├── LICENSE ├── README.md ├── adiabatic_memory.py ├── adiabatic_process.py ├── bell_state_generator.tex ├── bifurcation_graph.tex ├── bloch_sphere.py ├── chimera.tex ├── cnot_gate.tex ├── common_graphics_settings.py ├── convex_loss_functions.py ├── feedforward.tex ├── fredkin_gate.tex ├── graphics_utils.py ├── grover_operator.tex ├── grover_search.tex ├── hadamard_gate.tex ├── hopfield.tex ├── meter.svg ├── nonconvex_loss_functions.py ├── perceptron.tex ├── quantum_annealing.py ├── quantum_neural_network.tex ├── quantum_parallelism.tex ├── quantum_swap.tex ├── quantum_swap_gate.tex ├── quantum_tunneling.py ├── supervised.py ├── support_vectors.py ├── swap_test.tex ├── toffoli_gate.tex ├── transductive.py ├── unsupervised.py ├── vc_dimension_line.py ├── vc_dimension_sine.py └── xor_problem.py /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | {one line to give the program's name and a brief idea of what it does.} 635 | Copyright (C) {year} {name of author} 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | {project} Copyright (C) {year} {fullname} 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | This repository stores the source code of the figures in the book Quantum Machine Learning: What Quantum Computing Means to Data Mining. More information on the book is here: 2 | 3 | [http://peterwittek.com/book](http://peterwittek.com/book) 4 | 5 | Dependencies 6 | == 7 | The LaTeX files use tikz, which should be standard in most TeX distribution. 8 | 9 | The Python files use matplotlib, numpy, and seaborn. Furthermore, LaTeX is used for rendering text, hence a LaTeX compiler should be in the path. Plotting the Bloch sphere also requires the QuTIP toolbox. 10 | -------------------------------------------------------------------------------- /adiabatic_memory.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """ 3 | Created on Sun Apr 27 09:23:32 2014 4 | 5 | @author: wittek 6 | """ 7 | 8 | import matplotlib.pyplot as plt 9 | import numpy as np 10 | from common_graphics_settings import initialize_graphics 11 | 12 | #fig, axes = plt.subplots(2,2) 13 | #((ax1, ax2), (ax3, ax4)) = axes # unpack the axes 14 | 15 | colors = initialize_graphics() 16 | fig = plt.figure(1,figsize=(7,5)) 17 | ax1 = fig.add_subplot(111, autoscale_on=False, xlim=(0,32), ylim=(-7.5,1.1)) 18 | 19 | # Right side of the diagram 20 | domain = np.arange(0.0, 8*np.pi, 0.01) 21 | y1 = np.cos(domain) 22 | line, = ax1.plot(domain, y1, lw=3, color=colors[0]) 23 | y2 = [ (np.log(x+4)-7*np.exp(-(x-15)*(x-15)/100))/3.5-3 for x in domain ] 24 | line, = ax1.plot(domain, y2, lw=3, color=colors[0]) 25 | y3 = [ (np.cos(x)+np.log(x+4)-7*np.exp(-(x-15)*(x-15)/100))/3.5-6 for x in domain ] 26 | line, = ax1.plot(domain, y3, lw=3, color=colors[0]) 27 | for i in range(1,9,2): 28 | ax1.plot(i*np.pi, -0.7, 'o', color=colors[2]) # Stable states in H_mem 29 | ax1.plot(14.7, -3.8, 'o', color=colors[2]) # Stable state in H_inp 30 | ax1.plot(1.06*np.pi, -5.9, 'o', color=colors[2]) # Stable states in the sum 31 | ax1.plot(3.1*np.pi, -6.74, 'o', color=colors[2]) 32 | ax1.plot(4.95*np.pi, -7.1, 'o', color=colors[2]) 33 | ax1.plot(6.85*np.pi, -6.3, 'o', color=colors[2]) 34 | 35 | plt.text( 25, -1, '$H_{\mathrm{mem}}$',fontsize=20) 36 | plt.text( 25, -4, '$H_{\mathrm{inp}}$',fontsize=20) 37 | plt.text( 25, -7, '$H_{\mathrm{mem}}+H_{\mathrm{inp}}$',fontsize=20) 38 | 39 | plt.axis('off') 40 | plt.savefig('./adiabatic_memory.pdf',bbox_inches='tight') -------------------------------------------------------------------------------- /adiabatic_process.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """ 3 | Created on Sun Apr 27 09:23:32 2014 4 | 5 | @author: wittek 6 | """ 7 | 8 | import matplotlib.pyplot as plt 9 | import numpy as np 10 | from graphics_utils import initialize_graphics 11 | 12 | #fig, axes = plt.subplots(2,2) 13 | #((ax, ax2), (ax3, ax4)) = axes # unpack the axes 14 | 15 | colors=initialize_graphics() 16 | fig = plt.figure(1,figsize=(10,5)) 17 | ax = fig.add_subplot(111, autoscale_on=False, xlim=(-33.3,26), ylim=(-7.43,1.1)) 18 | 19 | # Right side of the diagram 20 | x = np.arange(0.0, 8*np.pi, 0.01) 21 | y = [ (3*np.cos(t)+np.log(t+4)-10*np.exp(-(t-15)*(t-15)/100))/3.5-4.5 for t in x ] 22 | ax.plot(x, y, lw=3, color=colors[0]) 23 | ax.plot(4.98*np.pi, -6.95, 'o', color=colors[2]) 24 | 25 | plt.text( 25, -7, '$H_1$',fontsize=20) 26 | 27 | # Left side of the diagram 28 | offset=25 29 | 30 | x = np.arange(-8-offset, 8-offset, 0.01) 31 | y4 = [ (t+offset)**2/20-2.5 for t in x] 32 | ax.plot(x, y4, lw=3, color=colors[0]) 33 | y5 = [ (t+offset)**2/20-7.4 for t in x] 34 | ax.plot(x, y5, lw=3, color=colors[0]) 35 | 36 | ax.plot(-31, 0, 'o', color=colors[2]) 37 | ax.plot(-offset, -7, 'o', color=colors[2]) 38 | 39 | #plt.text( -17, -2, '$H_1$',fontsize=20) 40 | plt.text( -17, -7, '$H_0$',fontsize=20) 41 | 42 | ax.annotate('', xy=(-offset, -4), xytext=(-offset, -2.7), 43 | arrowprops=dict(facecolor='black', shrink=0.05), 44 | ) 45 | 46 | ax.annotate('', xy=(-3 ,-6), xytext=(-13, -6), 47 | arrowprops=dict(facecolor='black', shrink=0.05), 48 | ) 49 | 50 | plt.axis('off') 51 | plt.savefig('./adiabatic_process.pdf',bbox_inches='tight') -------------------------------------------------------------------------------- /bell_state_generator.tex: -------------------------------------------------------------------------------- 1 | % Based on the answer by qubyte at 2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits 3 | \documentclass[12pt]{standalone} 4 | \usepackage{tikz} 5 | 6 | \usetikzlibrary{backgrounds} 7 | % Dirac Kets 8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}} 9 | 10 | \begin{document} 11 | \begin{tikzpicture}[thick,cross/.style={path picture={ 12 | \draw[black] 13 | (path picture bounding box.south) -- (path picture bounding box.north); 14 | }}] 15 | 16 | % `operator' will only be used by most gates. 17 | % `cnot' will refer to CNOT gates. 18 | % `phase' is used for controlled gates. 19 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em] 20 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt] 21 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt] 22 | % 23 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) { 24 | 25 | % First row. 26 | \coordinate (start1); &[-0.5cm] 27 | \node[operator] (O11) {H}; & 28 | \node[phase] (P12) {}; & 29 | \coordinate (end1);\\ 30 | 31 | \coordinate (start2); &[-0.5cm] 32 | & 33 | \node[cnot] (O22) {}; & 34 | \coordinate (end2);\\ 35 | }; 36 | 37 | \begin{pgfonlayer}{background} 38 | % Draw lines. 39 | \draw[thick] (start1) -- (end1) (start2) -- (end2) (P12) -- (O22); 40 | \end{pgfonlayer} 41 | % 42 | \end{tikzpicture} 43 | \end{document} 44 | -------------------------------------------------------------------------------- /bifurcation_graph.tex: -------------------------------------------------------------------------------- 1 | % Based on 2 | % http://www.texample.net/tikz/examples/red-black-tree/ 3 | 4 | \documentclass[12pt]{standalone} 5 | \usepackage{tikz} 6 | \usetikzlibrary{arrows} 7 | \definecolor{color1}{RGB}{0,114,178} 8 | \definecolor{color2}{RGB}{0,158,115} 9 | \definecolor{color3}{RGB}{213,94,0} 10 | 11 | 12 | \tikzset{ 13 | treenode/.style = {align=center, inner sep=0pt, text centered, 14 | font=\sffamily}, 15 | vertex/.style = {treenode, circle, black, font=\sffamily\bfseries, draw=color3, 16 | fill=color3, text width=0.3em}, 17 | } 18 | 19 | \begin{document} 20 | \begin{tikzpicture}[-,>=stealth',thick,draw=color1,level/.style={sibling distance = 7cm/#1, 21 | level distance = 1.5cm}] 22 | \node [vertex] {} 23 | child{ node [vertex] {} 24 | child{ node [vertex] {} 25 | child{ node [vertex] {} 26 | } 27 | child{ node [vertex] {} 28 | } 29 | } 30 | child{ node [vertex] {} 31 | child{ node [vertex] {} 32 | } 33 | child{ node [vertex] {} 34 | } 35 | } 36 | } 37 | child{ node [vertex] {} 38 | child{ node [vertex] {} 39 | child{ node [vertex] {}} 40 | child{ node [vertex] {}} 41 | } 42 | child{ node [vertex] {} 43 | child{ node [vertex] {}} 44 | child{ node [vertex] {}} 45 | } 46 | } 47 | ; 48 | \end{tikzpicture} 49 | \end{document} 50 | -------------------------------------------------------------------------------- /bloch_sphere.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """ 3 | Created on Mon May 5 14:15:02 2014 4 | 5 | @author: wittek 6 | """ 7 | from mpl_toolkits.mplot3d import Axes3D 8 | import matplotlib.pyplot as plt 9 | from qutip import Bloch 10 | from graphics_utils import initialize_graphics 11 | 12 | colors = initialize_graphics() 13 | 14 | fig = plt.figure() 15 | axes = Axes3D(fig) 16 | axes.grid = True 17 | axes.axis("off") 18 | axes.set_axis_off() 19 | 20 | b=Bloch() 21 | 22 | b.fig = fig 23 | b.axes = axes 24 | #b.fig = fig 25 | #b.frame_width=1 26 | b.sphere_color = 'white' 27 | b.sphere_alpha = 0.1 28 | #b.size = [10, 10] 29 | b.make_sphere() 30 | 31 | plt.savefig('./bloch_sphere.svg',bbox_inches='tight') 32 | #b.show() 33 | #b.save('bloch_sphere.pdf',format='pdf') 34 | -------------------------------------------------------------------------------- /chimera.tex: -------------------------------------------------------------------------------- 1 | % Based on 2 | % http://tex.stackexchange.com/questions/15088/bipartite-graphs 3 | 4 | \documentclass[12pt]{standalone} 5 | \usepackage[rgb]{xcolor} 6 | \definecolor{color1}{RGB}{0,114,178} 7 | \definecolor{color2}{RGB}{0,158,115} 8 | \definecolor{color3}{RGB}{213,94,0} 9 | 10 | \usepackage{tikz} 11 | \usetikzlibrary{chains,arrows} 12 | 13 | \begin{document} 14 | 15 | \begin{tikzpicture}[thick, 16 | leftnode/.style={circle,draw=color3,fill=color3}, 17 | rightnode/.style={circle,draw=color3,fill=color3}, 18 | blindnode/.style={draw=white,circle,fill=white} 19 | ] 20 | 21 | % blind nodes 22 | \begin{scope}[xshift=-1cm, yshift=4mm, start chain=going below,node distance=7mm] 23 | \foreach \i in {1,2,...,5} 24 | \node[blindnode,on chain] (bl\i) [] {}; 25 | \end{scope} 26 | \begin{scope}[xshift=5cm, yshift=4mm, start chain=going below,node distance=7mm] 27 | \foreach \i in {1,2,...,5} 28 | \node[blindnode,on chain] (br\i) [] {}; 29 | \end{scope} 30 | 31 | 32 | % the vertices of U 33 | \begin{scope}[start chain=going below,node distance=7mm] 34 | \foreach \i in {1,2,...,4} 35 | \node[leftnode,on chain] (l\i) [] {}; 36 | \end{scope} 37 | 38 | % the vertices of V 39 | \begin{scope}[xshift=4cm,start chain=going below,node distance=7mm] 40 | \foreach \i in {1,2,...,4} 41 | \node[rightnode,on chain] (r\i) [] {}; 42 | \end{scope} 43 | 44 | % the internal edges 45 | \foreach \i in {1,2,...,4} 46 | \foreach \j in {1,2,...,4} 47 | \draw[color1] (l\i) -- (r\j); 48 | 49 | % the external edges 50 | \foreach \i in {1,2,...,4} { 51 | \path[color1] (l\i) edge [bend left] node {} (bl\i) ; 52 | \pgfmathtruncatemacro{\j}{\i + 1}% 53 | \path[color1] (l\i) edge [bend right] node {} (bl\j) ; 54 | } 55 | \foreach \i in {1,2,...,4} { 56 | \path[color1] (r\i) edge [bend right] node {} (br\i) ; 57 | \pgfmathtruncatemacro{\j}{\i + 1}% 58 | \path[color1] (r\i) edge [bend left] node {} (br\j) ; 59 | } 60 | 61 | \end{tikzpicture} 62 | \end{document} 63 | -------------------------------------------------------------------------------- /cnot_gate.tex: -------------------------------------------------------------------------------- 1 | % Based on the answer by qubyte at 2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits 3 | \documentclass[12pt]{standalone} 4 | \usepackage{tikz} 5 | 6 | \usetikzlibrary{backgrounds} 7 | % Dirac Kets 8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}} 9 | 10 | \begin{document} 11 | \begin{tikzpicture}[thick,cross/.style={path picture={ 12 | \draw[black] 13 | (path picture bounding box.south) -- (path picture bounding box.north); 14 | }}] 15 | 16 | % `operator' will only be used by most gates. 17 | % `cnot' will refer to CNOT gates. 18 | % `phase' is used for controlled gates. 19 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em] 20 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt] 21 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt] 22 | % 23 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) { 24 | 25 | % First row. 26 | \coordinate (start1); & 27 | \node[phase] (P11) {}; & 28 | \coordinate (end1);\\ 29 | 30 | \coordinate (start2); & 31 | \node[cnot] (O21) {}; & 32 | \coordinate (end2);\\ 33 | }; 34 | 35 | \begin{pgfonlayer}{background} 36 | % Draw lines. 37 | \draw[thick] (start1) -- (end1) (start2) -- (end2) (P11) -- (O21); 38 | \end{pgfonlayer} 39 | % 40 | \end{tikzpicture} 41 | \end{document} 42 | -------------------------------------------------------------------------------- /common_graphics_settings.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """ 3 | Created on Thu Apr 10 14:48:01 2014 4 | 5 | @author: wittek 6 | """ 7 | 8 | import seaborn as sns 9 | import matplotlib.pyplot as plt 10 | from matplotlib import rcParams 11 | from matplotlib import rc 12 | 13 | FONT_SIZE=27.5 14 | MP_LINEWIDTH = 2.4 15 | MP_TICKSIZE = 20. 16 | 17 | def initialize_graphics(): 18 | rcParams.update({'figure.autolayout': True}) 19 | rc('text', usetex=True) 20 | # Configure palette and plotting to pgf/tikz 21 | sns.set(style="nogrid") 22 | return sns.color_palette("colorblind") 23 | 24 | def setup_figure(ax): 25 | 26 | # Setting up font sizes 27 | for item in ([ax.title, ax.xaxis.label, ax.yaxis.label] ): 28 | item.set_fontsize(FONT_SIZE) 29 | 30 | for tick in plt.gca().xaxis.get_major_ticks(): 31 | tick.label1.set_fontsize(0.85*FONT_SIZE) 32 | tick.tick1line.set_markeredgewidth(MP_LINEWIDTH) 33 | tick.tick1line.set_markersize(0.5*MP_TICKSIZE) 34 | for tick in plt.gca().yaxis.get_major_ticks(): 35 | tick.label1.set_fontsize(0.85*FONT_SIZE) 36 | tick.tick1line.set_markeredgewidth(MP_LINEWIDTH) 37 | tick.tick1line.set_markersize(0.5*MP_TICKSIZE) 38 | legend = ax.legend(loc='upper left', shadow=False, handlelength=5) 39 | 40 | # Set the fontsize in legend 41 | for label in legend.get_texts(): 42 | label.set_fontsize(FONT_SIZE) 43 | -------------------------------------------------------------------------------- /convex_loss_functions.py: -------------------------------------------------------------------------------- 1 | import matplotlib.pyplot as plt 2 | import numpy as np 3 | from numpy.random import rand 4 | 5 | from graphics_utils import initialize_graphics, cm2inch 6 | 7 | def hinge_loss(x): 8 | if x>1: 9 | return 0 10 | else: 11 | return 1-x 12 | 13 | def zero_one(x): 14 | if x<0: 15 | return 1 16 | else: 17 | return 0 18 | 19 | x = np.arange(-5,8,0.01) 20 | y_least_square = (1-x)**2 21 | y_hinge_loss = [hinge_loss(t) for t in x] 22 | y_boosting = [np.exp(-t) for t in x] 23 | y_zero_one = [zero_one(t) for t in x] 24 | 25 | colors = initialize_graphics() 26 | 27 | fig, ax = plt.subplots() 28 | fig.set_size_inches(cm2inch([10,7])) 29 | plt.plot(x, y_zero_one, color='black', linewidth=3, label='Zero-one') 30 | plt.plot(x, y_boosting, color=colors[0], linewidth=2, label='Exponential') 31 | plt.plot(x, y_hinge_loss, '--', color=colors[1], linewidth=2, label='Hinge loss') 32 | plt.plot(x, y_least_square, ':', color=colors[2], linewidth=3, label='Least square') 33 | 34 | handles, labels = ax.get_legend_handles_labels() 35 | ax.legend(handles, labels, loc=4) 36 | 37 | #plt.axis('off') 38 | ax.set_xlim([-5, 8]) 39 | ax.set_ylim([0, 5]) 40 | 41 | plt.savefig('./convex_loss_functions.pdf',bbox_inches='tight') 42 | -------------------------------------------------------------------------------- /feedforward.tex: -------------------------------------------------------------------------------- 1 | \documentclass[12pt]{standalone} 2 | % Based on http://www.texample.net/tikz/examples/neural-network/ 3 | 4 | \usepackage{tikz} 5 | 6 | \begin{document} 7 | 8 | \def\layersep{2.5cm} 9 | 10 | \begin{tikzpicture}[shorten >=1pt,->,draw=black!80, node distance=\layersep] 11 | \tikzstyle{every pin edge}=[<-,shorten <=1pt] 12 | \tikzstyle{neuron}=[circle,fill=black!25,minimum size=17pt,inner sep=0pt] 13 | \tikzstyle{annot} = [text width=4em, text centered] 14 | 15 | % Draw the input layer nodes 16 | \foreach \name / \y in {1/1,2/2,$d$/4} 17 | % This is the same as writing \foreach \name / \y in {1/1,2/2,3/3,4/4} 18 | \node[neuron] (I-\name) at (0,-\y) {\name}; 19 | \node (I-3) at (0,-3) {\vdots}; 20 | 21 | % Draw the hidden layer nodes 22 | \foreach \name / \y in {1/1,2/2,$K$/5} 23 | \path[yshift=0.5cm] 24 | node[neuron] (H-\name) at (\layersep,-\y cm) {\name}; 25 | \node (H-3) at (\layersep,-3) {\vdots}; 26 | 27 | \foreach \name / \y in {1/1.5,2/2.5,$M$/4.5} 28 | \path[yshift=0.5cm] 29 | node[neuron] (O-\name) at (2*\layersep,-\y cm) {\name}; 30 | \node (O-3) at (2*\layersep,-3) {\vdots}; 31 | 32 | % Connect every node in the input layer with every node in the 33 | % hidden layer. 34 | \foreach \source in {1,2,$d$} 35 | \foreach \dest in {1,2,$K$} 36 | \path (I-\source) edge (H-\dest); 37 | 38 | 39 | % Connect every node in the hidden layer with the output layer 40 | \foreach \source in {1,2,$K$} 41 | \foreach \dest in {1,2,$M$} 42 | \path (H-\source) edge (O-\dest); 43 | 44 | % Annotate the layers 45 | \node[annot,above of=H-1, node distance=1cm] (hl) {Hidden layer}; 46 | \node[annot,left of=hl] {Input layer}; 47 | \node[annot,right of=hl] {Output layer}; 48 | \end{tikzpicture} 49 | % End of code 50 | \end{document} 51 | -------------------------------------------------------------------------------- /fredkin_gate.tex: -------------------------------------------------------------------------------- 1 | % Based on the answer by qubyte at 2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits 3 | \documentclass[12pt]{standalone} 4 | \usepackage{tikz} 5 | 6 | \usetikzlibrary{backgrounds} 7 | % Dirac Kets 8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}} 9 | 10 | \begin{document} 11 | \begin{tikzpicture}[thick,cross/.style={path picture={ 12 | \draw[black] 13 | (path picture bounding box.south) -- (path picture bounding box.north); 14 | }},swap/.style={path picture={ 15 | \draw[black] 16 | (path picture bounding box.south west) -- (path picture bounding box.north east) (path picture bounding box.south east) -- (path picture bounding box.north west); 17 | }}] 18 | 19 | % `operator' will only be used by most gates. 20 | % `cnot' will refer to CNOT gates. 21 | % `phase' is used for controlled gates. 22 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em] 23 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt] 24 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt] 25 | % 26 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) { 27 | 28 | % First row. 29 | \coordinate (start1); & 30 | \node[phase] (P11) {}; & 31 | \coordinate (end1);\\ 32 | 33 | % Second row. 34 | \coordinate (start2); & 35 | \coordinate (swap21); 36 | \node[swap] (O21) {}; & 37 | \coordinate (end2);\\ 38 | 39 | % Third row 40 | \coordinate (start3); & 41 | \coordinate (swap31); 42 | \node[swap] (O31) {}; & 43 | \coordinate (end3);\\ 44 | }; 45 | 46 | \begin{pgfonlayer}{background} 47 | % Draw lines. 48 | \draw[thick] (start1) -- (end1) (start2) -- (end2) (start3) -- (end3) (P11) -- (swap21) (swap21) -- (swap31); 49 | \end{pgfonlayer} 50 | % 51 | \end{tikzpicture} 52 | \end{document} 53 | -------------------------------------------------------------------------------- /graphics_utils.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """ 3 | Created on Thu Apr 10 14:48:01 2014 4 | 5 | @author: wittek 6 | """ 7 | 8 | import matplotlib.pyplot as plt 9 | from matplotlib import rcParams 10 | from matplotlib import rc 11 | from matplotlib.transforms import Affine2D 12 | import mpl_toolkits.axisartist.floating_axes as floating_axes 13 | import seaborn as sns 14 | 15 | FONT_SIZE=12 16 | MP_LINEWIDTH = 2.4 17 | MP_TICKSIZE = 20. 18 | 19 | def initialize_graphics(): 20 | rcParams.update({'figure.autolayout': True}) 21 | rc('text', usetex=True) 22 | # Configure palette and plotting to pgf/tikz 23 | sns.set(style="nogrid") 24 | return sns.color_palette("colorblind") 25 | 26 | def setup_figure(ax): 27 | 28 | # Setting up font sizes 29 | for item in ([ax.title, ax.xaxis.label, ax.yaxis.label] ): 30 | item.set_fontsize(FONT_SIZE) 31 | 32 | for tick in plt.gca().xaxis.get_major_ticks(): 33 | tick.label1.set_fontsize(FONT_SIZE) 34 | tick.tick1line.set_markeredgewidth(MP_LINEWIDTH) 35 | tick.tick1line.set_markersize(0.5*MP_TICKSIZE) 36 | for tick in plt.gca().yaxis.get_major_ticks(): 37 | tick.label1.set_fontsize(FONT_SIZE) 38 | tick.tick1line.set_markeredgewidth(MP_LINEWIDTH) 39 | tick.tick1line.set_markersize(0.5*MP_TICKSIZE) 40 | legend = ax.legend(loc='upper left', shadow=False, handlelength=5) 41 | 42 | # Set the fontsize in legend 43 | for label in legend.get_texts(): 44 | label.set_fontsize(FONT_SIZE) 45 | 46 | 47 | def rotate(fig, degree): 48 | """Rotation of plot with impossible-to-remove, rotated frame. 49 | """ 50 | plot_extents = 0, 1, 0, 1 51 | transform = Affine2D().rotate_deg(degree) 52 | helper = floating_axes.GridHelperCurveLinear(transform, plot_extents) 53 | ax = floating_axes.FloatingSubplot(fig, 111, grid_helper=helper) 54 | fig.add_subplot(ax) 55 | aux_ax = ax.get_aux_axes(transform) 56 | return aux_ax 57 | 58 | 59 | def cm2inch(tupl): 60 | """Helper function to convert centimeters to inches. 61 | """ 62 | return tuple(i/2.54 for i in tupl) 63 | -------------------------------------------------------------------------------- /grover_operator.tex: -------------------------------------------------------------------------------- 1 | % Based on the answer by qubyte at 2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits 3 | \documentclass[12pt]{standalone} 4 | \usepackage{tikz} 5 | 6 | \usetikzlibrary{backgrounds} 7 | % Dirac Kets 8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}} 9 | 10 | \begin{document} 11 | \begin{tikzpicture}[thick, 12 | cross/.style={path picture={ 13 | \draw[black] 14 | (path picture bounding box.south) -- (path picture bounding box.north); 15 | }}, 16 | swap/.style={path picture={ 17 | \draw[black] 18 | (path picture bounding box.south west) -- (path picture bounding box.north east) 19 | (path picture bounding box.south east) -- (path picture bounding box.north west); 20 | }}, 21 | bundle/.style={path picture={ 22 | \draw[black] 23 | (path picture bounding box.south west) -- (path picture bounding box.north east); 24 | }}] 25 | 26 | % `operator' will only be used by most gates. 27 | % `cnot' will refer to CNOT gates. 28 | % `phase' is used for controlled gates. 29 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em] 30 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt] 31 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt] 32 | % 33 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) { 34 | 35 | % First row. 36 | \coordinate (start1); &[-0.5cm] 37 | \node[bundle] (B0) {}; 38 | \node[above right] (B0) {$n$}; & 39 | & 40 | \node[operator] (O12) {$H^{\otimes n}$}; 41 | & 42 | \node[operator] (O13) {$2|0\rangle\langle 0| - I$}; 43 | & 44 | \node[operator] (O14) {$H^{\otimes n}$}; 45 | &[-0.5cm] 46 | \coordinate (end1);\\ 47 | 48 | % Second row. 49 | \coordinate (start2); &[-0.5cm] 50 | & 51 | & 52 | & 53 | & 54 | &[-0.5cm] 55 | \coordinate (end2);\\ 56 | }; 57 | \draw [thick,black,fill=white] (-3.5,-2.3em) rectangle (-2.5,1.7em); 58 | \node at (-3,-0.15) (O) {$O$}; 59 | 60 | \begin{pgfonlayer}{background} 61 | % Draw lines. 62 | \draw[thick] (start1) -- (end1) (start2) -- (end2) 63 | ; 64 | \end{pgfonlayer} 65 | % 66 | \end{tikzpicture} 67 | \end{document} 68 | -------------------------------------------------------------------------------- /grover_search.tex: -------------------------------------------------------------------------------- 1 | % Based on the answer by qubyte at 2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits 3 | \documentclass[12pt]{standalone} 4 | \usepackage{tikz} 5 | \pgfdeclareimage[height=1.5em]{meter}{meter} 6 | 7 | \usetikzlibrary{backgrounds} 8 | % Dirac Kets 9 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}} 10 | 11 | \begin{document} 12 | \begin{tikzpicture}[thick, 13 | cross/.style={path picture={ 14 | \draw[black] 15 | (path picture bounding box.south) -- (path picture bounding box.north); 16 | }}, 17 | swap/.style={path picture={ 18 | \draw[black] 19 | (path picture bounding box.south west) -- (path picture bounding box.north east) 20 | (path picture bounding box.south east) -- (path picture bounding box.north west); 21 | }}, 22 | bundle/.style={path picture={ 23 | \draw[black] 24 | (path picture bounding box.south west) -- (path picture bounding box.north east); 25 | }}] 26 | 27 | % `operator' will only be used by most gates. 28 | % `cnot' will refer to CNOT gates. 29 | % `phase' is used for controlled gates. 30 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em] 31 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt] 32 | \tikzstyle{meter} = [draw,color=white,fill=white,minimum size=1.7em] 33 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt] 34 | % 35 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) { 36 | 37 | % First row. 38 | \node (S0) {$|0\rangle$};&[-0.5cm] 39 | \node[bundle] (B0) {}; 40 | \node[above right] (B0) {$n$}; &[-0.5cm] 41 | \node[operator] (O12) {$H^{\otimes n}$}; 42 | & 43 | & 44 | & 45 | \node (O14) {\ldots}; 46 | & 47 | & 48 | & 49 | \node[meter] (M11) {\pgfbox[center,center]{\pgfuseimage{meter}}}; 50 | \coordinate (end1);\\ 51 | 52 | % Second row. 53 | \node (S1) {$|1\rangle$};&[-0.5cm] 54 | & 55 | \node[operator] (O22) {$H$};& 56 | & 57 | & 58 | \node (O24) {\ldots}; 59 | & 60 | & 61 | & 62 | \coordinate (end2);\\ 63 | }; 64 | \draw [thick,black,fill=white] (-0.7,-2.2em) rectangle (0.3,1.8em); 65 | \node at (-0.2,-0.14) (O) {$G$}; 66 | \draw [thick,black,fill=white] (2.1,-2.2em) rectangle (3.1,1.8em); 67 | \node at (2.6,-0.14) (O) {$G$}; 68 | 69 | \begin{pgfonlayer}{background} 70 | % Draw lines. 71 | \draw[thick] (S0) -- (O14) (O14) -- (end1) (S1) -- (O24) (O24) -- (end2) 72 | ; 73 | \end{pgfonlayer} 74 | % 75 | \end{tikzpicture} 76 | \end{document} 77 | -------------------------------------------------------------------------------- /hadamard_gate.tex: -------------------------------------------------------------------------------- 1 | % Based on the answer by qubyte at 2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits 3 | \documentclass[12pt]{standalone} 4 | \usepackage{tikz} 5 | 6 | \usetikzlibrary{backgrounds} 7 | % Dirac Kets 8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}} 9 | 10 | \begin{document} 11 | \begin{tikzpicture}[thick,cross/.style={path picture={ 12 | \draw[black] 13 | (path picture bounding box.south) -- (path picture bounding box.north); 14 | }}] 15 | 16 | % `operator' will only be used by most gates. 17 | % `cnot' will refer to CNOT gates. 18 | % `phase' is used for controlled gates. 19 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em] 20 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt] 21 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt] 22 | % 23 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) { 24 | 25 | % First row. 26 | \coordinate (start1); & 27 | \node[operator] (O11) {H}; & 28 | \coordinate (end1);\\ 29 | }; 30 | 31 | \begin{pgfonlayer}{background} 32 | % Draw lines. 33 | \draw[thick] (start1) -- (end1); 34 | \end{pgfonlayer} 35 | % 36 | \end{tikzpicture} 37 | \end{document} 38 | -------------------------------------------------------------------------------- /hopfield.tex: -------------------------------------------------------------------------------- 1 | \documentclass[12pt]{standalone} 2 | % Based on http://www.texample.net/tikz/examples/neural-network/ 3 | 4 | \usepackage[rgb]{xcolor} 5 | \definecolor{color1}{RGB}{0,114,178} 6 | \definecolor{color2}{RGB}{0,158,115} 7 | \definecolor{color3}{RGB}{213,94,0} 8 | 9 | \usepackage{tikz} 10 | 11 | \begin{document} 12 | 13 | \def\layersep{2.5cm} 14 | 15 | \begin{tikzpicture}[shorten >=1pt,->,draw=black!80, node distance=\layersep] 16 | \tikzstyle{every pin edge}=[<-,shorten <=1pt] 17 | \tikzstyle{neuron}=[circle,fill=black!25,minimum size=17pt,inner sep=0pt] 18 | \tikzstyle{phantomneuron}=[circle,fill=black!0,minimum size=17pt,inner sep=0pt] 19 | \tikzstyle{annot} = [text width=4em, text centered] 20 | 21 | % Draw the input layer nodes 22 | \foreach \name / \y in {1/1,2/2,$d$/4} 23 | \node[phantomneuron] (I-\y) at (0,-\y) {\name}; 24 | \node (I-3) at (0,-3) {\vdots}; 25 | 26 | % Draw the hidden layer nodes 27 | \foreach \name / \y in {1/1,2/2,$K$/4} 28 | \node[neuron] (H-\y) at (\layersep,-\y) {\name}; 29 | \node (H-3) at (\layersep,-3) {\vdots}; 30 | 31 | \foreach \name / \y in {1/1,2/2,$d$/4} 32 | \node[phantomneuron] (O-\y) at (2*\layersep,-\y) {}; 33 | 34 | % Connect every node in the input layer with every node in the 35 | % hidden layer. 36 | \foreach \source in {1,2,4} 37 | \path[very thick] (I-\source) edge (H-\source); 38 | 39 | % Connect every node in the hidden layer with the output layer 40 | \foreach \source in {1,2,4} 41 | \path[very thick] (H-\source) edge (O-\source); 42 | 43 | \foreach \dest / \y in {1/1, 2/2, $d$/4} 44 | \draw[thick,color=color1] (H-1) -- + (0.5, 0.5) -- + (0.5, 1.1) --+ (-1.1, 1.1) -- + (-1.1, -\y+1.3) -- + (H-\y); 45 | 46 | \foreach \dest / \y in {1/1, 2/2, $d$/4} 47 | \draw[thick,color=color2] (H-2) -- + (0.7, 0.5) -- + (0.7, 1.9) -- + (-0.9, 1.9) -- + (-0.9, -\y+2.5) -- + (H-\y); 48 | 49 | \foreach \dest / \y in {1/1, 2/2, $d$/4} 50 | \draw[thick,color=color3] (H-4) -- + (0.9, 0.5) -- + (0.9,3.7) -- + (-0.7, 3.7) -- + (-0.7, -\y+4.7) -- + (H-\y); 51 | 52 | 53 | \end{tikzpicture} 54 | % End of code 55 | \end{document} 56 | -------------------------------------------------------------------------------- /meter.svg: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 18 | 20 | 27 | 33 | 34 | 41 | 47 | 48 | 49 | 71 | 73 | 74 | 76 | image/svg+xml 77 | 79 | 80 | 81 | 82 | 83 | 88 | 95 | 98 | 111 | 116 | 121 | 122 | 123 | 124 | -------------------------------------------------------------------------------- /nonconvex_loss_functions.py: -------------------------------------------------------------------------------- 1 | import matplotlib.pyplot as plt 2 | import numpy as np 3 | from numpy.random import rand 4 | 5 | from graphics_utils import initialize_graphics, cm2inch 6 | 7 | def zero_one(x): 8 | if x<0: 9 | return 1 10 | else: 11 | return 0 12 | 13 | def savage_loss(x): 14 | return 4/(1+np.exp(2*x))**2 15 | 16 | def tangent_loss(x): 17 | return (2*np.arctan(x)-1)**2 18 | 19 | x = np.arange(-6,8,0.01) 20 | y_zero_one = [zero_one(t) for t in x] 21 | y_savage_loss = [savage_loss(t) for t in x] 22 | y_tangent_loss = [tangent_loss(t) for t in x] 23 | colors = initialize_graphics() 24 | 25 | fig, ax = plt.subplots() 26 | fig.set_size_inches(cm2inch([10,7])) 27 | plt.plot(x, y_zero_one, color='black', linewidth=3, label='Zero-one') 28 | plt.plot(x, y_savage_loss, color=colors[0], linewidth=2, label='Savage loss') 29 | plt.plot(x, y_tangent_loss, '--', color=colors[1], linewidth=2, label='Tangent loss') 30 | 31 | handles, labels = ax.get_legend_handles_labels() 32 | ax.legend(handles, labels, loc=1) 33 | 34 | #plt.axis('off') 35 | ax.set_xlim([-5, 8]) 36 | ax.set_ylim([0, 15]) 37 | 38 | plt.savefig('./nonconvex_loss_functions.pdf',bbox_inches='tight') 39 | -------------------------------------------------------------------------------- /perceptron.tex: -------------------------------------------------------------------------------- 1 | \documentclass[12pt]{standalone} 2 | % Based on http://www.texample.net/tikz/examples/neural-network/ 3 | 4 | \usepackage{tikz} 5 | 6 | \begin{document} 7 | 8 | \def\layersep{2.5cm} 9 | 10 | \begin{tikzpicture}[shorten >=1pt,->,draw=black!80, node distance=\layersep] 11 | \tikzstyle{every pin edge}=[<-,shorten <=1pt] 12 | \tikzstyle{neuron}=[circle,fill=black!25,minimum size=17pt,inner sep=0pt] 13 | \tikzstyle{phantomneuron}=[circle,fill=black!0,minimum size=17pt,inner sep=0pt] 14 | \tikzstyle{annot} = [text width=4em, text centered] 15 | 16 | % Draw the input layer nodes 17 | \foreach \name / \y in {1/1,2/2,$d$/4} 18 | % This is the same as writing \foreach \name / \y in {1/1,2/2,3/3,4/4} 19 | \node[phantomneuron] (I-\name) at (0,-\y) {\name}; 20 | \node (I-3) at (0, -3) {\vdots}; 21 | 22 | \node[neuron] (P) at (\layersep, -2 cm) {}; 23 | 24 | \node[phantomneuron] (O) at (2*\layersep,-2 cm) {$f(\mathbf{x})$}; 25 | % Connect every node in the input layer with every node in the 26 | % hidden layer. 27 | \foreach \source in {1,2,$d$} 28 | \path (I-\source) edge (P); 29 | \path (P) edge (O); 30 | 31 | % Connect every node in the hidden layer with the output layer 32 | %\foreach \source in {1,2,$K$} 33 | % \foreach \dest in {1,2,$M$} 34 | % \path (H-\source) edge (O-\dest); 35 | 36 | \end{tikzpicture} 37 | % End of code 38 | \end{document} 39 | -------------------------------------------------------------------------------- /quantum_annealing.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """ 3 | Created on Sun Apr 27 09:23:32 2014 4 | 5 | @author: wittek 6 | """ 7 | 8 | import matplotlib.pyplot as plt 9 | import numpy as np 10 | from common_graphics_settings import initialize_graphics 11 | 12 | colors = initialize_graphics() 13 | fig = plt.figure(1,figsize=(5,5)) 14 | ax1 = fig.add_subplot(111) 15 | 16 | # Right side of the diagram 17 | domain = np.arange(0.0, 8*np.pi, 0.01) 18 | y3 = [ 10*((2*np.cos(x)+np.log(x+4)-7*np.exp(-(x-15)*(x-15)/100))/3.5) for x in domain ] 19 | line, = ax1.plot(domain, y3, lw=3, color=colors[0]) 20 | ax1.annotate('', xy=(11.6, -4), xytext=(9.7, -12.1), 21 | arrowprops=dict(facecolor=colors[1], shrink=0.05), 22 | ) 23 | plt.text( 11.5, -3.3, 'Thermal\n annealing',fontsize=14) 24 | ax1.annotate('', xy=(14.8, -13.1), xytext=(9.5, -13.1), 25 | arrowprops=dict(facecolor=colors[2], shrink=0.05), 26 | ) 27 | plt.text( 8.3, -16.5, 'Quantum\n tunneling',fontsize=14) 28 | 29 | plt.axis('off') 30 | plt.savefig('./quantum_annealing.pdf',bbox_inches='tight') -------------------------------------------------------------------------------- /quantum_neural_network.tex: -------------------------------------------------------------------------------- 1 | \documentclass[12pt]{standalone} 2 | % Based on http://www.texample.net/tikz/examples/neural-network/ 3 | 4 | \usepackage{tikz} 5 | 6 | \begin{document} 7 | 8 | \def\layersep{2.5cm} 9 | 10 | \begin{tikzpicture}[shorten >=1pt,->,draw=black!80, node distance=\layersep] 11 | \tikzstyle{every pin edge}=[<-,shorten <=1pt] 12 | \tikzstyle{neuron}=[circle,fill=black!25,minimum size=17pt,inner sep=0pt] 13 | \tikzstyle{annot} = [text width=4em, text centered] 14 | 15 | % Draw the input layer nodes 16 | \foreach \name / \y in {1/1,2/2,$d$/4} 17 | % This is the same as writing \foreach \name / \y in {1/1,2/2,3/3,4/4} 18 | \node[neuron] (I-\name) at (0,-\y) {}; 19 | \node (I-3) at (0,-3) {\vdots}; 20 | 21 | % Draw the hidden layer nodes 22 | \foreach \name / \y in {1/1,2/2,$K$/4} 23 | \node[neuron] (H-\name) at (\layersep,-\y cm) {}; 24 | \node (H-3) at (\layersep,-3) {\vdots}; 25 | 26 | \foreach \name / \y in {1/1,2/2,$M$/4} 27 | \node[neuron] (O-\name) at (2*\layersep,-\y cm) {}; 28 | \node (O-3) at (2*\layersep,-3) {\vdots}; 29 | 30 | \foreach \source in {-1,-2,-4}{ 31 | \draw [black,-,dotted,thick,domain=-80:80] plot ({0.3+0.3*cos(\x)}, {\source+0.3*sin(\x)}); 32 | \draw [black,-,dotted,thick,domain=-80:80] plot ({0.6+0.6*cos(\x)}, {\source+0.6*sin(\x)}); 33 | \draw [black,-,dotted,thick,domain=-80:80] plot ({0.9+0.9*cos(\x)}, {\source+0.9*sin(\x)}); 34 | } 35 | 36 | % Connect every node in the hidden layer with the output layer 37 | \foreach \source in {1,2,$K$} 38 | \foreach \dest in {1,2,$M$} 39 | \path (H-\source) edge (O-\dest); 40 | 41 | \end{tikzpicture} 42 | % End of code 43 | \end{document} 44 | -------------------------------------------------------------------------------- /quantum_parallelism.tex: -------------------------------------------------------------------------------- 1 | % Based on the answer by qubyte at 2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits 3 | \documentclass[12pt]{standalone} 4 | \usepackage{tikz} 5 | 6 | \usetikzlibrary{backgrounds,calc,decorations.pathreplacing} 7 | % Dirac Kets 8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}} 9 | 10 | \begin{document} 11 | \begin{tikzpicture}[thick,cross/.style={path picture={ 12 | \draw[black] 13 | (path picture bounding box.south) -- (path picture bounding box.north); 14 | }}] 15 | 16 | % `operator' will only be used by most gates. 17 | % `cnot' will refer to CNOT gates. 18 | % `phase' is used for controlled gates. 19 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em] 20 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt] 21 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt] 22 | % 23 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) { 24 | 25 | % First row. 26 | \node (q1) {\ket{0}}; 27 | \coordinate (start1); &[-0.5cm] 28 | \node[operator] (O11) {H}; & 29 | & 30 | &[-0.5cm] 31 | \coordinate (end1);\\ 32 | 33 | \node (q2) {\ket{0}}; 34 | \coordinate (start2); &[-0.5cm] 35 | & 36 | & 37 | &[-0.5cm] 38 | \coordinate (end2);\\ 39 | }; 40 | \draw [thick,black,fill=white] (0.3,-2em) rectangle (1.3,2em); 41 | \node at (0.8,0) (Uf) {$U_f$}; 42 | 43 | 44 | \draw[decorate,decoration={brace},thick] 45 | ($(circuit.north east)-(0cm,0.3cm)$) 46 | to node[midway,right] (bracket) {$\displaystyle\frac{\ket{0,f(0)}+\ket{1,f(1)}}{\sqrt{2}}$} 47 | ($(circuit.south east)+(0cm,0.3cm)$); 48 | \begin{pgfonlayer}{background} 49 | % Draw lines. 50 | \draw[thick] (q1) -- (end1) (q2) -- (end2); 51 | \end{pgfonlayer} 52 | % 53 | \end{tikzpicture} 54 | \end{document} 55 | -------------------------------------------------------------------------------- /quantum_swap.tex: -------------------------------------------------------------------------------- 1 | % Based on the answer by qubyte at 2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits 3 | \documentclass[12pt]{standalone} 4 | \usepackage{tikz} 5 | 6 | \usetikzlibrary{backgrounds} 7 | % Dirac Kets 8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}} 9 | 10 | \begin{document} 11 | \begin{tikzpicture}[thick,cross/.style={path picture={ 12 | \draw[black] 13 | (path picture bounding box.south) -- (path picture bounding box.north); 14 | }}] 15 | 16 | % `operator' will only be used by most gates. 17 | % `cnot' will refer to CNOT gates. 18 | % `phase' is used for controlled gates. 19 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em] 20 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt] 21 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt] 22 | % 23 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) { 24 | 25 | % First row. 26 | \node (q1) {\ket{A}}; &[-0.5cm] 27 | \node[phase] (P11) {}; & 28 | \node[cnot] (C12) {}; & 29 | \node[phase] (P13) {}; &[-0.3cm] 30 | \node (q1end) {\ket{B}};\\ 31 | 32 | % Second row. 33 | \node (q2) {\ket{B}}; & 34 | \node[cnot] (C21) {}; & 35 | \node[phase] (P22) {}; & 36 | \node[cnot] (C23) {}; &[-0.3cm] 37 | \node (q2end) {\ket{A}}; \\ 38 | }; 39 | 40 | \begin{pgfonlayer}{background} 41 | % Draw lines. 42 | \draw[thick] (q1) -- (q1end) (q2) -- (q2end) (P11) -- (C21) (C12) -- (P22) (P13) -- (C23); 43 | \end{pgfonlayer} 44 | % 45 | \end{tikzpicture} 46 | \end{document} 47 | -------------------------------------------------------------------------------- /quantum_swap_gate.tex: -------------------------------------------------------------------------------- 1 | % Based on the answer by qubyte at 2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits 3 | \documentclass[12pt]{standalone} 4 | \usepackage{tikz} 5 | 6 | \usetikzlibrary{backgrounds} 7 | % Dirac Kets 8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}} 9 | 10 | \begin{document} 11 | \begin{tikzpicture}[thick,cross/.style={path picture={ 12 | \draw[black] 13 | (path picture bounding box.south) -- (path picture bounding box.north); 14 | }},swap/.style={path picture={ 15 | \draw[black] 16 | (path picture bounding box.south west) -- (path picture bounding box.north east) (path picture bounding box.south east) -- (path picture bounding box.north west); 17 | }}] 18 | 19 | % `operator' will only be used by most gates. 20 | % `cnot' will refer to CNOT gates. 21 | % `phase' is used for controlled gates. 22 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em] 23 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt] 24 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt] 25 | % 26 | \draw [white] (-2,0.5) rectangle (2,0.5); 27 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) { 28 | 29 | % First row. 30 | \coordinate (start1); & 31 | \coordinate (swap11); 32 | \node[swap] (O11) {}; & 33 | \coordinate (end1);\\ 34 | 35 | \coordinate (start2); & 36 | \coordinate (swap21); 37 | \node[swap] (O21) {}; & 38 | \coordinate (end2);\\ 39 | }; 40 | 41 | \begin{pgfonlayer}{background} 42 | % Draw lines. 43 | \draw[thick] (start1) -- (end1) (start2) -- (end2) (swap11) -- (swap21); 44 | \end{pgfonlayer} 45 | % 46 | \end{tikzpicture} 47 | \end{document} 48 | -------------------------------------------------------------------------------- /quantum_tunneling.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """ 3 | Created on Sun May 4 15:56:25 2014 4 | 5 | @author: wittek 6 | """ 7 | from mpl_toolkits.axes_grid.axislines import SubplotZero 8 | import matplotlib.pyplot as plt 9 | import numpy as np 10 | from graphics_utils import initialize_graphics, cm2inch 11 | 12 | def potential_barrier(x,x1,x2,V0): 13 | if x>x1 and xx2: 22 | return amplitude2*np.sin(2*np.pi*omega*x) 23 | else: 24 | return 0 25 | 26 | x1 = 6.5 27 | x2 = 8.5 28 | V0 = 2 29 | omega = 0.5 30 | amplitude1 = 1 31 | amplitude2 = 0.2 32 | 33 | full_range = np.arange(0, 5*np.pi, 0.01) 34 | potential = [ potential_barrier(x, x1, x2, V0) for x in full_range] 35 | 36 | until_x1 = np.arange(0.0, x1, 0.01) 37 | wave_until_x1 = [tunneling_wave(t, x1, x2, omega, amplitude1, amplitude2) for t in until_x1] 38 | from_x2 = np.arange(x2+0.01, 5*np.pi, 0.01) 39 | wave_from_x2 = [tunneling_wave(t, x1, x2, omega, amplitude1, amplitude2) for t in from_x2] 40 | 41 | 42 | colors=initialize_graphics() 43 | 44 | fig = plt.figure(1) 45 | ax = SubplotZero(fig, 111) 46 | fig.add_subplot(ax) 47 | #fig, ax = plt.subplots() 48 | fig.set_size_inches(cm2inch([10,5])) 49 | 50 | ax.plot(full_range, potential, lw=2, color=colors[2]) 51 | ax.plot(until_x1, wave_until_x1, lw=2, color=colors[0]) 52 | ax.plot(from_x2, wave_from_x2, lw=2, color=colors[0]) 53 | 54 | ax.annotate('$U(x)$', xy=(x2, V0), xytext=(x2+0.3, V0-0.2)) 55 | 56 | ax.set_frame_on(False) 57 | #ax.axes.get_yaxis().set_visible(False) 58 | ax.axes.get_xaxis().set_ticks([x1, x2, 5*np.pi+0.5]) 59 | ax.axes.get_xaxis().set_ticklabels(['$x_1$','$x_2$', '$x$']) 60 | ax.axis["xzero"].set_axisline_style("-|>") 61 | ax.axis["xzero"].set_visible(True) 62 | ax.axis["yzero"].set_visible(False) 63 | 64 | for direction in ["left", "right", "bottom", "top"]: 65 | ax.axis[direction].set_visible(False) 66 | 67 | ax.set_xlim([-0.5, 5*np.pi+0.5]) 68 | 69 | plt.savefig('./quantum_tunneling.pdf') 70 | -------------------------------------------------------------------------------- /supervised.py: -------------------------------------------------------------------------------- 1 | import matplotlib.pyplot as plt 2 | import numpy as np 3 | from numpy.random import rand 4 | 5 | from graphics_utils import initialize_graphics, cm2inch 6 | 7 | x = rand(40)-0.5 8 | z = x*x+0.4 9 | y = z+rand(40)/3 10 | w = z-rand(40)/3 11 | 12 | xx = np.arange(-0.55,0.55,0.01) 13 | yy = xx*xx+0.4 14 | 15 | colors = initialize_graphics() 16 | 17 | fig, ax = plt.subplots() 18 | fig.set_size_inches(cm2inch([10,10])) 19 | plt.plot(x, y, 'D' , color=colors[0], label='Class 1') 20 | plt.plot(x, w, 's', color=colors[1], label='Class 2') 21 | plt.plot(xx, yy, color=colors[2], linewidth=4, label='Decision\n surface') 22 | 23 | handles, labels = ax.get_legend_handles_labels() 24 | ax.legend(handles, labels, loc=4) 25 | 26 | plt.axis('off') 27 | ax.set_ylim([-0.2, 0.9]) 28 | 29 | plt.savefig('./supervised.pdf',bbox_inches='tight') 30 | -------------------------------------------------------------------------------- /support_vectors.py: -------------------------------------------------------------------------------- 1 | import matplotlib.pyplot as plt 2 | from matplotlib.patches import Circle 3 | import numpy as np 4 | from numpy.random import rand 5 | 6 | from graphics_utils import initialize_graphics, cm2inch 7 | 8 | x = rand(40)-0.5 9 | z = x+0.4 10 | y = z+rand(40)/2+0.3 11 | w = z-rand(40)/2-0.3 12 | 13 | xx = np.arange(-0.8,0.8,0.01) 14 | yy = xx+0.4 15 | 16 | margin_one = xx+0.4+0.2 17 | margin_two = xx+0.4-0.2 18 | 19 | colors = initialize_graphics() 20 | 21 | fig, ax = plt.subplots() 22 | fig.set_size_inches(cm2inch([10,10])) 23 | plt.plot(x, y, 'D' , color=colors[0], label='Class 1') 24 | plt.plot(x, w, 's', color=colors[1], label='Class 2') 25 | plt.plot(xx, yy, color=colors[2], linewidth=4, label='Decision\n surface') 26 | plt.plot(xx, margin_one, '--', color=colors[2], linewidth=2, label='Margin') 27 | plt.plot(xx, margin_two, '--', color=colors[2], linewidth=2) 28 | 29 | support_vectors_x1 = [-0.4, 0.3] 30 | support_vectors_y1 = [-0.4+0.6, 0.3+0.6] 31 | plt.plot(support_vectors_x1, support_vectors_y1, 'D' , color=colors[0]) 32 | for x1, y1 in zip(support_vectors_x1, support_vectors_y1): 33 | circle1 = Circle((x1, y1), 0.06, facecolor='none', edgecolor=colors[0], linewidth=1) 34 | ax.add_patch(circle1) 35 | 36 | support_vectors_x2 = [-0.1, 0.5] 37 | support_vectors_y2 = [-0.1+0.2, 0.5+0.2] 38 | plt.plot(support_vectors_x2, support_vectors_y2, 's' , color=colors[1]) 39 | for x2, y2 in zip(support_vectors_x2, support_vectors_y2): 40 | circle2 = Circle((x2, y2), 0.06, facecolor='none', edgecolor=colors[1], linewidth=1) 41 | ax.add_patch(circle2) 42 | 43 | 44 | handles, labels = ax.get_legend_handles_labels() 45 | ax.legend(handles, labels, loc=4) 46 | 47 | plt.axis('off') 48 | ax.set_xlim([-1.1,1.1]) 49 | ax.set_ylim([-0.7, 1.5]) 50 | 51 | plt.savefig('./support_vectors.pdf',bbox_inches='tight') 52 | -------------------------------------------------------------------------------- /swap_test.tex: -------------------------------------------------------------------------------- 1 | % Based on the answer by qubyte at 2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits 3 | \documentclass[12pt]{standalone} 4 | \usepackage{tikz} 5 | 6 | \usetikzlibrary{backgrounds} 7 | % Dirac Kets 8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}} 9 | \pgfdeclareimage[height=1.5em]{meter}{meter} 10 | 11 | \begin{document} 12 | \begin{tikzpicture}[thick,cross/.style={path picture={ 13 | \draw[black] 14 | (path picture bounding box.south) -- (path picture bounding box.north); 15 | }},swap/.style={path picture={ 16 | \draw[black] 17 | (path picture bounding box.south west) -- (path picture bounding box.north east) (path picture bounding box.south east) -- (path picture bounding box.north west); 18 | }}] 19 | 20 | % `operator' will only be used by most gates. 21 | % `cnot' will refer to CNOT gates. 22 | % `phase' is used for controlled gates. 23 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em] 24 | \tikzstyle{meter} = [draw,color=white,fill=white,minimum size=1.7em] 25 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt] 26 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt] 27 | % 28 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) { 29 | 30 | % First row. 31 | \node (q1) {\ket{0}}; &[-0.5cm] 32 | \node[operator] (O11) {H}; & 33 | \node[phase] (P12) {}; & 34 | \node[operator] (O13) {H}; & 35 | \node[meter] (M11) {\pgfbox[center,center]{\pgfuseimage{meter}}};\\ 36 | 37 | % Second row. 38 | \node (q2) {\ket{\psi}}; & 39 | & 40 | \coordinate (swap22); 41 | \node[swap] (O22) {}; & 42 | & 43 | \coordinate (end2); \\ 44 | 45 | % Third row. 46 | \node (q3) {\ket{\phi}}; & 47 | & 48 | \coordinate (swap32); 49 | \node[swap] (O32) {}; & 50 | & 51 | \coordinate (end3); \\ 52 | }; 53 | 54 | \begin{pgfonlayer}{background} 55 | % Draw lines. 56 | \draw[thick] (q1) -- (M11) (q2) -- (end2) (q3) -- (end3) (P12) -- (swap22) (swap22) -- (swap32); 57 | \end{pgfonlayer} 58 | % 59 | \end{tikzpicture} 60 | \end{document} 61 | -------------------------------------------------------------------------------- /toffoli_gate.tex: -------------------------------------------------------------------------------- 1 | % Based on the answer by qubyte at 2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits 3 | \documentclass[12pt]{standalone} 4 | \usepackage{tikz} 5 | 6 | \usetikzlibrary{backgrounds} 7 | % Dirac Kets 8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}} 9 | 10 | \begin{document} 11 | \begin{tikzpicture}[thick,cross/.style={path picture={ 12 | \draw[black] 13 | (path picture bounding box.south) -- (path picture bounding box.north); 14 | }}] 15 | 16 | % `operator' will only be used by most gates. 17 | % `cnot' will refer to CNOT gates. 18 | % `phase' is used for controlled gates. 19 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em] 20 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt] 21 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt] 22 | % 23 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) { 24 | 25 | % First row. 26 | \coordinate (start1); & 27 | \node[phase] (P11) {}; & 28 | \coordinate (end1);\\ 29 | 30 | % Second row. 31 | \coordinate (start2); & 32 | \node[phase] (P21) {}; & 33 | \coordinate (end2);\\ 34 | 35 | % Third row 36 | \coordinate (start3); & 37 | \node[cnot] (O31) {}; & 38 | \coordinate (end3);\\ 39 | }; 40 | 41 | \begin{pgfonlayer}{background} 42 | % Draw lines. 43 | \draw[thick] (start1) -- (end1) (start2) -- (end2) (start3) -- (end3) (P11) -- (P21) (P21) -- (O31); 44 | \end{pgfonlayer} 45 | % 46 | \end{tikzpicture} 47 | \end{document} 48 | -------------------------------------------------------------------------------- /transductive.py: -------------------------------------------------------------------------------- 1 | import matplotlib.pyplot as plt 2 | import numpy as np 3 | from numpy.random import rand 4 | 5 | from graphics_utils import initialize_graphics, cm2inch 6 | 7 | r = rand(8)/5 8 | t = rand(8) 9 | x = r/2 * np.cos(2*np.pi*t) - 0.2 10 | y = r * np.sin(2*np.pi*t) - 0.2 11 | r = rand(40)/5 12 | t = rand(40) 13 | xz = r/2 * np.cos(2*np.pi*t) - 0.2 14 | z = r * np.sin(2*np.pi*t) - 0.2 15 | 16 | r = rand(8)/5 17 | t = rand(8) 18 | xx = r * np.cos(2*np.pi*t) + 0.2 19 | yy = r/3 * np.sin(2*np.pi*t) 20 | r = rand(40)/5 21 | t = rand(40) 22 | xzz = r * np.cos(2*np.pi*t) + 0.2 23 | zz = r/3 * np.sin(2*np.pi*t) 24 | 25 | colors = initialize_graphics() 26 | 27 | fig, ax = plt.subplots() 28 | fig.set_size_inches(cm2inch([10,10])) 29 | ax.plot(xz, z, 'o',color=colors[0], label='Unlabeled instances') 30 | ax.plot(x, y, 'D', color=colors[1], label='Class 1') 31 | ax.plot(xzz, zz, 'o',color=colors[0]) 32 | ax.plot(xx, yy, 's', color=colors[2], label='Class 2') 33 | 34 | handles, labels = ax.get_legend_handles_labels() 35 | ax.legend(handles, labels, loc=4) 36 | 37 | plt.axes().set_aspect('equal') 38 | plt.axis('off') 39 | 40 | plt.savefig('./transductive.pdf',bbox_inches='tight') 41 | -------------------------------------------------------------------------------- /unsupervised.py: -------------------------------------------------------------------------------- 1 | import matplotlib.pyplot as plt 2 | from matplotlib.patches import Ellipse 3 | import numpy as np 4 | from numpy.random import rand 5 | 6 | from graphics_utils import initialize_graphics, cm2inch 7 | 8 | r = rand(40)/5 9 | t = rand(40) 10 | x = r * np.cos(2*np.pi*t) - 0.3 11 | y = r * np.sin(2*np.pi*t) - 0.3 12 | 13 | r = rand(40)/5 14 | t = rand(40) 15 | xx = r * np.cos(2*np.pi*t) + 0.3 16 | yy = r/3 * np.sin(2*np.pi*t) + 0.3 17 | 18 | 19 | r = rand(40)/5 20 | t = rand(40) 21 | xxx = r/2 * np.cos(2*np.pi*t) - 0.15 22 | yyy = r * np.sin(2*np.pi*t) + 0.15 23 | 24 | colors = initialize_graphics() 25 | circle1 = Ellipse((-0.3, -0.3), 0.42, 0.42, facecolor='none', edgecolor=colors[1], linewidth=4, label='Decision boundary') 26 | circle2 = Ellipse((0.3, 0.3), 0.42, 0.22, facecolor='none', edgecolor=colors[1], linewidth=4) 27 | circle3 = Ellipse((-0.15, +0.15), 0.22, 0.42, facecolor='none', edgecolor=colors[1], linewidth=4) 28 | 29 | fig, ax = plt.subplots() 30 | fig.set_size_inches(cm2inch([10,10])) 31 | plt.plot(x, y, 'o', color=colors[0], label='Unlabeled instances') 32 | plt.plot(xx, yy, 'o', color=colors[0]) 33 | plt.plot(xxx, yyy, 'o', color=colors[0]) 34 | 35 | ax.add_patch(circle1) 36 | ax.add_patch(circle2) 37 | ax.add_patch(circle3) 38 | 39 | handles, labels = ax.get_legend_handles_labels() 40 | ax.legend(handles, labels, loc=4) 41 | 42 | plt.axes().set_aspect('equal') 43 | plt.axis('off') 44 | ax.set_xlim([-0.52, 0.52]) 45 | ax.set_ylim([-0.52, 0.52]) 46 | 47 | plt.savefig('./unsupervised.pdf',bbox_inches='tight') 48 | -------------------------------------------------------------------------------- /vc_dimension_line.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """ 3 | Created on Sun Apr 27 09:23:32 2014 4 | 5 | @author: wittek 6 | """ 7 | 8 | import matplotlib.pyplot as plt 9 | import numpy as np 10 | from numpy.random import rand 11 | from graphics_utils import initialize_graphics, cm2inch 12 | 13 | x = np.arange(0.0, 10, 0.01) 14 | y = x 15 | 16 | colors=initialize_graphics() 17 | 18 | fig, ax = plt.subplots() 19 | fig.set_size_inches(cm2inch([10,10])) 20 | 21 | ax.plot(x, y, lw=3, color=colors[0]) 22 | 23 | ax.plot(5, 6, 'o', color=colors[1]) 24 | ax.plot(3, 7, 'o', color=colors[1]) 25 | ax.plot(7, 4, 'D', color=colors[2]) 26 | 27 | ax.set_xlim([-1, 11]) 28 | ax.set_ylim([-2, 11]) 29 | 30 | plt.axis('off') 31 | 32 | plt.savefig('./vc_dimension_line.pdf',bbox_inches='tight') 33 | -------------------------------------------------------------------------------- /vc_dimension_sine.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """ 3 | Created on Sun Apr 27 09:23:32 2014 4 | 5 | @author: wittek 6 | """ 7 | 8 | import matplotlib.pyplot as plt 9 | import numpy as np 10 | from numpy.random import rand 11 | from graphics_utils import initialize_graphics, cm2inch 12 | 13 | x = np.arange(0.0, 10*np.pi, 0.01) 14 | y = np.cos(x) 15 | 16 | colors=initialize_graphics() 17 | 18 | fig, ax = plt.subplots() 19 | fig.set_size_inches(cm2inch([10,10])) 20 | 21 | ax.plot(x, y, lw=3, color=colors[0]) 22 | for i in range(0,11,2): 23 | ax.plot(i*np.pi + 2*(rand(1)-0.5), -0.1, 'o', color=colors[1]) 24 | for i in range(1,11,2): 25 | ax.plot(i*np.pi + 2*(rand(1)-0.5), -0.1, 'D', color=colors[2]) 26 | 27 | 28 | ax.set_ylim([-1.5, 1.5]) 29 | 30 | plt.axis('off') 31 | 32 | plt.savefig('./vc_dimension_sine.pdf',bbox_inches='tight') -------------------------------------------------------------------------------- /xor_problem.py: -------------------------------------------------------------------------------- 1 | import matplotlib.pyplot as plt 2 | import numpy as np 3 | 4 | from graphics_utils import initialize_graphics, cm2inch 5 | 6 | 7 | xx = np.arange(-0.1, 1.1,0.01) 8 | yy = -xx+0.9 9 | 10 | x1 = [0, 1] 11 | y1 = [1, 0] 12 | x2 = [1 ,0] 13 | y2 = [1, 0] 14 | 15 | colors = initialize_graphics() 16 | 17 | fig, ax = plt.subplots() 18 | fig.set_size_inches(cm2inch([10,10])) 19 | plt.plot(x1, y1, 'D' , color=colors[0], label='Class 1') 20 | plt.plot(x2, y2, 's', color=colors[1], label='Class 2') 21 | plt.plot(xx, yy, color=colors[2], linewidth=4, label='Decision\n surface') 22 | 23 | handles, labels = ax.get_legend_handles_labels() 24 | ax.legend(handles, labels, loc=7) 25 | 26 | plt.axis('off') 27 | ax.set_ylim([-0.1, 1.1]) 28 | 29 | plt.savefig('./xor_problem.pdf',bbox_inches='tight') 30 | --------------------------------------------------------------------------------