Can Calibre access TeX and pstricks?
Here's a basic file which will embed a QR code in a .pdf --- I'm sure someone can adapt it:
\documentclass{standalone}
\usepackage{pst-barcode,xcolor}
\begin{document}
\fboxsep=0pt
\colorbox{white}{%
\begin{pspicture}(-0.1in,-0.1in) (0.9in,0.9in)
\psbarcode{http://www.frycomm.com/}{}{qrcode}
\end{pspicture}}
\end{document}
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