First git Initialize

.gitignore

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+.ipynb_checkpoints
+./nickel/Solutions
+.vscode
+.venv
+.git

README.md

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+# QNickel
+
+Welcome to QNickel, a repository dedicated to exploring quantum computing with the Qiskit framework using the Nickel quantum processor.
+
+## Overview
+
+QNickel provides a collection of quantum programs and examples that demonstrate various concepts and algorithms in quantum computing. Whether you are a beginner or an experienced quantum programmer, this repository aims to provide you with a hands-on learning experience.Solutions added
+
+## Getting Started
+
+To get started with QNickel, follow these steps:
+
+1. Clone the repository: `git clone https://github.com/qworld/qnickel.git`
+2. Install the required dependencies: `pip install -r requirements.txt`
+3. Explore the examples and programs in the repository.
+4. Run the programs using the Nickel quantum processor.
+
+## Contents
+
+The repository is organized into the following directories:
+
+- `examples`: Contains a collection of example programs showcasing different quantum algorithms and concepts.
+- `tutorials`: Provides step-by-step tutorials to help you understand and implement quantum algorithms.
+- `resources`: Includes additional resources such as papers, articles, and presentations related to quantum computing.
+
+## Contributing
+
+We welcome contributions from the community to enhance QNickel. If you have any ideas, bug fixes, or improvements, feel free to open an issue or submit a pull request.
+
+## License
+
+QNickel is licensed under the [MIT License](LICENSE).

content.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<table width=\"100%\"><tr style=\"background-color:white;\">\n",
+    "    <td style=\"text-align:left;padding:0px;width:142px'\">\n",
+    "        <a href=\"https://qworld.net\" target=\"_blank\">\n",
+    "            <img src=\"qworld/images/QWorld.png\"></a></td>\n",
+    "    <td width=\"*\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</td>\n",
+    "    <!-- ############################################# -->\n",
+    "    <td style=\"padding:0px;width:90px;\">\n",
+    "        <img align=\"right\" src=\"qworld/images/follow_us.png\" height=\"40px\"></td>\n",
+    "    <td style=\"padding:0px;width:40px;\">\n",
+    "        <a href=\"https://twitter.com/QWorld19\" target=\"_blank\">\n",
+    "        <img align=\"right\" src=\"qworld/images/Twitter.png\" width=\"40px\"></a> </td>\n",
+    "    <td style=\"padding:0px;width:5px;\"></td>\n",
+    "    <td style=\"padding:0px;width:40px;\">\n",
+    "        <a href=\"https://www.facebook.com/qworld19/\" target=\"_blank\">\n",
+    "        <img align=\"right\" src=\"qworld/images/Fb.png\"></a></td>\n",
+    "    <td style=\"padding:0px;width:5px;\"></td>\n",
+    "    <td style=\"padding:0px;width:40px;\">\n",
+    "        <a href=\"https://www.linkedin.com/company/qworld19\" target=\"_blank\">\n",
+    "        <img align=\"right\" src=\"qworld/images/LinkedIn.png\"></a></td>\n",
+    "    <td style=\"padding:0px;width:5px;\"></td>\n",
+    "    <td style=\"padding:0px;width:40px;\">\n",
+    "        <a href=\"https://youtube.com/QWorld19?sub_confirmation=1\" target=\"_blank\">\n",
+    "        <img align=\"right\" src=\"qworld/images/YT.png\"></a></td>\n",
+    "    <!-- ############################################# -->\n",
+    "    <td style=\"padding:0px;width:60px;\">\n",
+    "        <img align=\"right\" src=\"qworld/images/join.png\" height=\"40px\"></td>\n",
+    "    <td style=\"padding:0px;width:40px;\">\n",
+    "        <a href=\"https://discord.com/invite/akCvr7U87g\"\n",
+    "           target=\"_blank\">\n",
+    "        <img align=\"right\" src=\"qworld/images/Discord.png\"></a></td>\n",
+    "    <!-- ############################################# -->\n",
+    "    <td style=\"padding:0px;width:72px;\">\n",
+    "        <img align=\"right\" src=\"qworld/images/w3.png\" height=\"40px\"></td>\n",
+    "    <td style=\"padding:0px;width:40px;\">\n",
+    "        <a href=\"https://qworld.net\" target=\"_blank\">\n",
+    "        <img align=\"right\" src=\"qworld/images/www.png\"></a></td>\n",
+    "</tr></table>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<h1 align=\"center\" style=\"color: #A9A9A9;\"> Welcome to QWorld's Nickel </h1>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<font style=\"color: #A9A9A9;size:+1;\"><b>Nickel</b></font> is the continuation of our introductory material Bronze about the basics of quantum computation and quantum programming. It is a big collection of [Jupyter notebooks](https://jupyter.org).\n",
+    "\n",
+    "In Nickel, we focus on oracular quantum algorithms.\n",
+    "\n",
+    "*If you are using Jupyter notebooks for the first time, you can check our very short <a href=\"python/R00_Intro_to_Notebooks.ipynb\" target=\"_blank\">Introduction for Notebooks</a>.*\n",
+    "\n",
+    "**The open-source toolkits we are using:**\n",
+    "- Programming language: <a href=\"https://www.python.org\" target=\"_blank\">python</a>\n",
+    "- Quantum programming libraries:</u> <a href=\"https://qiskit.org\" target=\"_blank\">Qiskit</a>, and <a href=\"https://github.com/quantumlib/Cirq\" target=\"_blank\">Cirq</a>\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Installation and Test\n",
+    "\n",
+    "_Python libraries including quantum ones are often updated. Therefore, there might appear some problems due to different versions._\n",
+    "\n",
+    "Before starting to use Nickel, please test your system by using the following notebook(s)!\n",
+    "\n",
+    "[Qiskit installation and test](test/Qiskit_installation_and_test.ipynb) \n",
+    "\n",
+    "[Cirq installation and test](test/Cirq_installation_and_test.ipynb) "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Reference notebboks\n",
+    "\n",
+    "[Python Reference](nickel/R01_Python_Reference.ipynb) &nbsp;|&nbsp;\n",
+    "[Python: Drawing](nickel/R02_Python_Drawing.ipynb) \n",
+    "\n",
+    "<hr>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Conventional Quantum Algorithms in Qiskit\n",
+    "[Introduction to Qiskit](nickel/A00_Qiskit_Introduction.ipynb)\n",
+    "\n",
+    "[Classical gates](nickel/A01_Classical_Gates.ipynb) &nbsp;|&nbsp;\n",
+    "[Phase kickback](nickel/A02_Phase_Kickback.ipynb) &nbsp;|&nbsp;\n",
+    "[Deutsch Algorithm](nickel/A03_Deutsch_Algorithm.ipynb)\n",
+    "\n",
+    "[Deutsch-Jozsa Algorithm](nickel/A04_Deutsch_Jozsa_Algorithm.ipynb) &nbsp;|&nbsp;\n",
+    "[Bernstein-Vazirani Algorithm](nickel/A05_Bernstein_Vazirani_Algorithm.ipynb) &nbsp;|&nbsp;\n",
+    "[Simon's Algorithm](nickel/A06_Simons_Algorithm.ipynb)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Solving Max-Cut problem using Grover's Search in Cirq\n",
+    "\n",
+    "[Introduction to Cirq](nickel/D00_Cirq_Introduction.ipynb)&nbsp;|&nbsp;\n",
+    "[Grover Algorithm revisited](nickel/B01_Grover_Algorithm_Revisited.ipynb)\n",
+    "\n",
+    "[Max-Cut Problem and Bipartite Graphs](nickel/B02_Max_Cut_Problem.ipynb) &nbsp;|&nbsp;\n",
+    "[Adders and Numbers Checking](nickel/B03_Adders_And_Numbers_Checking.ipynb)\n",
+    "\n",
+    "[Grover algorithm for Max-Cut Problem](nickel/B04_Grover_Algorithm_For_Max-Cut_Problem.ipynb)\n",
+    "<hr>\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "[Credits](nickel/N00_Credits.ipynb)\n",
+    "[References](nickel/N01_References.ipynb)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}

include/drawing.py

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+import matplotlib.pyplot as plt
+
+# drawing used for math
+
+def plot_2D_plane(right=5,up=5,left=-5,down=-5,fsize=(8,8)):
+    hpoints, vpoints = [],[]
+    for i in range(left,right+1):
+        if i!=0: hpoints.append(i)
+    for i in range(down,up+1):
+        if i!=0: vpoints.append(i)
+
+    ax = plt.figure(figsize=fsize).gca()
+
+    # Set identical scales for both axes
+    ax.set(xlim=(left-1,right+1), ylim=(down-1, up+1), aspect='equal')
+    # Remove top and right spines
+    ax.spines['top'].set_visible(False)
+    ax.spines['right'].set_visible(False)
+    # Set bottom and left spines as x and y axes of coordinate system
+    ax.spines['bottom'].set_position('zero')
+    ax.spines['left'].set_position('zero')
+    # Create minor ticks placed at each integer to enable drawing of minor grid
+    ax.set_xticks(hpoints)
+    ax.set_yticks(vpoints)
+    # Draw major and minor grid lines
+    ax.grid(which='both', color='grey', linewidth=1, linestyle='-', alpha=0.2)
+    # Create 'x' and 'y' labels placed at the end of the axes
+    ax.set_xlabel('x', size=14, labelpad=-24, x=1.03)
+    ax.set_ylabel('y', size=14, labelpad=-21, y=1.02, rotation=0)
+    # Draw arrows
+    arrow_fmt = dict(markersize=4, color='black', clip_on=False)
+    ax.plot((1), (0), marker='>', transform=ax.get_yaxis_transform(), **arrow_fmt)
+    ax.plot((0), (0), marker='<', transform=ax.get_yaxis_transform(), **arrow_fmt)
+    ax.plot((0), (1), marker='^', transform=ax.get_xaxis_transform(), **arrow_fmt)
+    ax.plot((0), (0), marker='v', transform=ax.get_xaxis_transform(), **arrow_fmt)
+
+def draw_sides(x=1,y=2,side_color="b",lwidth=1):
+    plt.arrow(x,0,0,y,color=side_color,linestyle="dotted",width=0.001*lwidth)
+    plt.arrow(0,y,x,0,color=side_color,linestyle="dotted",width=0.001*lwidth)
+
+def draw_vector(x=1,y=2,vname="v",show_name=True,vcolor="b",sides=False,side_color="b",lwidth=1):
+    plt.quiver(0,0,x,y,scale=1,scale_units='xy',angles = 'xy',color=vcolor,width=0.008*lwidth)
+    dx = x
+    if y<0: dy=y-0.3
+    else: dy = y+0.3
+
+    if show_name:
+        vector_name="$"+vname+"=("+str(x)+","+str(y)+")$"
+        plt.text(dx,dy,vector_name,color=vcolor)
+
+    if sides:
+        draw_sides(x,y,side_color)
+
+def place_text(x,y,text,tcolor="blue"):
+    plt.text(x,y,text,color=tcolor)
+
+def show_plt():
+    plt.show()
+
+# drawing used for quantum
+def draw_axes():
+	points = [ [1.2,0], [0,1.2], [-1.2,0], [0,-1.2] ] # dummy points for zooming out
+	arrows = [ [1.1,0], [0,1.1], [-1.1,0], [0,-1.1] ] # coordinates for the axes
+	for p in points: 
+		plt.plot(p[0],p[1]+0.1) # drawing dummy points
+	for a in arrows: 
+		plt.arrow(0,0,a[0],a[1],head_width=0.04, head_length=0.08) # drawing the axes
+
+
+def draw_unit_circle():
+    unit_circle= plt.Circle((0,0),1,color='black',fill=False)
+    plt.gca().add_patch(unit_circle)
+
+def draw_quantum_state(x,y,name):
+	# shorten the line length to 0.92
+	# line_length + head_length should be 1
+	x1 = 0.92 * x
+	y1 = 0.92 * y
+	plt.arrow(0,0,x1,y1,head_width=0.04,head_length=0.08,color="blue")
+	x2 = 1.15 * x
+	y2 = 1.15 * y
+	plt.text(x2,y2,name)
+
+def draw_qubit():
+	# draw a figure
+	plt.figure(figsize=(6,6), dpi=60)
+	# draw the origin
+	plt.plot(0,0,'ro') # a point in red color
+	# drawing the axes by using one of our predefined function
+	draw_axes()
+	# drawing the unit circle by using one of our predefined function
+	draw_unit_circle()
+	# drawing |0>
+	plt.plot(1,0,"o")
+	plt.text(1.05,0.05,"|0>")
+	# drawing |1>
+	plt.plot(0,1,"o")
+	plt.text(0.05,1.05,"|1>")
+	# drawing -|0>
+	plt.plot(-1,0,"o")
+	plt.text(-1.2,-0.1,"-|0>")
+	# drawing -|1>
+	plt.plot(0,-1,"o")
+	plt.text(-0.2,-1.1,"-|1>")
+
+def draw_qubit_grover():
+	# draw a figure
+	plt.figure(figsize=(7,7), dpi=60)
+	# draw the origin
+	plt.plot(0,0,'ro') # a point in red color
+	# drawing the axes by using one of our predefined function
+	draw_axes()
+	# drawing the unit circle by using one of our predefined function
+	draw_unit_circle()
+	# drawing |0>
+	plt.plot(1,0,"o")
+	plt.text(1.05,0.05,"|unmarked>")
+	# drawing |1>
+	plt.plot(0,1,"o")
+	plt.text(0.05,1.05,"|marked>")
+	# drawing -|0>
+	plt.plot(-1,0,"o")
+	plt.text(-0.98,-0.09,"-|unmarked>")
+	# drawing -|1>
+	plt.plot(0,-1,"o")
+	plt.text(-0.4,-1.1,"-|marked>")

include/helpers.py

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+
+def contFrac(N):
+    import math
+    cf=[]
+    while True:
+        cf.append(int(N))
+        f = N - N//1
+        if f < 0.0001:  # or whatever precision you consider close enough to 0
+            break
+        N = 1/f
+        if(math.ceil(N)-N<0.0001):
+            N=round(N)
+    return cf
+
+
+def convergents(cf):
+    from fractions import Fraction 
+    c=[] 
+    cv=[]
+
+    for i in range(len(cf)):
+        c.append(cf[i])
+        for j in range(i-1,-1,-1):
+            c[i] = 1/c[i]+ cf[j]
+        cv.append(Fraction(c[i]).limit_denominator(10000))
+    return cv