From 93f310d8436daca2e7cb73f9a9b118fbb912be74 Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Sat, 25 Apr 2026 18:49:03 +0200 Subject: [PATCH] Add bit-flip noise and modify phenomenological and circuit-level noise figures --- src/thesis/chapters/3_fault_tolerant_qec.tex | 143 +++++++++++-------- 1 file changed, 83 insertions(+), 60 deletions(-) diff --git a/src/thesis/chapters/3_fault_tolerant_qec.tex b/src/thesis/chapters/3_fault_tolerant_qec.tex index f3b5578..07be8b2 100644 --- a/src/thesis/chapters/3_fault_tolerant_qec.tex +++ b/src/thesis/chapters/3_fault_tolerant_qec.tex @@ -41,53 +41,75 @@ } }]{\phantom{1}}} - \begin{subfigure}{0.48\textwidth} - \centering - % tex-fmt: off - \begin{quantikz}[row sep=4mm, column sep=4mm] - \lstick[3]{$\ket{\psi}$} & \xyzerr & \ctrl{3} & & & & & \\ - & \xyzerr & & \ctrl{2} & \ctrl{3} & & & \\ - & \xyzerr & & & & \ctrl{2} & & \\ - \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\ - \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & \meter{} & \setwiretype{c} - \end{quantikz} - % tex-fmt: on + \begin{minipage}{0.7\textwidth} + \begin{minipage}{\textwidth} + \centering + % tex-fmt: off + \begin{quantikz}[row sep=4mm, column sep=4mm] + \lstick[3]{$\ket{\psi}_\text{L}$} & \xerr & \ctrl{3} & & & & & \\ + & \xerr & & \ctrl{2} & \ctrl{3} & & & \\ + & \xerr & & & & \ctrl{2} & & \\ + \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\ + \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & \meter{} & \setwiretype{c} + \end{quantikz} + % tex-fmt: on - \caption{Depolarizing channel.} - \end{subfigure}% - \begin{subfigure}{0.48\textwidth} - \centering - % tex-fmt: off - \begin{quantikz}[row sep=4mm, column sep=4mm] - \lstick[3]{$\ket{\psi}$} & \xerr & \ctrl{3} & & & & & & \\ - & \xerr & & \ctrl{2} & \ctrl{3} & & & & \\ - & \xerr & & & & \ctrl{2} & & & \\ - \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & \xerr & \meter{} & \setwiretype{c} \\ - \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & \xerr & \meter{} & \setwiretype{c} - \end{quantikz} - % tex-fmt: on + \subcaption{Bit-flip noise.} + \end{minipage} - \caption{Phenomenological noise.} - \end{subfigure} + \vspace*{5mm} - \vspace*{3mm} - \centering - \begin{subfigure}[c]{0.75\textwidth} - \centering - % tex-fmt: off - \begin{quantikz}[row sep=4mm, column sep=2mm] - \lstick[3]{$\ket{\psi}$} & \xyzerr & \ctrl{3} & \xyzerr \wire[d][3]{q} & & & & & & & & & \\ - & \xyzerr & & & \ctrl{2} & \xyzerr \wire[d][2]{q} & \ctrl{3} & \xyzerr \wire[d][3]{q} & & & & & \\ - & \xyzerr & & & & & & & \ctrl{2} & \xyzerr \wire[d][2]{q} & & & \\ - \lstick{$\ket{0}_{\text{A}_1}$} & \xyzerr & \targ{} & \xyzerr & \targ{} & \xyzerr & & & & & \xerr & \meter{} & \setwiretype{c} \\ - \lstick{$\ket{0}_{\text{A}_2}$} & \xyzerr & & & & & \targ{} & \xyzerr & \targ{} & \xyzerr & \xerr & \meter{} & \setwiretype{c} - \end{quantikz} - % tex-fmt: on + \begin{minipage}{\textwidth} + \centering + % tex-fmt: off + \begin{quantikz}[row sep=4mm, column sep=4mm] + \lstick[3]{$\ket{\psi}_\text{L}$} & \xyzerr & \ctrl{3} & & & & & \\ + & \xyzerr & & \ctrl{2} & \ctrl{3} & & & \\ + & \xyzerr & & & & \ctrl{2} & & \\ + \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\ + \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & \meter{} & \setwiretype{c} + \end{quantikz} + % tex-fmt: on - \caption{Circuit-level noise.} - \end{subfigure}% + \subcaption{Depolarizing channel.} + \end{minipage} + + \vspace*{5mm} + + \begin{minipage}{\textwidth} + \centering + % tex-fmt: off + \begin{quantikz}[row sep=4mm, column sep=4mm] + \lstick[3]{$\ket{\psi}_\text{L}$} & \xerr & \ctrl{3} & & & & & & \xerr & & \setwiretype{n} & \\ + & \xerr & & \ctrl{2} & \ctrl{3} & & & & \xerr & & \setwiretype{n} & \gate[style={left,draw=none}]{\cdots} \\ + & \xerr & & & & \ctrl{2} & & & \xerr & & \setwiretype{n} & \\ + \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & \xerr & \meter{} & \setwiretype{c} \\ + \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & \xerr & \meter{} & \setwiretype{c} + \end{quantikz} + % tex-fmt: on + + \subcaption{Phenomenological noise.} + \end{minipage} + + \vspace*{5mm} + + \begin{minipage}{\textwidth} + \centering + % tex-fmt: off + \begin{quantikz}[row sep=4mm, column sep=2mm] + \lstick[3]{$\ket{\psi}_\text{L}$} & \xyzerr & \ctrl{3} & \xyzerr \wire[d][3]{q} & & & & & & & & & \xyzerr & & \setwiretype{n} & \\ + & \xyzerr & & & \ctrl{2} & \xyzerr \wire[d][2]{q} & \ctrl{3} & \xyzerr \wire[d][3]{q} & & & & & \xyzerr & & \setwiretype{n} & \gate[style={left,draw=none,xshift=3.5mm}]{\cdots} \\ + & \xyzerr & & & & & & & \ctrl{2} & \xyzerr \wire[d][2]{q} & & & \xyzerr & & \setwiretype{n} & \\ + \lstick{$\ket{0}_{\text{A}_1}$} & \xyzerr & \targ{} & \xyzerr & \targ{} & \xyzerr & & & & & \xerr & \meter{} & \setwiretype{c} \\ + \lstick{$\ket{0}_{\text{A}_2}$} & \xyzerr & & & & & \targ{} & \xyzerr & \targ{} & \xyzerr & \xerr & \meter{} & \setwiretype{c} + \end{quantikz} + % tex-fmt: on + + \subcaption{Circuit-level noise.} + \end{minipage} + \end{minipage}% \hfill% - \begin{subfigure}[c]{0.25\textwidth} + \begin{minipage}{0.23\textwidth} \centering % tex-fmt: off \begin{quantikz}[row sep=4mm, column sep=2mm] @@ -97,7 +119,7 @@ \setwiretype{n} & \gate{\phantom{1}} & \end{quantikz} % tex-fmt: on - \end{subfigure} + \end{minipage} \caption{Types of noise models.} \label{fig:Types of noise models.} @@ -144,7 +166,7 @@ \begin{minipage}{0.5\textwidth} % tex-fmt: off \begin{quantikz}%[row sep=4mm, column sep=4mm] - \lstick[3]{$\ket{\psi}$} & \ctrl{3} & & & & & \\ + \lstick[3]{$\ket{\psi}_\text{L}$} & \ctrl{3} & & & & & \\ & & \ctrl{2} & \ctrl{3} & & & \\ & & & & \ctrl{2} & & \\ \lstick{$\ket{0}_{\text{A}_1}$} & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\ @@ -252,7 +274,7 @@ } ] % tex-fmt: off - \lstick[3]{$\ket{\psi}$} & \preperr{E_0} & \ctrl{3} & & & & & & \ctrl{5} & & & & & & \ctrl{7} & & & & & \\ + \lstick[3]{$\ket{\psi}_\text{L}$} & \preperr{E_0} & \ctrl{3} & & & & & & \ctrl{5} & & & & & & \ctrl{7} & & & & & \\ & \preperr{E_1} & & \ctrl{2} & \ctrl{3} & & & & & \ctrl{4} & \ctrl{5} & & & & & \ctrl{6} & \ctrl{7} & & & \\ & \preperr{E_2} & & & & \ctrl{2} & & & & & & \ctrl{4} & & & & & & \ctrl{6} & & \\ \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\ @@ -345,15 +367,15 @@ % tex-fmt: off \begin{quantikz}[row sep=4mm, column sep=3mm, wire types={q,q,q,q,q,n,n,n,n}] - \lstick[3]{$\ket{\psi}$} & \preperr{E_0} & \ctrl{3} & & & & \preperr{E_5} & & \ctrl{5} & & & & \preperr{E_{10}} & & \ctrl{7} & & & & & & \\ - & \preperr{E_1} & & \ctrl{2} & \ctrl{3} & & \noise\redwire{14} & & & \redctrl{4} & \redctrl{5} & & \preperr{E_{11}} & & & \redctrl{6} & \redctrl{7} & & & & \\ - & \preperr{E_2} & & & & \ctrl{2} & \preperr{E_7} & & & & & \ctrl{4} & \preperr{E_{12}} & & & & & \ctrl{6} & & & \\ - \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & & & & & & & \preperr{E_3} & \meter{} & \setwiretype{c} \\ - \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & & & & & & & \preperr{E_4} & \meter{} & \setwiretype{c} \\ - & & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \targ{} & \redtarg\redwire{10} & & & & & & & & & \preperr{E_8} & \redmeter\wire[r][1][style={draw=red,double, line width=1.5pt}]{q} & \setwiretype{n} \\ - & & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \redtarg\redwire{9} & \targ{} & & & & & & & \preperr{E_9} & \redmeter\wire[r][1][style={draw=red,double, line width=1.5pt}]{q} & \setwiretype{n} \\ - & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_5}$} & \setwiretype{q} & \targ{} & \redtarg\redwire{4} & & & \preperr{E_{13}} & \redmeter\wire[r][1][style={draw=red,double, line width=1.5pt}]{q} & \setwiretype{n} \\ - & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_6}$} & \setwiretype{q} & & & \redtarg\redwire{3} & \targ{} & \preperr{E_{14}} & \redmeter\wire[r][1][style={draw=red,double, line width=1.5pt}]{q} & \setwiretype{n} + \lstick[3]{$\ket{\psi}_\text{L}$} & \preperr{E_0} & \ctrl{3} & & & & \preperr{E_5} & & \ctrl{5} & & & & \preperr{E_{10}} & & \ctrl{7} & & & & & & \\ + & \preperr{E_1} & & \ctrl{2} & \ctrl{3} & & \noise\redwire{14} & & & \redctrl{4} & \redctrl{5} & & \preperr{E_{11}} & & & \redctrl{6} & \redctrl{7} & & & & \\ + & \preperr{E_2} & & & & \ctrl{2} & \preperr{E_7} & & & & & \ctrl{4} & \preperr{E_{12}} & & & & & \ctrl{6} & & & \\ + \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & & & & & & & \preperr{E_3} & \meter{} & \setwiretype{c} \\ + \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & & & & & & & \preperr{E_4} & \meter{} & \setwiretype{c} \\ + & & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \targ{} & \redtarg\redwire{10} & & & & & & & & & \preperr{E_8} & \redmeter\wire[r][1][style={draw=red,double, line width=1.5pt}]{q} & \setwiretype{n} \\ + & & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \redtarg\redwire{9} & \targ{} & & & & & & & \preperr{E_9} & \redmeter\wire[r][1][style={draw=red,double, line width=1.5pt}]{q} & \setwiretype{n} \\ + & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_5}$} & \setwiretype{q} & \targ{} & \redtarg\redwire{4} & & & \preperr{E_{13}} & \redmeter\wire[r][1][style={draw=red,double, line width=1.5pt}]{q} & \setwiretype{n} \\ + & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_6}$} & \setwiretype{q} & & & \redtarg\redwire{3} & \targ{} & \preperr{E_{14}} & \redmeter\wire[r][1][style={draw=red,double, line width=1.5pt}]{q} & \setwiretype{n} \end{quantikz} % tex-fmt: on @@ -431,14 +453,15 @@ % tex-fmt: off \begin{quantikz}[row sep=2mm, column sep=4mm, wire types={q,q,q,n,n,n}] - & \gate[3]{\text{SE}_1} & & \gate[3]{\text{SE}_2} & & \gate[3]{\text{SE}_3} & & \gate[3]{\text{SE}_4} & \\ - \lstick{$\ket{\psi}$} & & & & & & & & & \setwiretype{n} & \ldots \\ - & \wire[d][3]{c} & & \wire[d][1]{c} & & \wire[d][1]{c} & & \wire[d][1]{c} & \\ - & \ctrl[wire=c]{0}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \\ - & & \wire[r][1]{c} & \targ{}\wire[d][1]{c} & \wire[r][1]{c} & \targ{}\wire[d][1]{c} & \wire[r][1]{c} & \targ{}\wire[d][1]{c} & \\ - & \gate[1]{\bm{D}_1} & & \gate[1]{\bm{D}_2} & & \gate[1]{\bm{D}_3} & & \gate[1]{\bm{D}_4} & \\ + \lstick[3]{$\ket{\psi}_\text{L}$} & \gate[3]{\text{SE}_1} & & \gate[3]{\text{SE}_2} & & \gate[3]{\text{SE}_3} & & \gate[3]{\text{SE}_4} & \\ + & & & & & & & & & \setwiretype{n} & \ldots \\ + & \wire[d][3]{c} & & \wire[d][1]{c} & & \wire[d][1]{c} & & \wire[d][1]{c} & \\ + & \ctrl[wire=c]{0}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \\ + & & \wire[r][1]{c} & \targ{}\wire[d][1]{c} & \wire[r][1]{c} & \targ{}\wire[d][1]{c} & \wire[r][1]{c} & \targ{}\wire[d][1]{c} & \\ + & \gate[1]{\bm{D}_1} & & \gate[1]{\bm{D}_2} & & \gate[1]{\bm{D}_3} & & \gate[1]{\bm{D}_4} & \\ \end{quantikz} % tex-fmt: on \caption{Construction of detectors from measurements in the general case.} \end{figure} +