\documentclass[tikz]{standalone}
\usepackage{physics,amssymb}
\usepackage{circuitikz}
\usetikzlibrary{shapes.geometric}
\definecolor{darkgreen}{HTML}{009900}
\begin{document}

\begin{tikzpicture}[]

	% frame
%	\draw[-,thick] (0,0) -- (5.5,0);
%	\draw[-,dashed,thick] (5.5,0) -- (6.5,0);
%	\draw[->,thick] (6.5,0) -- (8,0) node[anchor=north west]{$\text{time} = N \tau $};
%	\draw[->,thick] (0,0)  node[anchor=north ]{$0$} -- (0,4) node[anchor=north east]{states};
	
	% vertical lines
%	\draw[-] (1,0) node[anchor=north]{$1$} -- (1,4);
%	\draw[-] (2,0) node[anchor=north]{$2$} -- (2,4);
%	\draw[-] (3,0) node[anchor=north]{$3$} -- (3,4);
%	\draw[-] (4,0) node[anchor=north]{$4$} -- (4,4);
%	\draw[-] (5,0) node[anchor=north]{$5$} -- (5,4);
%	\draw[-] (7,0) node[anchor=north]{$N$} -- (7,4);
	
	% initial and final states
%	\draw[] (0,2) node[anchor=east]{$\ket{i_0}$};
%	\draw[] (7,3) node[anchor=west]{$\ket{i}$};
%	\draw[] (8,3) node[anchor=west]{$\displaystyle \ket{\Phi_0} = \sum_i c_i \ket{i}$};
%	\draw[] (8,2) node[anchor=west]{$\displaystyle  c_i \sim \sum_{\substack{\text{all paths} \\ \text{ending at $\ket{i}$}}} \prod_{k}^{\infty} W_{i_k i_{k+1}}$};
	
	% paths
	\draw[thick] (2,2) node[scale=0.5]{$\blacksquare$} -- node[currarrow,midway,sloped,scale=0.5]{} (3,2.5);
	\draw[thick] (3,2.5) node[scale=0.5]{$\bullet$} -- node[currarrow,midway,sloped,scale=0.5]{} (3.25,3.5);
	\draw[thick] (3.25,3.5) node[scale=0.5]{$\bullet$} -- node[currarrow,midway,sloped,scale=0.5]{} (4,4);
	\draw[thick] (4,4) node[scale=0.5]{$\blacksquare$} -- node[currarrow,midway,sloped,scale=0.5]{} (5,3);
	\draw[thick] (5,3) node[scale=0.5]{$\bullet$} -- node[currarrow,midway,sloped,scale=0.5]{} (6,4);
	\draw[thick] (6,4) node[scale=0.5]{$\blacksquare$} -- node[currarrow,midway,sloped,scale=0.5]{} (7,3);
	\draw[thick] (7,3) node[scale=0.5]{$\bullet$} -- node[currarrow,midway,sloped,scale=0.5]{} (5,3);
	\draw[thick] (5,3) node[scale=0.5]{$\bullet$} -- node[currarrow,midway,sloped,scale=0.5]{} (5.75,1.5);
	\draw[thick] (5.75,1.5) node[scale=0.5]{$\blacksquare$} -- node[currarrow,midway,sloped,scale=0.5]{} (6.25,0.5);
	\draw[thick,dashed] (6.25,0.5) node[scale=0.5]{$\blacksquare$} -- (7,0.25);
	
	% states
	\draw[] (2,2) node[scale=0.5,anchor=north]{$\ket{i_0} = \ket{I_0}$};
	\draw[] (3,2.5) node[scale=0.5,anchor=north west]{$\ket{i_1}$};
	\draw[] (3.25,3.5) node[scale=0.5,anchor=north west]{$\ket{i_2}$};
	\draw[] (4,4) node[scale=0.5,anchor=west]{$\ket{i_3} = \ket{I_1}$};
	\draw[] (5,3) node[scale=0.5,anchor=east]{$\ket{i_4} = \ket{i_7}$};
	\draw[] (6,4) node[scale=0.5,anchor=south]{$\ket{i_5} = \ket{I_2}$};
	\draw[] (7,3) node[scale=0.5,anchor=west]{$\ket{i_6}$};
	\draw[] (5.75,1.5) node[scale=0.5,anchor=west]{$\ket{i_8} = \ket{I_3}$};
	\draw[] (6.25,0.251) node[scale=0.5,anchor=east]{$\ket{i_9} = \ket{I_4}$};
	
	% domains
	\draw[thick,magenta,fill,opacity=0.2] (2.9,2.4) circle (1.5);
	\draw[thick,cyan,fill,opacity=0.2] (4.25,3.25) circle (1.25);
	\draw[thick,green,fill,opacity=0.2] (6,3.5) circle (1.5);
	\draw[thick,orange,fill,opacity=0.2] (5.75,1.5) circle (0.45);
    
    \draw[magenta] (2,3) node[scale=0.75]{$\mathcal{D}_{I_0}$};
    \draw[cyan] (4.25,4.25) node[scale=0.75]{$\mathcal{D}_{I_1}$};
    \draw[darkgreen] (6,4.75) node[scale=0.75]{$\mathcal{D}_{I_2}$};
    \draw[orange] (5.6,1.3) node[scale=0.75]{$\mathcal{D}_{I_3}$};
    
\end{tikzpicture}

\end{document}