From 86e859364200f33f55ad28d521bb62cbd3349888 Mon Sep 17 00:00:00 2001 From: "Victor V. Albert" Date: Mon, 30 Oct 2023 10:19:09 +1100 Subject: [PATCH] refs --- codes/quantum/properties/quantum_concatenated.yml | 2 ++ codes/quantum/qubits/small_distance/small/steane.yml | 3 +++ 2 files changed, 5 insertions(+) diff --git a/codes/quantum/properties/quantum_concatenated.yml b/codes/quantum/properties/quantum_concatenated.yml index 4eaa62cdb..d3088c021 100644 --- a/codes/quantum/properties/quantum_concatenated.yml +++ b/codes/quantum/properties/quantum_concatenated.yml @@ -12,6 +12,8 @@ description: 'A combination of two codes, an inner code \(C\) and an outer code #protection: '' features: + decoders: + - 'The effective channel for a concatenation of codes is the composition of the codes'' effective channels \cite{arxiv:quant-ph/0206061}.' threshold: - 'The first method to achieve a fault-tolerant computational threshold uses concatenated stabilizer codes \cite{arxiv:quant-ph/9702058,arxiv:quant-ph/9906129,arXiv:quant-ph/9705031,arXiv:quant-ph/0504218}. Such methods require constant-space and polylogarithmic time overhead, but concatentions using quantum Hamming codes improve this to quasi-polylogarithmic time \cite{arxiv:2207.08826}.' diff --git a/codes/quantum/qubits/small_distance/small/steane.yml b/codes/quantum/qubits/small_distance/small/steane.yml index 2845533ae..bd963e4bf 100644 --- a/codes/quantum/qubits/small_distance/small/steane.yml +++ b/codes/quantum/qubits/small_distance/small/steane.yml @@ -65,6 +65,9 @@ relations: - code_id: diagonal_clifford - code_id: quantum_hamming_css - code_id: single_qubit_clifford + cousins: + - code_id: quantum_concatenated + detail: 'The concatenated Steane code is one of the first codes to admit a concatenated threshold \cite{arxiv:quant-ph/9702058,arxiv:quant-ph/9809054,arxiv:quant-ph/0207119}. Randomized compiling helps reduce logical error rate for some noise models \cite{arxiv:2303.06846}.' # detail: 'Steane code is the smallest member of a family of Reed-Muller-based CSS codes.' # detail: 'Steane code is the smallest member of a family of Hamming-based CSS codes.'