[Demo] Add: Unitary synthesis with recursive KAK decompositions

_static/demonstration_assets/unitary_synthesis_kak/AIII_generic_CSG.tex

@@ -0,0 +1,20 @@
+\documentclass[]{standalone}
+\usepackage{amsmath,quantikz,graphicx,xcolor}
+
+
+\begin{document}
+% \begin{align*}
+\begin{quantikz}
+    & & \gate{R_Y}\wire[d][3]{q} & \\
+    & \qwbundle{n-3} & |[operator]| & \\
+    & & |[operator]| & \\
+    & & |[operator]| &
+\end{quantikz}
+=
+\begin{quantikz}
+    & & \gate{R_Y(\theta_0)} & \gate{R_Y(\theta_1)} & \gate{R_Y(\theta_2)} & \ \ldots \ & \gate{R_Y(\theta_{2^{n-1}-1})} & \\
+    & \qwbundle{n-3} & \octrl{-1} & \octrl{-1} & \octrl{-1} & \ \ldots \ & \ctrl{-1} & \\
+    & & \octrl{-1} & \octrl{-1} & \ctrl{-1} & \ \ldots \ & \ctrl{-1} & \\
+    & & \octrl{-1} & \ctrl{-1} & \octrl{-1} & \ \ldots \ & \ctrl{-1} &
+\end{quantikz}
+\end{document}

_static/demonstration_assets/unitary_synthesis_kak/AIII_generic_complete.tex

@@ -0,0 +1,17 @@
+\documentclass[]{standalone}
+\usepackage{amsmath,quantikz,graphicx,xcolor}
+
+
+\begin{document}
+% \begin{align*}
+\begin{quantikz}
+    & & \gate[2]{U(2^n)} &\\
+    & \qwbundle{n-1} & &
+\end{quantikz}
+=
+\begin{quantikz}
+    & & |[operator]| & \gate{R_Y}\wire[d]{q} & |[operator]| &\\
+    & \qwbundle{n-1} & \gate{U(2^{n-1})}\wire[u]{q} & |[operator]| & \gate{U(2^{n-1})}\wire[u]{q} & 
+\end{quantikz}
+
+\end{document}

_static/demonstration_assets/unitary_synthesis_kak/A_generic_complete.tex

@@ -0,0 +1,17 @@
+\documentclass[]{standalone}
+\usepackage{amsmath,quantikz,graphicx,xcolor}
+
+
+\begin{document}
+% \begin{align*}
+\begin{quantikz}
+    & \ghost{R_Z} & |[operator]| &\\
+    & \qwbundle{n-1} & \gate{U(2^{n-1})}\wire[u]{q} &
+\end{quantikz}
+=
+\begin{quantikz}
+    & & & \gate{R_Z}\wire[d]{q} & &\\
+    & \qwbundle{n-1} & \gate{U(2^{n-1})} & |[operator]| & \gate{U(2^{n-1})} & 
+\end{quantikz}
+
+\end{document}

_static/demonstration_assets/unitary_synthesis_kak/KAK_generic.tex

@@ -0,0 +1,49 @@
+\documentclass[]{standalone}
+\usepackage{amsmath,quantikz,graphicx,xcolor}
+
+\begin{document}
+% \begin{align*}
+\begin{quantikz}
+    & \gate[2]{G} & \\
+    &&
+\end{quantikz}
+=
+\begin{quantikz}
+    & \gate[2]{K_2} & \gate[2]{A} & \gate[2]{K_1} & \\
+    &&&&
+\end{quantikz}
+% \end{align*}
+% Iterate the above:
+
+% \begin{align*}
+% \begin{quantikz}
+%     & \ctrl[open]{1} & \ctrl[open]{1} & \ctrl{1} & \ctrl{1} & \\
+%     & \ctrl[open]{1} & \ctrl{1} & \ctrl[open]{1} & \ctrl{1} & \\
+%     & \gate{A} & \gate{B} & \gate{C} & \gate{D} &
+% \end{quantikz}
+% &=
+% \begin{quantikz}
+%     & \ctrl[open]{1} & \ctrl{1} & \\
+%     & \gate[2]{A\oplus B} & \gate[2]{C\oplus D} & \\
+%     & & &
+% \end{quantikz}\\
+% &=
+% \begin{quantikz}
+%     & & \ctrl{1} & \\
+%     & \gate[2]{A\oplus B} & \gate[2]{A^\dagger C\oplus B^\dagger D} & \\
+%     & & &
+% \end{quantikz}\\
+% &=
+% \begin{quantikz}
+%     & & & \ctrl{1} & \ctrl{1} & \\
+%     & \ctrl[open]{1} & \ctrl{1} & \ctrl[open]{1} & \ctrl{1} & \\
+%     & \gate{A} & \gate{B} & \gate{A^\dagger C} & \gate{B^\dagger D} &
+% \end{quantikz}\\
+% &=
+% \begin{quantikz}
+%     & & & \ctrl{2} & \ctrl{1} & \\
+%     & & \ctrl{1} & & \ctrl{1} & \\
+%     & \gate{A} & \gate{A^\dagger B} & \gate{A^\dagger C} & \gate{C^\dagger A B^\dagger D} &
+% \end{quantikz}
+% \end{align*}
+\end{document}

_static/demonstration_assets/unitary_synthesis_kak/QSD.tex

@@ -0,0 +1,17 @@
+\documentclass[]{standalone}
+\usepackage{amsmath,quantikz,graphicx,xcolor}
+
+
+\begin{document}
+% \begin{align*}
+\begin{quantikz}
+    & & \gate[2]{U(2^n)} &\\
+    & \qwbundle{n-1} & &
+\end{quantikz}
+=
+\begin{quantikz}
+    & & & \gate{R_Z}\wire[d]{q} & & \gate{R_Y}\wire[d]{q} & & \gate{R_Z}\wire[d]{q} & &\\
+    & \qwbundle{n-1} & \gate{U(2^{n-1})} & |[operator]| & \gate{U(2^{n-1})} & |[operator]| & \gate{U(2^{n-1})} & |[operator]| & \gate{U(2^{n-1})} & 
+\end{quantikz}
+
+\end{document}

_static/demonstration_assets/unitary_synthesis_kak/block_zxz_optimization.tex

@@ -0,0 +1,46 @@
+\documentclass[]{article}
+\usepackage{amsmath,quantikz,graphicx,xcolor,amssymb,amsfonts}
+
+\definecolor{yellow}{HTML}{E2A300}
+\definecolor{blue}{HTML}{4D53C8}
+\definecolor{green}{HTML}{52BD7C}
+\definecolor{red}{HTML}{D7333B}
+
+
+
+\begin{document}
+\begin{align*}
+\hspace{-5cm}\begin{quantikz}
+    & & \gate[3]{U(2^n)} &\\
+    & & &\\
+    & \qwbundle{n-2} & &
+\end{quantikz}
+&=
+\begin{quantikz}
+    & & & \gate{R_Z}\wire[d][2]{q} & & \gate{R_X}\wire[d][2]{q} & & \gate{R_Z}\wire[d][2]{q} & &\\
+    & & \gate[2]{U(2^{n-1})} & |[operator]| & \gate[2]{U(2^{n-1})} & |[operator]| & \gate[2]{U(2^{n-1})} & |[operator]| & \gate[2]{U(2^{n-1})} & \\
+    & \qwbundle{n-2} & & |[operator]| & & |[operator]| & & |[operator]| & & 
+\end{quantikz}\\
+&=\begin{quantikz}
+    & & & \gate{R_Z}\wire[d][2]{q} & \gate{H} & \gategroup[3,steps=3,style={inner
+sep=3pt, rounded corners,color=green}]{} & \gate{R_Z}\wire[d][2]{q} & & \gate{H} & \gate{R_Z}\wire[d][2]{q} & &\\
+    & & \gate[2]{U(2^{n-1})} & |[operator]| & & \gate[2]{U(2^{n-1})} & |[operator]| & \gate[2]{U(2^{n-1})} & & |[operator]| & \gate[2]{U(2^{n-1})} & \\
+    & \qwbundle{n-2} &  & |[operator]| & &  & |[operator]| &  & & |[operator]| &  & 
+\end{quantikz}\\
+&=\begin{quantikz}
+    & & & \gate{R_Z}\wire[d][2]{q} & \targ{}\gategroup[2,steps=3,style={inner
+sep=0pt, rounded corners,color=yellow}]{} & \gate{H} & \ctrl{0}\gategroup[3,steps=3,style={inner
+sep=3pt, rounded corners,color=blue}]{} & |[operator]| & \ctrl{0}\gategroup[2,steps=3,style={inner
+sep=0pt, rounded corners,color=yellow}]{} & \gate{H} & \targ{} & \gate{R_Z}\wire[d][2]{q} & &\\
+    & & \gate[2]{U(2^{n-1})} & |[operator]| & \ctrl{-1} & &\ctrl{-1} & \gate[2]{U(2^{n-1})}\wire[u]{q} & \ctrl{-1} & & \ctrl{-1}& |[operator]| & \gate[2]{U(2^{n-1})} & \\
+    & \qwbundle{n-2} &  & |[operator]| & & & & & & & & |[operator]| &  & 
+\end{quantikz}\\
+&=\begin{quantikz}
+    & & & \gate{R_Z}\wire[d][2]{q}\gategroup[3,steps=2,style={inner
+sep=0pt, rounded corners,color=red}]{} & \targ{} & & \gate{R_X}\wire[d][2]{q} & & \targ{}\gategroup[3,steps=2,style={inner
+sep=0pt, rounded corners,color=red}]{} & \gate{R_Z}\wire[d][2]{q} & &\\
+    & & \gate[2]{U(2^{n-1})} & |[operator]| & \ctrl{-1} & \gate[2]{U(2^{n-1})} & |[operator]| & \gate[2]{U(2^{n-1})} & \ctrl{-1} & |[operator]| & \gate[2]{U(2^{n-1})} & \\
+    & \qwbundle{n-2} &  & |[operator]| & & & |[operator]| & & & |[operator]| &  & 
+\end{quantikz}
+\end{align*}
+\end{document}

_static/demonstration_assets/unitary_synthesis_kak/block_zxz_transformations.tex

@@ -0,0 +1,43 @@
+\documentclass[]{article}
+\usepackage{amsmath,quantikz,graphicx,xcolor,amssymb,amsfonts}
+
+
+\begin{document}
+\begin{align*}
+\begin{quantikz}
+    & & \gate[2]{U(2^n)} &\\
+    & \qwbundle{n-1} & &
+\end{quantikz}
+&=
+\begin{quantikz}
+    & & |[operator]| & \gate{R_X(\vec{\theta})}\wire[d]{q} & |[operator]| &\\
+    & \qwbundle{n-1} & \gate{W_0,W_1}\wire[u]{q} & |[operator]| & \gate{V_0,V_1}\wire[u]{q} & 
+\end{quantikz}\\
+&=
+\begin{quantikz}
+    & & |[operator]| & \gate{H} & \gate{R_Z(\vec{\theta})}\wire[d]{q} & \gate{H} & |[operator]| &\\
+    & \qwbundle{n-1} & \gate{W_0,W_1}\wire[u]{q} & & |[operator]| & & \gate{V_0,V_1}\wire[u]{q} & 
+\end{quantikz}\\
+&=
+\begin{quantikz}
+    & & |[operator]| & \gate{H} & & \gate{R_Z(\vec{\theta})}\wire[d]{q} & \gate{H} & |[operator]| &\\
+    & \qwbundle{n-1} & \gate{W_0,W_1}\wire[u]{q} & \gate{W_0^\dagger} & \gate{W_0} & |[operator]| & & \gate{V_0,V_1}\wire[u]{q} & 
+\end{quantikz}\\
+&=
+\begin{quantikz}
+    & & |[operator]| & \gate{H} & \gate{R_Z(\vec{\theta})}\wire[d]{q} & & \gate{H} & |[operator]| &\\
+    & \qwbundle{n-1} & \gate{\mathbb{I},W_0^\dagger W_1}\wire[u]{q} & \gate{W_0} & |[operator]| & \gate{\Delta(-\vec{\theta})} & \gate{\Delta(\vec{\theta})} & \gate{V_0,V_1}\wire[u]{q} & 
+\end{quantikz}\\
+&=
+\begin{quantikz}
+    & & \ctrl{1} & \gate{H} & \ctrl{1} & & & \gate{H} & |[operator]| &\\
+    & \qwbundle{n-1} & \gate{W_0^\dagger W_1}\wire[u]{q} & \gate{W_0} & \gate{\Delta(-2\vec{\theta})} & \gate{W_0^\dagger} & \gate{W_0} & \gate{\Delta(\vec{\theta})} & \gate{V_0,V_1}\wire[u]{q} & 
+\end{quantikz}\\
+&=
+\begin{quantikz}
+    & & \ctrl{1} & \gate{H} & \ctrl{1} & \gate{H} & |[operator]| &\\
+    & \qwbundle{n-1} & \gate{W_0^\dagger W_1}\wire[u]{q} & & \gate{W_0^\dagger \Delta(-2\vec{\theta}) W_0} & & \gate{V_0 \Delta(\vec{\theta})W_0,V_1\Delta(\vec{\theta})W_0}\wire[u]{q} & 
+\end{quantikz}
+\end{align*}
+
+\end{document}

_static/demonstration_assets/unitary_synthesis_kak/magic_basis_rotation.tex

@@ -0,0 +1,13 @@
+\documentclass[]{standalone}
+\usepackage{amsmath,quantikz,graphicx,xcolor}
+
+
+\begin{document}
+\begin{quantikz}
+    & \gate[2]{E} & \midstick[2,brackets=none]{=} 
+    & \gate{R_Z(\tfrac{\pi}{2})} & \targ{} & & \\
+    & &
+    & \gate{R_X(-\tfrac{\pi}{2})} & \ctrl{-1} & \gate{R_Z(-\tfrac{\pi}{2})} &
+\end{quantikz}
+
+\end{document}

_static/demonstration_assets/unitary_synthesis_kak/multiplexer_decomp.tex

@@ -0,0 +1,33 @@
+\documentclass[]{standalone}
+\usepackage{amsmath,quantikz,graphicx,xcolor}
+
+
+\begin{document}
+% \begin{quantikz}
+%     & |[operator]| & \midstick[3,brackets=none]{=} & & \ctrl{2} & & \ctrl{2} & \\
+%     & |[operator]| & & |[operator]| & & |[operator]| & & \\
+%     & \gate{R_P}\wire[u][2]{q} & & \gate{R_P}\wire[u][1]{q} & \targ{} & \gate{R_P}\wire[u][1]{q} & \targ{} &
+% \end{quantikz}
+
+% \begin{quantikz}
+%     & |[operator]| & \midstick[3,brackets=none]{=} 
+%     & & \ctrl{2} & & \ctrl{2} & \midstick[3,brackets=none]{=}
+%     & & & & \ctrl{2} & & & & \ctrl{2} & \\
+%     & |[operator]| &
+%     & |[operator]| & & |[operator]| & & 
+%     & & \ctrl{1} & & & & \ctrl{1} & & & \\
+%     & \gate{R_P}\wire[u][2]{q} &
+%     & \gate{R_P}\wire[u][1]{q} & \targ{} & \gate{R_P}\wire[u][1]{q} & \targ{} &
+%     & \gate{R_P} & \targ{} & \gate{R_P} & \targ{} & \gate{R_P} & \targ{} & \gate{R_P} & \targ{} &
+% \end{quantikz}
+
+\begin{quantikz}
+    & |[operator]| & \midstick[3,brackets=none]{=} 
+    & & & & \ctrl{2} & & & & \ctrl{2} & \\
+    & |[operator]| &
+    & & \ctrl{1} & & & & \ctrl{1} & & & \\
+    & \gate{R_P}\wire[u][2]{q} &
+    & \gate{R_P} & \targ{} & \gate{R_P} & \targ{} & \gate{R_P} & \targ{} & \gate{R_P} & \targ{} &
+\end{quantikz}
+
+\end{document}

_static/demonstration_assets/unitary_synthesis_kak/multiplexer_decomp_CZ.tex

@@ -0,0 +1,33 @@
+\documentclass[]{standalone}
+\usepackage{amsmath,quantikz,graphicx,xcolor}
+
+
+\begin{document}
+% \begin{quantikz}
+%     & |[operator]| & \midstick[3,brackets=none]{=} & & \ctrl{2} & & \ctrl{2} & \\
+%     & |[operator]| & & |[operator]| & & |[operator]| & & \\
+%     & \gate{R_P}\wire[u][2]{q} & & \gate{R_P}\wire[u][1]{q} & \targ{} & \gate{R_P}\wire[u][1]{q} & \targ{} &
+% \end{quantikz}
+
+% \begin{quantikz}
+%     & |[operator]| & \midstick[3,brackets=none]{=} 
+%     & & \ctrl{2} & & \ctrl{2} & \midstick[3,brackets=none]{=}
+%     & & & & \ctrl{2} & & & & \ctrl{2} & \\
+%     & |[operator]| &
+%     & |[operator]| & & |[operator]| & & 
+%     & & \ctrl{1} & & & & \ctrl{1} & & & \\
+%     & \gate{R_P}\wire[u][2]{q} &
+%     & \gate{R_P}\wire[u][1]{q} & \targ{} & \gate{R_P}\wire[u][1]{q} & \targ{} &
+%     & \gate{R_P} & \targ{} & \gate{R_P} & \targ{} & \gate{R_P} & \targ{} & \gate{R_P} & \targ{} &
+% \end{quantikz}
+
+\begin{quantikz}
+    & |[operator]| & \midstick[3,brackets=none]{=} 
+    & & & & \ctrl{2} & & & & \ctrl{2} & \\
+    & |[operator]| &
+    & & \ctrl{1} & & & & \ctrl{1} & & & \\
+    & \gate{R_Y}\wire[u][2]{q} &
+    & \gate{R_Y} & \ctrl{0} & \gate{R_Y} & \ctrl{0} & \gate{R_Y} & \ctrl{0} & \gate{R_Y} & \ctrl{0} &
+\end{quantikz}
+
+\end{document}

_static/demonstration_assets/unitary_synthesis_kak/recursive_QSD.tex

@@ -0,0 +1,58 @@
+\documentclass[]{standalone}
+\usepackage{amsmath,quantikz,graphicx,xcolor}
+
+
+\begin{document}
+\begin{quantikz}
+    & & \gate[3]{U(2^n)} &\\
+    & & & \\ 
+    & \qwbundle{n-2} & &
+\end{quantikz}
+=
+\scalebox{0.75}{
+\begin{quantikz}
+    & & & & & & & & & \gate{R_Z}\wire[d][2]{q} &
+    & & & & & & & \gate{R_Y}\wire[d][2]{q} & & & 
+    & & & & & \gate{R_Z}\wire[d][2]{q} & & & & &
+    & & & \\
+    & & & \gate{R_Z}\wire[d]{q} & & \gate{R_Y}\wire[d]{q} & & \gate{R_Z}\wire[d]{q} & & |[operator]| &
+    & \gate{R_Z}\wire[d]{q} & & \gate{R_Y}\wire[d]{q} & & \gate{R_Z}\wire[d]{q} & & |[operator]| & & \gate{R_Z}\wire[d]{q} &
+    & \gate{R_Y}\wire[d]{q} & & \gate{R_Z}\wire[d]{q} & & |[operator]| & & \gate{R_Z}\wire[d]{q} & & \gate{R_Y}\wire[d]{q} &
+    & \gate{R_Z}\wire[d]{q} & & \\ 
+    & \qwbundle{n-2} & \gate{} & |[operator]| & \gate{} & |[operator]| & \gate{} &|[operator]| & \gate{} & |[operator]| &
+    \gate{} & |[operator]| & \gate{} & |[operator]| & \gate{} & |[operator]| & \gate{} & |[operator]| & \gate{} & |[operator]| &
+    \gate{} & |[operator]| & \gate{} & |[operator]| & \gate{} & |[operator]| & \gate{} & |[operator]| & \gate{} & |[operator]| &
+    \gate{} &|[operator]| & \gate{} & 
+\end{quantikz}
+}
+
+% \begin{quantikz}
+%     & & \gate[4]{U(2^n)} &\\
+%     & & & \\ 
+%     & & & \\
+%     & \qwbundle{n-3} & &
+% \end{quantikz}
+% =
+% \scalebox{0.75}{
+% \begin{quantikz}
+%     & & & & & & & & & \gate{R_Z}\wire[d][3]{q} &
+%     & & & & & & & \gate{R_Y}\wire[d][3]{q} & & & 
+%     & & & & & \gate{R_Z}\wire[d][3]{q} & & & & &
+%     & & & \\
+%     & & & \gate{R_Z}\wire[d][2]{q} & & \gate{R_Y}\wire[d][2]{q} & & \gate{R_Z}\wire[d][2]{q} & & |[operator]| &
+%     & \gate{R_Z}\wire[d][2]{q} & & \gate{R_Y}\wire[d][2]{q} & & \gate{R_Z}\wire[d][2]{q} & & |[operator]| & & \gate{R_Z}\wire[d][2]{q} &
+%     & \gate{R_Y}\wire[d][2]{q} & & \gate{R_Z}\wire[d][2]{q} & & |[operator]| & & \gate{R_Z}\wire[d][2]{q} & & \gate{R_Y}\wire[d][2]{q} &
+%     & \gate{R_Z}\wire[d][2]{q} & & \\ 
+%     & & \gate[2]{} & |[operator]| & \gate[2]{} & |[operator]| & \gate[2]{} &|[operator]| & \gate[2]{} & |[operator]| &
+%     \gate[2]{} & |[operator]| & \gate[2]{} & |[operator]| & \gate[2]{} & |[operator]| & \gate[2]{} & |[operator]| & \gate[2]{} & |[operator]| &
+%     \gate[2]{} & |[operator]| & \gate[2]{} & |[operator]| & \gate[2]{} & |[operator]| & \gate[2]{} & |[operator]| & \gate[2]{} & |[operator]| &
+%     \gate[2]{} &|[operator]| & \gate[2]{} & \\
+%     & \qwbundle{n-3} & & |[operator]| & & |[operator]| & & |[operator]| & & |[operator]| &
+%     & |[operator]| & & |[operator]| & & |[operator]| & & |[operator]| & & |[operator]| &
+%     & |[operator]| & & |[operator]| & & |[operator]| & & |[operator]| & & |[operator]| &
+%     & |[operator]| & & 
+% \end{quantikz}
+% }
+
+
+\end{document}

_static/demonstration_assets/unitary_synthesis_kak/single_multiplexer.tex

@@ -0,0 +1,21 @@
+\documentclass[]{standalone}
+\usepackage{amsmath,quantikz,graphicx,xcolor}
+
+
+\begin{document}
+% \begin{align*}
+\begin{quantikz}
+    & & \gate[2]{A\oplus B} & \\
+    & \qwbundle{n-1} & &
+\end{quantikz}
+=
+\begin{quantikz}
+    \ghost[2]{A\oplus B}& & |[operator]| & \\
+    & \qwbundle{n-1} & \gate{A,B}\wire[u]{q} &
+\end{quantikz}
+=
+\begin{quantikz}
+    \ghost[2]{A\oplus B}& & \octrl{1} & \ctrl{1} & \\
+    & \qwbundle{n-1} & \gate{A} & \gate{B} &
+\end{quantikz}
+\end{document}