floats
\begin{figure}[H]
\centering
\includegraphics[width=14cm]{Text/Images/phi_geometrical.jpg}
\caption{Depiction of Azimuth Angle\begin{math}\;\phi_{geom}\;\end{math} in 2
dimensions}
\label{fig:phi_geometrical}
\end{figure}
I am facing the error. Can anyone help me how to solve this ?
You can't really nest floating environments (it doesn't make sense logically). That's the main problem, and may stem from the fact that you think you need a table environment in order to place a tabular. That's not the case. You're probably after the following:
\documentclass{article}
\usepackage{braket}
\begin{document}
\begin{table}[ht]
\centering
\begin{tabular}[t]{| c | c |}
\hline
State & $1$-step \\ \hline
$\ket{n, \leftarrow, 0}$ & $\leftarrow$ \\
$\ket{n, \leftarrow, 1}$ & $\rightarrow$ \\
$\ket{n, \rightarrow, 0}$ & $\rightarrow$ \\
$\ket{n, \rightarrow, 1}$ & $\leftarrow$ \\
\hline
\end{tabular}\hfill%
\begin{tabular}[t]{| c | c |}
\hline
State & $2$-step \\ \hline
$\ket{n, \leftarrow, \leftarrow, 0}$ & $\leftarrow$ \\
$\ket{n, \leftarrow, \leftarrow, 1}$ & $\rightarrow$ \\
$\ket{n, \leftarrow, \rightarrow, 0}$ & $\rightarrow$ \\
$\ket{n, \leftarrow, \rightarrow, 1}$ & $\leftarrow$ \\
\hline
\end{tabular}\hfill%
\begin{tabular}[t]{| c | c |}
\hline
State & $3$-step \\ \hline
$\ket{n, \leftarrow, \leftarrow, \leftarrow, 0}$ & $\leftarrow$ \\
$\ket{n, \leftarrow, \leftarrow, \leftarrow, 1}$ & $\rightarrow$ \\
$\ket{n, \leftarrow, \leftarrow, \rightarrow, 0}$ & $\rightarrow$ \\
$\ket{n, \leftarrow, \leftarrow, \rightarrow, 1}$ & $\leftarrow$ \\
\hline
\end{tabular}
\caption{Directions}
\end{table}
\end{document}
You may also be interested in a booktabs implementation:
\documentclass{article}
\usepackage{braket,booktabs}
\begin{document}
\begin{table}[ht]
\centering
\begin{tabular}[t]{c c}
\toprule
State & $1$-step \\ \midrule
$\ket{n, \leftarrow, 0}$ & $\leftarrow$ \\
$\ket{n, \leftarrow, 1}$ & $\rightarrow$ \\
$\ket{n, \rightarrow, 0}$ & $\rightarrow$ \\
$\ket{n, \rightarrow, 1}$ & $\leftarrow$ \\
\bottomrule
\end{tabular}\hfill%
\begin{tabular}[t]{c c}
\toprule
State & $2$-step \\ \midrule
$\ket{n, \leftarrow, \leftarrow, 0}$ & $\leftarrow$ \\
$\ket{n, \leftarrow, \leftarrow, 1}$ & $\rightarrow$ \\
$\ket{n, \leftarrow, \rightarrow, 0}$ & $\rightarrow$ \\
$\ket{n, \leftarrow, \rightarrow, 1}$ & $\leftarrow$ \\
\bottomrule
\end{tabular}\hfill%
\begin{tabular}[t]{c c}
\toprule
State & $3$-step \\ \midrule
$\ket{n, \leftarrow, \leftarrow, \leftarrow, 0}$ & $\leftarrow$ \\
$\ket{n, \leftarrow, \leftarrow, \leftarrow, 1}$ & $\rightarrow$ \\
$\ket{n, \leftarrow, \leftarrow, \rightarrow, 0}$ & $\rightarrow$ \\
$\ket{n, \leftarrow, \leftarrow, \rightarrow, 1}$ & $\leftarrow$ \\
\bottomrule
\end{tabular}
\caption{Directions}
\end{table}
\end{document}
As an aside: You could have placed the entire table into a single tabular as well.
The easiest solution in these cases is to add \protect in front of the usual suspects; \subref is one of them because it has a *-variant.
\documentclass{article}
\usepackage{graphicx}
\usepackage{subfig}
\begin{document}
\begin{figure}[!ht]
\centering
\subfloat[]{%
\label{subfig1}%
\includegraphics[width=.4\linewidth]{fig1.pdf}%
}%
\qquad
\subfloat[]{%
\label{subfig2}%
\includegraphics[width=.4\linewidth]{fig2.pdf}%
}
\caption{A caption for figures \protect\subref{subfig1} and \protect\subref{subfig2}.}
\label{myfig}
\end{figure}
\end{document}
Note where I added/removed % at end of lines and the position of \label{myfig} after \caption.
This might be annoying if you have several appearances of \subref in moving arguments. In this case you can “robustify” the command:
\documentclass{article}
\usepackage{graphicx}
\usepackage{subfig}
\usepackage{etoolbox} % for \robustify
\robustify{\subref}
\begin{document}
\begin{figure}[!ht]
\centering
\subfloat[]{%
\label{subfig1}%
\includegraphics[width=.4\linewidth]{fig1.pdf}%
}%
\qquad
\subfloat[]{%
\label{subfig2}%
\includegraphics[width=.4\linewidth]{fig2.pdf}%
}
\caption{A caption for figures \subref{subfig1} and \subref{subfig2}.}
\label{myfig}
\end{figure}
\end{document}
Another solution is to avoid subfig for subcaption, which is the path I'd recommend:
\documentclass{article}
\usepackage{graphicx}
\usepackage{subcaption}
\begin{document}
\begin{figure}[!ht]
\centering
\subcaptionbox{\label{subfig1}}{%
\includegraphics[width=.4\linewidth]{fig1.pdf}%
}%
\qquad
\subcaptionbox{\label{subfig2}}{%
\includegraphics[width=.4\linewidth]{fig2.pdf}%
}
\caption{A caption for figures \subref{subfig1} and \subref{subfig2}.}
\label{myfig}
\end{figure}
\end{document}
Best Answer
\begin{math}is fragile and should be\protected or better replaced by$: