Resolving tikzcd/externalize/align incompatibilities

Question

I've been trying to follow the insights from the following posts:

• Are the TikZ libraries cd and external incompatible with one another?
• How to avoid redefining ampersand & globally?
• Use & inside commands

(The user tobiasBora seems to be interested in achieving very similar things to me.) However, I've ended up in a jumble of nothing quite working in all possible cases.

In short, I want to use a tikzcd environment that

• works as you would expect it to (duh!)
• also works in conjunction with the externalize package
• also works if you want to embed it in an amsmath align environment
• works with the beamer document class

My current attempt is in the MWE below:

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath,xparse,etoolbox}
\usetikzlibrary{cd,external}
%we don't actually need externalisation to demonstrate the problem, so turn it off for now
%\tikzexternalize
\makeatletter
\NewDocumentEnvironment{quantikz}{O{}+b}{%
   %local redefinition of catcode
  \begingroup \catcode`&=\active
  \def@temp{\tikzcd@[#1]\scantokens{#2}}%
  \expandafter@temp\endtikzcd\endgroup
}{}
%replace commands with environment. seems to help with externalize.
\patchcmd\tikzcd@{\tikzpicture}{\begin{tikzpicture}}{}{}
\patchcmd\endtikzcd{\endtikzpicture}{\end{tikzpicture}}{}{}
\makeatother
\tikzcdset{nodes in empty cells}
%this works
%also works with external switched on
%also works when documentclass is beamer
\begin{document}
\begin{quantikz}
H & \ar[l] 
\end{quantikz}
%this does not work
%neither does ampersand replacement
% \begin{align}
% \begin{quantikz}
% & \ar[l] 
% \end{quantikz}
% \end{align}
%original environment works with ampersand replacement
%but does not externalize
\begin{align}
\begin{tikzcd}[ampersand replacement=&]
 H & \ar[l] 
\end{tikzcd}
\end{align}
\end{document}

I had wondered if a simple solution would be to get ampersand replacement working again within the new environment. But even if I directly replace all instances of & with \pgfmatrixnextcell, the quantikz environment doesn't seem to work inside align.

Answer 1

Here's a defintion of quantikz that grabs the body and replaces every & in it with a \pgfmatrixnextcell.

Then, it places a tikzpicture environment in a way that the external accepts it (having \end{tikzpicture} not hidden in another macro) and disables the tikzpicture environment inside tikzcd. For this the options to \tikzcd (\begin{tikzcd}) will be moved to the tikzpicture environment which is where it's usually placed anyway.

This does not patch the tikzcd environment in any regard but only provides a new quantikz environment which should work like the original tikzcd environment but with & even inside an argument to a macro and with activated externalization.

Code

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usetikzlibrary{cd, external}
\tikzexternalize
\ExplSyntaxOn
\NewDocumentEnvironment{quantikz}{O{}+b}{
  \begin{tikzpicture}[commutative~diagrams/.cd, every~diagram, #1]
    \tl_set:Nn \l_tmpa_tl { #2 }
    \tl_replace_all:Nnn \l_tmpa_tl { & } { \pgfmatrixnextcell }
    \begingroup
      \def\tikzpicture[##1]{}
      \let\endtikzpicture\relax
      \tikzcd
        \l_tmpa_tl
      \endtikzcd
    \endgroup
  \end{tikzpicture}
}{}
\ExplSyntaxOff
\tikzcdset{
  nodes in empty cells,
  diagrams={baseline=-axis_height}}% https://tex.stackexchange.com/a/678935/16595
\begin{document}
\begin{quantikz}
H & \ar[l] 
\end{quantikz}
\begin{align}
\left{\begin{quantikz}
 H & \ar[l] X \
 B \ar[ur]
\end{quantikz}\right}
& = { x + 2 }
\end{align}
\end{document}