From f1596aa189a99ac2d737450dba3d88fcdf52c397 Mon Sep 17 00:00:00 2001 From: "Victor V. Albert" Date: Fri, 3 Jan 2025 12:17:22 -0500 Subject: [PATCH] ~ --- codes/quantum/qubits/qubits_into_qubits.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/codes/quantum/qubits/qubits_into_qubits.yml b/codes/quantum/qubits/qubits_into_qubits.yml index 7d98d5340..2d427960a 100644 --- a/codes/quantum/qubits/qubits_into_qubits.yml +++ b/codes/quantum/qubits/qubits_into_qubits.yml @@ -128,7 +128,7 @@ features: - '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}.' decoders: - - 'Incorporating faulty syndrome measurements can be done using the \textit{phenomenological noise model}, which simulates errors during syndrome extraction by flipping some of the bits of the measured syndrome bitstring. In the more involved \textit{circuit-level noise model}, every component of the syndrome extraction circuit can be faulty.' + - 'Syndrome measurements are assumed to be perfect in the \textit{code-capacity model}. Incorporating faulty syndrome measurements can be done using the \textit{phenomenological noise model}, which simulates errors during syndrome extraction by flipping some of the bits of the measured syndrome bitstring. In the more involved \textit{circuit-level noise model}, every component of the syndrome extraction circuit can be faulty.' - 'The decoder determining the most likely error given a noise channel is called the \textit{maximum probability error} (MPE) decoder. For few-qubit codes (\(n\) is small), MPE decoding can be based by creating 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.' - '\begin{defterm}{Effective distance and hook errors} \label{topic:effective-distance}