I found a copy of the class at
https://raw.githubusercontent.com/beatrizgoa/latex/master/ieeeaccess.cls
I will assume the version you are using is similar.
The class breaks LaTeX in several ways but in particular here it redefines the \year
TeX primitive which breaks any date calculations in TeX (and so in pgfmath)
The class has
\def\year#1{\gdef\theyear{#1}}
which is to say the least not a good idea.
You should report this to the class maintainers but
\let\realyear\year
\documentclass{ieeeaccess}
\let\classyear\year
\let\year\realyear
\usepackage{tikz}
\usetikzlibrary{quantikz}
\begin{document}
\end{document}
Probably patches it enough so that LaTeX isn't completely broken.
If you are reporting it
\def\textit#1{{\it #1}}%
\def\textbf#1{{\bf #1}}%
Should be removed as well.