22
33\usepackage [T1 ]{fontenc }
44\usepackage [utf8 ]{inputenc }
5- \usepackage { lmodern }
5+
66\usepackage {amsmath,amssymb,amsfonts }
77\usepackage {physics }
88\usepackage {bm }
99\usepackage {mathtools }
10- \usepackage {quantikz }
10+ \usepackage {tikz }
11+ \usetikzlibrary {quantikz,arrows.meta,positioning}
1112\usepackage {graphicx }
1213\usepackage {booktabs }
1314\usepackage {hyperref }
173174
174175\begin {frame }{QPE Circuit}
175176\centering
177+ \begin {tikzpicture }
178+ \node [scale=0.9] {
176179\begin {quantikz }
177180\lstick {$ \ket {0}$ } & \gate {H} & \ctrl {3} & \qw & \qw & \gate [3]{\mathrm {QFT}^\dagger } & \meter {} \\
178181\lstick {$ \ket {0}$ } & \gate {H} & \qw & \ctrl {2} & \qw & \ghost {\mathrm {QFT}^\dagger } & \meter {} \\
179182\lstick {$ \ket {0}$ } & \gate {H} & \qw & \qw & \ctrl {1} & \ghost {\mathrm {QFT}^\dagger } & \meter {} \\
180183\lstick {$ \ket {\psi }$ } & \qw & \gate {U^4} & \gate {U^2} & \gate {U} & \qw & \qw
181184\end {quantikz }
185+ };
186+ \end {tikzpicture }
182187
183188\vspace {0.5em}
184189
@@ -375,12 +380,16 @@ \section{Quantum Phase Estimation}
375380\end {frame }
376381
377382\begin {frame }{Phase Estimation Circuit}
383+ \begin {tikzpicture }
384+ \node [scale=0.85] {
378385\begin {quantikz }[row sep=0.35cm, column sep=0.45cm]
379386\lstick {$ |0 \rangle $ } & \gate {H} & \ctrl {3} & \qw & \qw & \gate [wires=3]{\mathrm {QFT}^\dagger } & \meter {} \\
380387\lstick {$ |0 \rangle $ } & \gate {H} & \qw & \ctrl {2} & \qw & & \meter {} \\
381388\lstick {$ |0 \rangle $ } & \gate {H} & \qw & \qw & \ctrl {1} & & \meter {} \\
382389\lstick {$ |u\rangle $ } & \qw & \gate {U} & \gate {U^2} & \gate {U^4} & \qw & \qw
383390\end {quantikz }
391+ };
392+ \end {tikzpicture }
384393\end {frame }
385394
386395\begin {frame }{How the Phases Accumulate}
@@ -441,11 +450,15 @@ \section{The HHL Algorithm}
441450\end {frame }
442451
443452\begin {frame }{Full HHL Circuit Schematic}
453+ \begin {tikzpicture }
454+ \node [scale=0.85] {
444455\begin {quantikz }[row sep=0.35cm, column sep=0.38cm]
445456\lstick {$ |0 \rangle $ } & \qw & \gate [style={fill=blue!10}]{R(\lambda ^{-1})} & \qw & \meter {} \\
446457\lstick {$ |0 \rangle ^{\otimes m}$ } & \gate [wires=2, style={fill=green!10}]{\mathrm {QPE}(e^{iAt})} & \qw & \gate [wires=2, style={fill=green!10}]{\mathrm {QPE}^\dagger } & \qw \\
447458\lstick {$ |b\rangle $ } & \qw & \qw & \qw & \rstick {$ |x\rangle\propto A^{-1}|b\rangle $ }
448459\end {quantikz }
460+ };
461+ \end {tikzpicture }
449462\end {frame }
450463
451464
@@ -692,13 +705,15 @@ \section{The HHL Algorithm}
692705
693706
694707\begin {frame }{High-Level HHL Circuit}
695- \[
708+ \begin {tikzpicture }
709+ \node [scale=0.85] {
696710\begin {quantikz }[row sep=0.35cm, column sep=0.42cm]
697- \lstick {\ket {0}_a } & \qw & \gate [style={fill=blue!10}]{R(\lambda ^{-1})} & \qw & \meter {} \\
698- \lstick {\ket {0} ^{\otimes m}_p} & \gate [wires=2, style={fill=green!10}]{\mathrm {QPE}(e^{iAt})} & \qw & \gate [wires=2, style={fill=green!10}]{\mathrm {QPE}^\dagger } & \qw \\
699- \lstick {\ket {b}_s} & \qw & \qw & \qw & \rstick {\ket {x} \ propto A^{-1}\ket {b} }
711+ \lstick {$ | 0 \rangle _a $ } & \qw & \gate [style={fill=blue!10}]{R(\lambda ^{-1})} & \qw & \meter {} \\
712+ \lstick {$ | 0 \rangle ^{\otimes m}_p$ } & \gate [wires=2, style={fill=green!10}]{\mathrm {QPE}(e^{iAt})} & \qw & \gate [wires=2, style={fill=green!10}]{\mathrm {QPE}^\dagger } & \qw \\
713+ \lstick {$ |b \rangle _s $ } & \qw & \qw & \qw & \rstick {$ |x \rangle\ propto A^{-1}|b \rangle $ }
700714\end {quantikz }
701- \]
715+ };
716+ \end {tikzpicture }
702717
703718\medskip
704719
@@ -1990,12 +2005,16 @@ \section{Second Example: 1D Poisson Equation}
19902005
19912006\begin {frame }{QPE Circuit Block}
19922007\centering
2008+ \begin {tikzpicture }
2009+ \node [scale=0.85] {
19932010\begin {quantikz }[row sep=0.35cm, column sep=0.3cm]
19942011\lstick {$ |u_j\rangle $ } & \qw & \qw & \qw & \qw & \qw \\
19952012\lstick {$ |0 \rangle $ } & \gate {H} & \ctrl {-1} & \qw & \qw & \gate [wires=3]{\text {QFT}^{-1}} & \qw \\
19962013\lstick {$ |0 \rangle $ } & \gate {H} & \qw & \ctrl {-2} & \qw & \qw & \qw \\
19972014\lstick {$ |0 \rangle $ } & \gate {H} & \qw & \qw & \ctrl {-3} & \qw & \qw
19982015\end {quantikz }
2016+ };
2017+ \end {tikzpicture }
19992018
20002019Here the controlled gates are
20012020\[
@@ -2021,11 +2040,15 @@ \section{Second Example: 1D Poisson Equation}
20212040
20222041\begin {frame }{High-Level HHL Circuit}
20232042\centering
2043+ \begin {tikzpicture }
2044+ \node [scale=0.75] {
20242045\begin {quantikz }[row sep=0.35cm, column sep=0.42cm]
20252046\lstick {$ |b\rangle $ } & \qw & \gate [wires=2,style={fill=blue!15,draw=blue}]{\text {QPE}} & \qw & \gate [wires=2,style={fill=yellow!20,draw=orange}]{\text {Controlled } \lambda ^{-1}} & \qw & \gate [wires=2,style={fill=blue!15,draw=blue}]{\text {QPE}^{\dagger }} & \qw & \qw \\
20262047\lstick {$ |0 \rangle ^{\otimes m}$ } & \qw & \ghost {\text {QPE}} & \qw & \ghost {\text {Controlled } \lambda ^{-1}} & \qw & \ghost {\text {QPE}^{\dagger }} & \qw & \qw \\
20272048\lstick {$ |0 \rangle _a$ } & \qw & \qw & \qw & \gate {R_y(\theta (\lambda ))} & \qw & \qw & \meter {} & \qw
20282049\end {quantikz }
2050+ };
2051+ \end {tikzpicture }
20292052
20302053\begin {itemize }
20312054\item Blue block: spectral decomposition and recombination.
@@ -2467,7 +2490,3 @@ \section{Second Example: 1D Poisson Equation}
24672490
24682491\end {document }
24692492
2470-
2471-
2472- \end {document }
2473-
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