From 64cf0e2269372f3715ee0204ac648fbb4258b19a Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Wed, 29 Apr 2026 20:31:41 +0200 Subject: [PATCH] Introduce LER --- src/thesis/chapters/2_fundamentals.tex | 6 ++++++ src/thesis/chapters/3_fault_tolerant_qec.tex | 3 +-- 2 files changed, 7 insertions(+), 2 deletions(-) diff --git a/src/thesis/chapters/2_fundamentals.tex b/src/thesis/chapters/2_fundamentals.tex index 9fa71f6..9269d5c 100644 --- a/src/thesis/chapters/2_fundamentals.tex +++ b/src/thesis/chapters/2_fundamentals.tex @@ -1660,6 +1660,12 @@ Algorithm \ref{alg:bpgd} shows this process. Note that as the Tanner graph only has $n$ \acp{vn}, this is a natural constraint on the maximum number of outer iterations of the algorithm. +Quantum degeneracy additionally necessitates some care in the way +error rates are computed in simulations. +We must consider the fact that multiple solutions are valid by +comparing the logical states, computed by measuring the logical operators. +This way, we obtain the \ac{ler}. + % TODO: Explain that setting the channel LLR to infinity is the same % as a hard decision and ignoring the VN in the further decoding % tex-fmt: off diff --git a/src/thesis/chapters/3_fault_tolerant_qec.tex b/src/thesis/chapters/3_fault_tolerant_qec.tex index 2e9e860..88c4c36 100644 --- a/src/thesis/chapters/3_fault_tolerant_qec.tex +++ b/src/thesis/chapters/3_fault_tolerant_qec.tex @@ -1040,9 +1040,8 @@ $p_\text{phys}$. % Per-round LER -% TODO: Introduce the logical error rate Another aspect that is important to consider is the meaning of the -logical error rate in the context of a \ac{qec} system with multiple +\ac{ler} in the context of a \ac{qec} system with multiple rounds of syndrome measurements. In order to facilitate the comparability of results obtained from simulations with different numbers of syndrome extraction rounds, we