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4 | 4 | \usepackage[T1]{fontenc} |
5 | 5 | \usepackage{amsmath,amssymb,amsfonts,bm,mathtools} |
6 | 6 | \usepackage{physics} |
7 | | -\usepackage{braket} |
8 | 7 | \usepackage{quantikz} |
9 | 8 | \usepackage{graphicx} |
10 | 9 | \usepackage{booktabs} |
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13 | 12 | \usetheme{Madrid} |
14 | 13 |
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15 | 14 | \title{Quantum Simulation and the HHL Algorithm} |
16 | | -\subtitle{with Phase Estimation Circuits and a Worked Example for the 1D Poisson Equation} |
17 | | -\author{} |
18 | | -\date{} |
| 15 | +%\subtitle{with Phase Estimation Circuits and a Worked Example for the 1D Poisson Equation} |
| 16 | +\author{Morten Hjorth-Jensen} |
| 17 | +\date{Spring 2026} |
19 | 18 |
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20 | 19 | \begin{document} |
21 | 20 |
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@@ -92,14 +91,12 @@ \section{Quantum Phase Estimation} |
92 | 91 | \end{frame} |
93 | 92 |
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94 | 93 | \begin{frame}{Phase Estimation Circuit} |
95 | | -\[ |
96 | 94 | \begin{quantikz}[row sep=0.35cm, column sep=0.45cm] |
97 | | -\lstick{\ket{0}} & \gate{H} & \ctrl{3} & \qw & \qw & \gate[wires=3]{QFT^\dagger} & \meter{} \\ |
98 | | -\lstick{\ket{0}} & \gate{H} & \qw & \ctrl{2} & \qw & & \meter{} \\ |
99 | | -\lstick{\ket{0}} & \gate{H} & \qw & \qw & \ctrl{1} & & \meter{} \\ |
100 | | -\lstick{\ket{u}} & \qw & \gate{U} & \gate{U^2} & \gate{U^4} & \qw & \qw |
| 95 | +\lstick{$|0\rangle$} & \gate{H} & \ctrl{3} & \qw & \qw & \gate[wires=3]{\mathrm{QFT}^\dagger} & \meter{} \\ |
| 96 | +\lstick{$|0\rangle$} & \gate{H} & \qw & \ctrl{2} & \qw & & \meter{} \\ |
| 97 | +\lstick{$|0\rangle$} & \gate{H} & \qw & \qw & \ctrl{1} & & \meter{} \\ |
| 98 | +\lstick{$|u\rangle$} & \qw & \gate{U} & \gate{U^2} & \gate{U^4} & \qw & \qw |
101 | 99 | \end{quantikz} |
102 | | -\] |
103 | 100 | \end{frame} |
104 | 101 |
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105 | 102 | \begin{frame}{How the Phases Accumulate} |
@@ -160,13 +157,11 @@ \section{The HHL Algorithm} |
160 | 157 | \end{frame} |
161 | 158 |
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162 | 159 | \begin{frame}{Full HHL Circuit Schematic} |
163 | | -\[ |
164 | 160 | \begin{quantikz}[row sep=0.35cm, column sep=0.38cm] |
165 | | -\lstick{\ket{0}} & \qw & \gate[style={fill=blue!10}]{R(\lambda^{-1})} & \qw & \meter{} \\ |
166 | | -\lstick{\ket{0}^{\otimes m}} & \gate[wires=2, style={fill=green!10}]{\mathrm{QPE}(e^{iAt})} & \qw & \gate[wires=2, style={fill=green!10}]{\mathrm{QPE}^\dagger} & \qw \\ |
167 | | -\lstick{\ket{b}} & \qw & \qw & \qw & \rstick{\ket{x}\propto A^{-1}\ket{b}} |
| 161 | +\lstick{$|0\rangle$} & \qw & \gate[style={fill=blue!10}]{R(\lambda^{-1})} & \qw & \meter{} \\ |
| 162 | +\lstick{$|0\rangle^{\otimes m}$} & \gate[wires=2, style={fill=green!10}]{\mathrm{QPE}(e^{iAt})} & \qw & \gate[wires=2, style={fill=green!10}]{\mathrm{QPE}^\dagger} & \qw \\ |
| 163 | +\lstick{$|b\rangle$} & \qw & \qw & \qw & \rstick{$|x\rangle\propto A^{-1}|b\rangle$} |
168 | 164 | \end{quantikz} |
169 | | -\] |
170 | 165 | \end{frame} |
171 | 166 |
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172 | 167 | \begin{frame}{HHL State Evolution} |
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