diff --git a/src/thesis/bibliography.bib b/src/thesis/bibliography.bib index 67eca35..aa2ba37 100644 --- a/src/thesis/bibliography.bib +++ b/src/thesis/bibliography.bib @@ -1040,3 +1040,12 @@ author = {Griffiths, Robert B.}, year = {2001}, } + +@misc{gottesman_fault-tolerant_2014, + title = {Fault-{Tolerant} {Quantum} {Computation} with {Constant} {Overhead}}, + doi = {10.48550/arXiv.1310.2984}, + publisher = {arXiv}, + author = {Gottesman, Daniel}, + month = jul, + year = {2014}, +} diff --git a/src/thesis/chapters/4_decoding_under_dems.tex b/src/thesis/chapters/4_decoding_under_dems.tex index acb8edb..447ca43 100644 --- a/src/thesis/chapters/4_decoding_under_dems.tex +++ b/src/thesis/chapters/4_decoding_under_dems.tex @@ -484,6 +484,359 @@ standard circuit-based depolarizing noise model, etc.)} \subsection{Belief Propagation with Guided Decimation} \label{subsec:Belief Propagation with Guided Decimation} +\begin{figure}[H] + \centering + \begin{tikzpicture} + \begin{axis}[ + width=\figwidth, + height=\figheight, + ymode=log, + legend style={ + cells={anchor=west}, + cells={align=left}, + }, + enlargelimits=false, + ymin=1e-5, ymax=2e-1, + grid=both, + legend pos = south east, + xtick={0.001,0.0015,...,0.004}, + xticklabel style={/pgf/number format/fixed}, + xticklabel style={/pgf/number format/precision=4}, + scaled x ticks=false, + xlabel={Physical error rate}, + ylabel={Per-round-LER}, + ] + + \foreach \W/\col/\mark in + {3/KITred/triangle*,4/KITblue/diamond*,5/KITorange/square*} { + \edef\temp{\noexpand + \addplot+[mark=\mark, solid, mark options={fill=\col}, \col] + table[ + col sep=comma, x=physical_p, + y=LER_per_round, + ] + {res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_False/F_1/W_\W/LERs.csv}; + } + \temp + + \addlegendentryexpanded{$W = \W$} + } + + \addplot+[mark=*, solid, mark options={fill=black}, black] + table[ + col sep=comma, x=physical_p, + y=LER_per_round, + ] + {res/sim/whole/SyndromeMinSumDecoder/max_iter_200/LERs.csv}; + + \addlegendentry{Whole} + \end{axis} + \end{tikzpicture} + + \caption{ + Comparison of the decoding performance of the $\llbracket + 144,12,12 \rrbracket$ \ac{bb} code under min-sum decoding + ($200$ iterations) for different window sizes. + The step size was fixed to $F=1$, $12$ rounds of syndrome + extraction were performed and the noise model is + standard circuit-based depolarizing noise. + } +\end{figure} + +\begin{figure}[H] + \centering + \begin{tikzpicture} + \begin{axis}[ + width=\figwidth, + height=\figheight, + ymode=log, + legend style={ + cells={anchor=west}, + cells={align=left}, + }, + enlargelimits=false, + ymin=1e-5, ymax=2e-1, + grid=both, + legend pos = south east, + xtick={0.001,0.0015,...,0.004}, + xticklabel style={/pgf/number format/fixed}, + xticklabel style={/pgf/number format/precision=4}, + scaled x ticks=false, + xlabel={Physical error rate}, + ylabel={Per-round-LER}, + extra description/.code={ + \node[rotate=90, anchor=south] + at ([xshift=10mm]current axis.east) + {Warm s. (---), Cold s. (- - -)}; + }, + ] + + \foreach \W/\col/\mark in + {3/KITred/triangle,4/KITblue/diamond,5/KITorange/square} { + \edef\temp{\noexpand + \addplot+[ + mark=\mark, densely dashed, mark options={fill=\col}, + \col, forget plot + ] + table[ + col sep=comma, x=physical_p, + y=LER_per_round, + ] + {res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_False/F_1/W_\W/LERs.csv}; + } + \temp + } + + \foreach \W/\col/\mark in + {3/KITred/triangle*,4/KITblue/diamond*,5/KITorange/square*} { + \edef\temp{\noexpand + \addplot+[mark=\mark, solid, mark options={fill=\col}, \col] + table[ + col sep=comma, x=physical_p, + y=LER_per_round, + ] + {res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_True/F_1/W_\W/LERs.csv}; + } + \temp + + \addlegendentryexpanded{$W = \W$} + } + + \addplot+[mark=*, solid, mark options={fill=black}, black] + table[ + col sep=comma, x=physical_p, + y=LER_per_round, + ] + {res/sim/whole/SyndromeMinSumDecoder/max_iter_200/LERs.csv}; + + \addlegendentry{Whole} + \end{axis} + \end{tikzpicture} + + \caption{ + Comparison of the decoding performance of cold and warm-start + decoding under the $\llbracket 144,12,12 \rrbracket$ \ac{bb} + code for different window sizes. + Decoding was performed using the min-sum algorithm ($200$ + iterations). + The step size was fixed to $F=1$, $12$ rounds of syndrome + extraction were performed and the noise model is + standard circuit-based depolarizing noise. + } +\end{figure} + +\begin{figure}[H] + \centering + \begin{tikzpicture} + \begin{axis}[ + width=\figwidth, + height=\figheight, + ymode=log, + % xmode=log, + legend style={ + cells={anchor=west}, + cells={align=left}, + }, + enlargelimits=false, + ymin=1e-3, ymax=1e-1, + grid=both, + legend pos = north east, + xtick={32,512,1024,2048,4096}, + % xtick={0.001,0.0015,...,0.004}, + xticklabels = + {$32$,$512$,$1{,}024$,,$2{,}048$,,$3{,}072$,,$4{,}096$}, + xtick={32, 512, 1024, 1536, 2048, 2560, 3072, 3584, 4096}, + xticklabel style={/pgf/number format/fixed}, + xticklabel style={/pgf/number format/precision=4}, + scaled x ticks=false, + xlabel={Number of BP iterations}, + ylabel={Per-round-LER}, + extra description/.code={ + \node[rotate=90, anchor=south] + at ([xshift=10mm]current axis.east) + {Warm s. (---), Cold s. (- - -)}; + }, + ] + + \foreach \W/\col/\mark in + {3/KITred/triangle,4/KITblue/diamond,5/KITorange/square} { + \edef\temp{\noexpand + \addplot+[mark=\mark, densely dashed, forget plot, \col] + table[ + col sep=comma, x=max_iter, + y=LER_per_round, + ] + {res/sim/max_iter/WindowingSyndromeMinSumDecoder/p_0.0025/pass_soft_info_False/F_1/W_\W/LERs.csv}; + } + \temp + } + + \foreach \W/\col/\mark in + {3/KITred/triangle*,4/KITblue/diamond*,5/KITorange/square*} { + \edef\temp{\noexpand + \addplot+[mark=\mark, solid, mark options={fill=\col}, \col] + table[ + col sep=comma, x=max_iter, + y=LER_per_round, + ] + {res/sim/max_iter/WindowingSyndromeMinSumDecoder/p_0.0025/pass_soft_info_True/F_1/W_\W/LERs.csv}; + } + \temp + + \addlegendentryexpanded{$W = \W$} + } + \end{axis} + \end{tikzpicture} + + \caption{ + Comaprison of cold and warm-start sliding-window + min-sum decoding of the $\llbracket 144, 12, 12 \rrbracket$ \ac{bb} code + under circuit-level noise. + The noise chosen model is standard circuit-based depolarizing + noise and the physical error probabilty was fixed to + $0.0025$. + The step size was set to $F=1$. + } +\end{figure} + +\begin{figure}[H] + \centering + \begin{tikzpicture} + \begin{axis}[ + width=\figwidth, + height=\figheight, + ymode=log, + % xmode=log, + legend style={ + cells={anchor=west}, + cells={align=left}, + }, + enlargelimits=false, + ymin=1e-3, ymax=1e-1, + grid=both, + legend pos = north east, + xtick={32,512,1024,2048,4096}, + % xtick={0.001,0.0015,...,0.004}, + xticklabels = + {$32$,$512$,$1{,}024$,,$2{,}048$,,$3{,}072$,,$4{,}096$}, + xtick={32, 512, 1024, 1536, 2048, 2560, 3072, 3584, 4096}, + xticklabel style={/pgf/number format/fixed}, + xticklabel style={/pgf/number format/precision=4}, + scaled x ticks=false, + xlabel={Number of BP iterations}, + ylabel={Per-round-LER}, + extra description/.code={ + \node[rotate=90, anchor=south] + at ([xshift=10mm]current axis.east) + {Warm s. (---), Cold s. (- - -)}; + }, + ] + + \foreach \F/\col/\mark in + {3/KITred/triangle,2/KITblue/diamond,1/KITorange/square} { + \edef\temp{\noexpand + \addplot+[mark=\mark, densely dashed, forget plot, \col] + table[ + col sep=comma, x=max_iter, + y=LER_per_round, + ] + {res/sim/max_iter/WindowingSyndromeMinSumDecoder/p_0.0025/pass_soft_info_False/F_\F/W_5/LERs.csv}; + } + \temp + } + + \foreach \F/\col/\mark in + {3/KITred/triangle*,2/KITblue/diamond*,1/KITorange/square*} { + \edef\temp{\noexpand + \addplot+[mark=\mark, solid, mark options={fill=\col}, \col] + table[ + col sep=comma, x=max_iter, + y=LER_per_round, + ] + {res/sim/max_iter/WindowingSyndromeMinSumDecoder/p_0.0025/pass_soft_info_True/F_\F/W_5/LERs.csv}; + } + \temp + + \addlegendentryexpanded{$F = \F$} + } + \end{axis} + \end{tikzpicture} + + \caption{ + Comaprison of cold and warm-start sliding-window + min-sum decoding of the $\llbracket 144, 12, 12 \rrbracket$ \ac{bb} code + under circuit-level noise. + The noise chosen model is standard circuit-based depolarizing + noise and the physical error probabilty was fixed to + $0.0025$. + The window size was set to $F=5$. + } +\end{figure} + +% \begin{figure}[H] +% \centering +% \begin{tikzpicture} +% \begin{axis}[ +% width=\figwidth, +% height=\figheight, +% ymode=log, +% legend style={ +% cells={anchor=west}, +% cells={align=left}, +% }, +% enlargelimits=false, +% ymin=1e-5, ymax=2e-1, +% grid=both, +% legend pos = south east, +% xtick={0.001,0.0015,...,0.004}, +% xticklabel style={/pgf/number format/fixed}, +% xticklabel style={/pgf/number format/precision=4}, +% scaled x ticks=false, +% xlabel={Physical error rate}, +% ylabel={Per-round-LER}, +% extra description/.code={ +% \node[rotate=90, anchor=south] +% at ([xshift=10mm]current axis.east) +% {Warm s. (---), Cold s. (- - -)}; +% }, +% ] +% +% \foreach \W/\col in +% {3/KITred,4/KITblue,5/KITorange} { +% \edef\temp{\noexpand +% \addplot+[mark=*, solid, mark options={fill=\col}, \col] +% table[ +% col sep=comma, x=physical_p, +% y=LER_per_round, +% ] +% {res/sim/WF/WindowingSyndromeSpaGdDecoder/max_iter_200/pass_soft_info_True/F_1/W_\W/LERs.csv}; +% } +% \temp +% +% \addlegendentryexpanded{$W = \W$} +% +% \edef\temp{\noexpand +% \addplot+[mark=o, densely dashed, \col, forget plot] +% table[ +% col sep=comma, x=physical_p, +% y=LER_per_round, +% ] +% {res/sim/WF/WindowingSyndromeSpaGdDecoder/max_iter_200/pass_soft_info_False/F_1/W_\W/LERs.csv}; +% } +% \temp +% } +% \end{axis} +% \end{tikzpicture} +% +% \caption{ +% Comparison of the decoding performance of the $\llbracket +% 144,12,12 \rrbracket$ \ac{bb} code under min-sum decoding for +% different window sizes. The noise model standard-circuit +% based depolarizing noise. $12$ rounds of syndrome extraction +% were performed. +% } +% \end{figure} + % Results when passing all info % Results when passing only messages