\documentclass{standalone}
\usepackage{pgfgantt}
\usepgflibrary{patterns}
\begin{document}
\definecolor{techpurple}{RGB}{79,41,132}
\newganttchartelement{responsibility}{responsibility/.style={fill=techpurple!25}}
\newganttchartelement{lead}{lead/.style={fill=techpurple!100}}
\begin{ganttchart}[
hgrid, vgrid,
expand chart=6.5in,
canvas/.style={draw=none},
y unit title=.2in,
y unit chart=.2in,
bar/.style={pattern=north east lines,draw=black},
title/.style={draw=none},
]{1}{13}
\gantttitle{Project Year 1}{4} \gantttitle{Project Year 2}{4}
\gantttitle[title/.style={draw=none}]{}{1} \gantttitle{Responsibility}{4} \\
\gantttitlelist[title list options={var=\y, evaluate=\y as \x using "Q{\y}"}]{1,...,4}{1}
\gantttitlelist[title list options={var=\y, evaluate=\y as \x using "Q{\y}"}]{1,...,4}{1}
\gantttitle[title/.style={draw=none}]{}{1}
\gantttitle{R}{1} \gantttitle{G}{1} \gantttitle{H}{1} \gantttitle{K}{1} \\
\ganttbar{Meeting/planning (PIs)}{1}{8} \ganttlead{}{10}{10} \ganttresponsibility{}{11}{13} \\
\ganttbar{Review final equipment specs and quotes}{1}{1} \ganttlead{}{10}{10} \ganttresponsibility{}{11}{13} \\
\ganttbar{Hardware ordered, delivered}{1}{2} \ganttlead{}{13}{13} \ganttresponsibility{}{10}{10} \\
\ganttbar{Final report}{8}{8} \ganttlead{}{10}{10} \ganttresponsibility{}{11}{13}
\end{ganttchart}
\end{document}

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