref[topic:quantum-gv-bound]{quantum GV bound}, various quantum linear programming (LP) bounds \cite{arxiv:quant-ph/9611001,arxiv:quant-ph/9709049} (see the book \cite{preset:GottesmanBook}), and other bounds \cite{doi:10.1109/TIT.2005.862086,arxiv:1007.3655}. A code whose parameters attain the quantum Hamming bound (quantum Singleton bound) is called a perfect quantum code (a quantum MDS code). \begin{defterm}{Quantum GV bound} diff --git a/codes/quantum/qubits/ea_qubits_into_qubits.yml b/codes/quantum/qubits/ea_qubits_into_qubits.yml index c27340f7d..67dcfa655 100644 --- a/codes/quantum/qubits/ea_qubits_into_qubits.yml +++ b/codes/quantum/qubits/ea_qubits_into_qubits.yml @@ -12,6 +12,10 @@ name: 'EA qubit code' description: | Qubit code designed to utilize pre-shared entanglement between sender and receiver. +protection: | + The \hyperref[topic:quantum-gv-bound]{quantum GV bound} and Plotkin bound have been extended to EA qubit codes \cite{arxiv:1010.5506}. + + features: rate: 'There are EA versions of classical and quantum capacities \cite{arxiv:quant-ph/9904023}. EA hashing bounds on the minimum entanglement required to achieve the entanglement-assisted channel capacity are derived \cite{arXiv:quant-ph/0205117}.' encoders: diff --git a/codes/quantum/qubits/small_distance/small/stab_5_1_3.yml b/codes/quantum/qubits/small_distance/small/stab_5_1_3.yml index 9d41bba6c..11796c9aa 100644 --- a/codes/quantum/qubits/small_distance/small/stab_5_1_3.yml +++ b/codes/quantum/qubits/small_distance/small/stab_5_1_3.yml @@ -30,6 +30,8 @@ description: | It is the unique code for its parameters, up to local equivalence \cite[Corr. 10]{arxiv:quant-ph/9704043}. Any 5 qubit \(2T\)-transversal stabilizer code with distance \(d>1\) must be the five-qubit code \cite{arxiv:2306.12526,manual:{Ian Teixeira, private communication, 2024}}. + This code is sometimes referred to as the DiVincenzo-Shor code after a paper that studied the code's syndrome extraction circuits \cite{arxiv:quant-ph/9605031} + protection: 'Smallest stabilizer code that protects against a single error on any one qubit. Detects two-qubit errors.' features: diff --git a/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/toric/toric.yml b/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/toric/toric.yml index d1a9ba43b..4c8677ca6 100644 --- a/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/toric/toric.yml +++ b/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/toric/toric.yml @@ -52,7 +52,7 @@ features: Above values are for one type of noise only, and the ML threshold for combined \(X\) and \(Z\) noise is \(2p_X - p_X^2 \approx 20.6\%\).' - 'Depolarizing noise: between \(17\%\) and \(18.5\%\) under BSV tensor-network decoding \cite{arxiv:1405.4883}, \(14\%\) under GBP decoding \cite{arxiv:2212.03214}, \(16.5\%\) under recursive MWPM \cite{arxiv:2212.11632}, between \(16\%\) and \(17.5\%\) under AMBP4 (depending on whether surface or toric code is considered) \cite{arxiv:2104.13659}, and between \(15\%\) and \(16\%\) under RG \cite{arxiv:0911.0581}, Markov-chain \cite{arxiv:1302.2669}, or MWPM \cite{arxiv:0905.0531} decoding. The threshold under ML decoding corresponds to the value of a critical point of the disordered eight-vertex Ising model, calculated to be \(18.9(3)\%\) \cite{arxiv:1202.1852} (see also APS Physics viewpoint \cite{doi:10.1103/Physics.5.50}).' - - 'Erasure noise: \(50\%\) for square tiling \cite{arxiv:,arxiv:0912.1159}. + - 'Erasure noise: \(50\%\) for square tiling \cite{arxiv:0904.3556,arxiv:0912.1159}. There is an inverse relationship between coordination number of the syndrome graph, with the threshold corresponding to a percolation transition \cite{arxiv:1810.09621}.' - 'Correlated noise: \(10.04(6)\%\) under mildly correlated bit-flip noise \cite{arxiv:1809.10704}.' # The latter work considers \(X\)-type noise only, but this is equivalent since \(X\)- and \(Z\)-type noise is corrected independently. diff --git a/codes/quantum/qubits/stabilizer/topological/surface/higher_d/4d_surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/higher_d/4d_surface.yml index fbc291ca6..6bfbbe088 100644 --- a/codes/quantum/qubits/stabilizer/topological/surface/higher_d/4d_surface.yml +++ b/codes/quantum/qubits/stabilizer/topological/surface/higher_d/4d_surface.yml @@ -29,6 +29,9 @@ description: | The construction has been extended to modular qudits \cite{arxiv:2112.02137}. +features: + decoders: + - 'Lindbladian-based dissipative encoding, for which codespace is steady-state space of a Lindbladian \cite{arxiv:1010.2901}.' features: transversal_gates: