From 34f2fa666afb576590665f09263dc5ef24bfabc3 Mon Sep 17 00:00:00 2001 From: "Victor V. Albert" Date: Mon, 16 Oct 2023 10:18:11 -0400 Subject: [PATCH] single shot --- codes/quantum/properties/block/single_shot.yml | 9 ++++++++- 1 file changed, 8 insertions(+), 1 deletion(-) diff --git a/codes/quantum/properties/block/single_shot.yml b/codes/quantum/properties/block/single_shot.yml index 81dcfe728..d83d23281 100644 --- a/codes/quantum/properties/block/single_shot.yml +++ b/codes/quantum/properties/block/single_shot.yml @@ -9,7 +9,14 @@ name: 'Single-shot code' introduced: \cite{arxiv:1404.5504} description: | - A block quantum code admitting a fault-tolerant error-correcting protocol against noisy syndrome measurements that requires a number of error-correcting rounds that is independent of the number of subsystems \(n\). + Measurement errors during decoding can yield the wrong syndrome outcome, which can cause error correction to fail even against correctable data errors. + A single-shot code is a block quantum code admitting a fault-tolerant error-correcting protocol that does not ``fail too badly'' when faced with noisy syndrome measurements. + + In the loosest form of the single-shot property for qubit, modular qudit, or Galois qudit codes, given some data error \(e\), ideal data error syndrome \(s\), and measurement error \(m\), there exists an error-correction protocol that outputs a correction \(f\) such that the Hamming weight of the residual error after correction, \(e+f\), is \textit{polynomial} in the weight of \(m\). + + The single-shot property usually implies that a sufficiently large number of error-correction rounds will keep both data and measurement errors bounded, as opposed to causing to eventually become uncorrectable. + +# In other words, the single-shot property implies that the number of error-correcting rounds necessary for successful error correction is independent of the number of subsystems \(n\). relations: