tutorials/04_Improved_version.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TSP + QAOA - improvements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the previous part we have implemented an algorithm for solving TSP, we implemented the constraints for this problem, but the results were still not very convincing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial you will learn the following:\n",
    "\n",
    "- How to improve your QAOA algorithm\n",
    "- How to make sure that the improvements are real"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scripts.forest_tsp_solver_naive import ForestTSPSolverNaive\n",
    "import numpy as np\n",
    "from scripts import utilities\n",
    "from scripts import analysis\n",
    "from scripts import plots\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cities = np.array([[0, 4],[0, 0],[3, 0]])\n",
    "distance_matrix = utilities.get_distance_matrix(cities)\n",
    "plots.plot_cities(cities)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the most obvious and universal ways of improving the performance of an algorithm is changing it parameters. Some algorithms have very few parameters and some have a lot of them.\n",
    "We covered the parameters of QAOA in the second notebook, so if you don't remember what they are, you can come back there."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From all these parameters, there are three that we care about most for now:\n",
    "`steps`, `xtol` and `ftol`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`steps` specifies how many times we apply cost and driver operators. Higher value of `steps` should give better results, but also increase the size of our circuit and hence - runtime."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`xtol` and `ftol` are the parameters of the classical optimizer (in our case it's Nelder-Mead algorithm) we use to find the optimal values of `betas` and `gammas`. They say how small the changes should be so that we can say that our optimization converged. Generally - the smaller, the better results we should get but again, it will take more time. \n",
    "\n",
    "If you are interested, you can read more about Nelder-Mead method in the [scipy docs](https://docs.scipy.org/doc/scipy/reference/optimize.minimize-neldermead.html) or [wiki](https://en.wikipedia.org/wiki/Nelder–Mead_method)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the sake of simplicity we will assume that xtol and ftol always have the same values. We will call this parameter `tol`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we know what we are doing, please experiment with the values to find those for which we get reasonable results (defaults are `steps=1` and `xtol=ftol=10e-2`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: Fast method for expectation will be used. Noise\n",
      "                     models will be ineffective\n",
      "Solution: [0, 1, 2, 1, 2, 1, 2]\n",
      "Naive distribution: {(0, 2, 0, 2, 2): 34, (1, 2, 2, 0, 1): 12, (1, 2, 0, 2): 53, (0, 2, 1, 0): 60, (1, 1, 2, 1): 49, (1, 2, 0): 165, (0, 0, 2, 1, 2): 4, (0, 2, 1, 2, 1, 2): 18, (2, 0, 2, 0, 1): 8, (1, 0, 1, 2): 229, (0, 2, 1): 47, (1, 0, 2): 107, (1,): 37, (0, 1, 1, 1): 26, (0, 1, 2): 278, (0, 2, 0, 2): 38, (2, 0, 1, 0, 2): 24, (2, 0, 2): 99, (0, 1): 121, (0, 1, 2, 0, 1, 0, 1, 2): 57, (0, 2, 0, 1, 2, 0, 2): 34, (1, 0, 1): 63, (0, 2): 203, (0, 1, 2, 0, 1, 2, 0): 62, (1, 2, 0, 1): 62, (1, 0, 1, 0, 1): 12, (1, 2, 1, 1): 34, (0, 0): 31, (0, 1, 2, 1, 1, 2): 45, (0, 1, 0, 2, 2): 28, (1, 0, 1, 2, 2): 79, (1, 1, 0, 1, 2): 21, (0, 1, 1, 0): 49, (0, 1, 2, 2, 1, 2): 14, (0, 0, 1, 0): 34, (2, 0, 2, 0, 1, 2): 35, (0, 2, 0, 1): 78, (0, 2, 2, 0, 1): 6, (2, 0, 1): 44, (2, 0, 1, 0, 1, 2): 9, (0, 1, 2, 1, 2): 103, (0, 1, 2, 0): 116, (0, 0, 0): 83, (1, 0, 0, 1, 2): 55, (1, 1, 2, 0): 33, (0, 2, 2, 0, 2): 23, (0, 0, 0, 1, 2): 70, (1, 2, 1, 2, 0, 1, 2): 45, (1, 2, 1, 2): 56, (2,): 74, (0, 1, 1, 2): 147, (0, 1, 2, 1, 2, 2): 44, (0, 2, 1, 1): 54, (1, 2): 74, (0, 0, 1, 0, 2): 18, (2, 1, 0, 1): 27, (0, 1, 2, 2): 115, (2, 0, 1, 2): 124, (2, 2): 50, (0, 1, 2, 2, 1): 40, (2, 0, 1, 0, 1): 34, (1, 2, 2, 0, 1, 2): 72, (1, 1, 2, 0, 1, 2): 10, (0, 1, 2, 0, 2): 62, (2, 2, 1, 2): 18, (0, 0, 1, 2, 0, 2): 27, (2, 1, 2, 0, 1, 2): 64, (0, 2, 0): 44, (0, 1, 2, 1, 0, 1, 2): 17, (0, 1, 2, 0, 1, 2, 2): 49, (0, 1, 2, 0, 1, 0): 66, (0, 0, 0, 1): 7, (0, 1, 2, 1, 2, 1): 28, (1, 2, 0, 1, 2, 0, 2): 13, (2, 0, 0, 1, 2): 19, (0, 1, 0, 1): 86, (1, 2, 1): 124, (0, 2, 2, 1): 14, (1, 2, 2, 0): 29, (2, 0, 2, 2): 17, (1, 0, 1, 0): 36, (0, 1, 0, 1, 2): 153, (1, 0): 77, (0, 1, 2, 0, 2, 0): 37, (2, 0, 1, 0): 31, (0, 2, 1, 2): 76, (0, 0, 1, 1, 2): 30, (1, 2, 0, 1, 2): 237, (1, 0, 2, 0, 1, 2): 25, (2, 2, 0): 23, (2, 0): 168, (0, 1, 0, 1, 0, 1, 2): 36, (0, 2, 0, 1, 0): 52, (1, 1, 2): 109, (0, 1, 2, 0, 1, 2, 0, 1, 2): 67, (0, 0, 1, 2, 1): 20, (0, 1, 1): 127, (2, 1, 2): 75, (0,): 80, (0, 1, 2, 0, 1, 2): 90, (0, 1, 2, 2, 0, 2): 15, (0, 1, 2, 1, 2, 0, 1): 4, (0, 2, 1, 2, 0): 10, (0, 1, 2, 0, 0, 2): 13, (0, 0, 1): 61, (0, 1, 0, 2): 107, (1, 1, 2, 2): 25, (0, 0, 1, 0, 1): 27, (0, 2, 0, 1, 2, 2): 31, (1, 0, 1, 2, 0, 1, 2): 35, (0, 2, 0, 0, 1, 2): 10, (1, 0, 2, 1): 15, (0, 2, 0, 2, 0): 35, (0, 2, 0, 1, 1): 41, (1, 2, 0, 1, 2, 2): 10, (0, 1, 0, 1, 2, 0, 1, 2): 28, (0, 0, 1, 2): 49, (0, 1, 2, 1): 99, (1, 0, 1, 0, 2): 19, (2, 0, 2, 0): 2, (0, 1, 2, 0, 2, 1): 35, (1, 2, 2, 2): 16, (0, 1, 2, 2, 0, 1): 26, (0, 1, 0, 2, 0): 83, (0, 1, 0, 2, 1): 50, (0, 2, 0, 0): 40, (0, 1, 0, 1, 0): 39, (0, 0, 1, 2, 2): 37, (0, 1, 0, 2, 0, 2): 14, (1, 0, 2, 1, 2): 10, (1, 0, 0): 14, (2, 2, 1): 28, (0, 1, 2, 2, 2): 14, (0, 1, 1, 2, 1): 77, (0, 0, 2, 0): 9, (0, 1, 0, 1, 2, 0, 2): 40, (1, 1, 1): 16, (0, 0, 2): 60, (2, 1, 2, 2): 31, (0, 1, 2, 1, 2, 0, 2): 10, (0, 2, 0, 1, 2, 0, 1, 2): 28, (0, 1, 2, 0, 0): 13, (1, 2, 0, 2, 2): 91, (0, 2, 1, 1, 2): 43, (0, 1, 0, 1, 2, 0): 34, (1, 2, 0, 1, 0, 1, 2): 10, (2, 0, 1, 1, 2): 15, (0, 2, 1, 0, 1, 2): 39, (0, 2, 0, 1, 2, 0, 1): 18, (0, 2, 1, 0, 1): 10, (0, 0, 1, 1): 22, (1, 2, 2, 1): 17, (0, 1, 0): 87, (1, 2, 0, 2, 1, 2): 18, (0, 0, 1, 2, 1, 2): 13, (1, 2, 0, 1, 0, 2): 9, (1, 0, 2, 0, 1): 22, (0, 2, 2, 1, 2): 26, (2, 0, 2, 1): 26, (0, 1, 1, 0, 1): 4, (2, 1, 0, 1, 2): 16, (0, 1, 0, 0): 6, (1, 0, 1, 2, 1): 39, (1, 2, 0, 2, 0, 1, 2): 29, (0, 1, 2, 0, 1): 86, (0, 1, 0, 2, 0, 1, 2): 8, (1, 2, 0, 0, 1): 8, (0, 2, 0, 1, 1, 2): 17, (0, 0, 2, 1): 22, (0, 1, 2, 1, 0): 30, (0, 1, 0, 1, 0, 2): 20, (0, 2, 2): 45, (0, 1, 1, 2, 1, 2): 15, (2, 1): 87, (2, 2, 0, 1): 21, (0, 1, 2, 0, 2, 2): 38, (2, 1, 2, 1, 2): 14, (1, 0, 0, 1): 10, (1, 2, 0, 2, 0, 2): 34, (0, 1, 2, 0, 1, 2, 0, 2): 28, (2, 1, 2, 0): 27, (0, 1, 1, 2, 0, 1, 2): 8, (0, 2, 0, 2, 0, 1, 2): 11, (0, 1, 2, 2, 0, 1, 2): 14, (0, 0, 1, 2, 0): 31, (2, 1, 2, 1): 23, (1, 0, 1, 2, 0, 2): 16, (2, 0, 1, 1): 28, (0, 1, 2, 1, 2, 1, 2): 99, (0, 2, 0, 1, 2): 44, (0, 1, 1, 1, 2): 48, (1, 2, 0, 1, 2, 1): 18, (2, 0, 1, 2, 1): 19, (2, 0, 1, 2, 0, 1, 2): 17, (0, 2, 0, 1, 0, 2): 15, (0, 1, 0, 2, 0, 1): 24, (0, 1, 2, 0, 1, 0, 1): 22, (0, 0, 0, 2): 25, (1, 2, 1, 2, 0, 2): 19, (0, 1, 2, 0, 2, 0, 1, 2): 30, (1, 2, 0, 2, 0): 16, (0, 1, 2, 1, 2, 0): 16, (0, 2, 0, 1, 0, 1, 2): 5, (0, 1, 2, 0, 0, 1): 16, (2, 2, 2): 23, (1, 1, 2, 0, 2): 5, (1, 0, 0, 2): 7, (0, 1, 0, 1, 2, 1): 5, (0, 1, 2, 1, 0, 2): 13, (1, 2, 2, 1, 2): 27, (1, 0, 1, 2, 1, 2): 12, (1, 1, 0, 1): 17, (0, 1, 0, 1, 1): 9, (2, 0, 1, 2, 1, 2): 18, (1, 1, 2, 0, 1): 19, (1, 0, 1, 2, 0): 19, (0, 1, 0, 0, 1, 2): 15, (0, 1, 2, 0, 1, 1): 21, (0, 2, 0, 1, 0, 1): 15, (0, 2, 0, 0, 2): 10, (2, 1, 2, 0, 2): 7, (0, 1, 2, 0, 1, 2, 1, 2): 2, (1, 2, 1, 0): 16, (2, 0, 1, 2, 0, 2): 7, (0, 0, 1, 2, 0, 1): 42, (0, 2, 2, 0, 1, 2): 20, (0, 1, 2, 0, 1, 0, 2): 16, (1, 0, 1, 2, 0, 1): 18, (1, 2, 1, 0, 1): 14, (1, 2, 0, 1, 2, 0, 1, 2): 16, (2, 0, 0): 23, (0, 2, 1, 2, 2): 11, (0, 1, 0, 1, 2, 2): 8, (0, 0, 1, 0, 1, 2): 10, (0, 2, 1, 2, 1): 13, (1, 1): 28, (1, 2, 1, 2, 2): 33, (0, 2, 0, 2, 0, 1): 13, (0, 1, 1, 2, 0, 1): 8, (2, 1, 1): 5, (1, 0, 1, 0, 1, 2): 2, (0, 2, 0, 1, 2, 0): 6, (0, 1, 2, 0, 0, 1, 2): 9, (1, 0, 2, 2): 9, (2, 1, 1, 2): 9, (0, 1, 2, 1, 2, 0, 1, 2): 29, (0, 2, 1, 2, 0, 1): 8, (1, 2, 2): 11, (2, 0, 2, 1, 2): 1, (0, 1, 0, 0, 2): 13, (0, 1, 1, 0, 1, 2): 10, (0, 1, 2, 0, 1, 2, 0, 1): 2, (1, 0, 2, 0): 8, (0, 2, 0, 2, 1, 2): 7, (2, 1, 0, 2): 6, (2, 0, 1, 2, 0, 1): 3, (0, 2, 0, 2, 0, 2): 2, (0, 0, 2, 0, 2): 5, (1, 2, 1, 2, 0): 6, (0, 1, 2, 0, 1, 1, 2): 6, (2, 0, 1, 2, 2): 4, (0, 1, 1, 0, 2): 11, (0, 2, 1, 2, 0, 1, 2): 1, (2, 0, 0, 2): 6, (0, 2, 0, 1, 2, 1, 2): 4, (0, 1, 2, 1, 0, 1): 4, (0, 0, 2, 0, 1, 2): 1, (0, 1, 1, 2, 2): 10, (1, 2, 1, 0, 1, 2): 3, (1, 1, 0, 2): 7, (2, 0, 1, 2, 0): 3, (0, 1, 0, 2, 1, 2): 8, (0, 2, 0, 2, 1): 5, (0, 1, 2, 2, 0): 9, (0, 1, 0, 1, 0, 1): 5, (0, 2, 1, 2, 0, 2): 7, (1, 1, 2, 1, 2): 4, (0, 1, 2, 1, 1): 1, (0, 1, 2, 0, 2, 0, 2): 7, (1, 0, 2, 0, 2): 2, (1, 2, 0, 1, 0): 6, (0, 0, 1, 2, 0, 1, 2): 7, (2, 2, 0, 2): 5, (2, 1, 2, 0, 1): 1, (1, 2, 1, 1, 2): 2, (0, 1, 1, 2, 0): 5, (2, 2, 0, 1, 2): 5, (0, 1, 2, 0, 2, 0, 1): 7, (0, 0, 2, 2): 3, (2, 0, 2, 0, 2): 7, (0, 2, 2, 0): 2, (1, 0, 1, 1): 3, (0, 1, 2, 0, 2, 1, 2): 3, (0, 1, 1, 2, 0, 2): 7, (1, 2, 0, 1, 1): 2, (1, 2, 0, 2, 0, 1): 2, (1, 2, 0, 1, 2, 1, 2): 1, (2, 1, 0): 2, (1, 2, 0, 1, 2, 0, 1): 3, (2, 0, 0, 1): 2, (1, 2, 1, 2, 1, 2): 1, (): 1, (0, 2, 0, 0, 1): 5, (1, 2, 0, 1, 0, 1): 2, (1, 1, 1, 2): 3, (1, 2, 0, 1, 2, 0): 1, (1, 1, 0): 1, (1, 2, 0, 0, 2): 2, (0, 1, 0, 1, 1, 2): 2, (1, 2, 0, 0, 1, 2): 2, (1, 2, 1, 2, 1): 1, (0, 2, 1, 0, 2): 1, (1, 0, 1, 1, 2): 1}\n"
     ]
    }
   ],
   "source": [
    "steps = 1\n",
    "tol = 10e-2\n",
    "tsp_solver = ForestTSPSolverNaive(distance_matrix, steps=steps, xtol=tol, ftol=tol, use_constraints=True)\n",
    "solution, naive_distribution = tsp_solver.solve_tsp()\n",
    "print(\"Solution:\", solution)\n",
    "print(\"Naive distribution:\", naive_distribution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from scripts import plots\n",
    "\n",
    "states_with_probs = []\n",
    "for state in tsp_solver.sampling_results:\n",
    "    states_with_probs.append([''.join(map(str,state)), tsp_solver.sampling_results[state]/10000])\n",
    "states_with_probs = sorted(states_with_probs,key=lambda x: -x[1])\n",
    "plots.plot_state_histogram(states_with_probs[:10][::-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Are the improvements really significant?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One problem that we face here is that every time we get different result. And one time it might be a good solution, but the next time it's really crappy.\n",
    "To deal with this we need to run it multiple times to get some reasonable statistics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So I have a task for you.\n",
    "Write a funtion, which will do the following:\n",
    "    1. Run QAOA multiple times (let's say 10)\n",
    "    2. Specify the parameters of QAOA\n",
    "    3. For each run save the following results to a file:\n",
    "        - time of calculations\n",
    "        - total probability of all valid solutions\n",
    "        - cost of the best solution (if valid)\n",
    "        - probability of the best solution\n",
    "        - values of the parameters\n",
    "        - optimal cost\n",
    "\n",
    "Then we will analyze this data to determine what is the best set of parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the format of the file we want:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`steps,tol,time,valid_prob,best_prob,best_valid,best_cost,optimal_cost`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below there are a couple of functions stubs to help you start:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def analyze_singe_QAOA_run(distance_matrix, steps, tol, filename):\n",
    "    # Open proper file\n",
    "    # Run ForestTSPSolverNaive\n",
    "    # Calculate all the variables you need (time, probabilities, costs, etc.)\n",
    "    pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_probability_of_valid_solutions(sampling_results):\n",
    "    pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_if_solution_is_valid(solution):\n",
    "    pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_cost_of_solution(solution):\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you get stuck, you can check out `analysis.py` for my implementation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that you have all these functions, let's run it for given set of parameters and see how well does it perform."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# %%capture \n",
    "filename = \"results.csv\"\n",
    "# cities = utilities.create_cities(3)\n",
    "for i in range(50):\n",
    "    for steps in [1, ??, ??]:\n",
    "        for tol in [10e-2, ??, ??]:\n",
    "            print(i, steps, tol)\n",
    "            distance_matrix = utilities.get_distance_matrix(cities)\n",
    "            analysis.analyze_singe_QAOA_run(distance_matrix, steps, tol, filename)    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I know these calculations might take a long time, so if you don't want to wait, for the next step feel free to use the data I provided in `results_notebook_04.csv`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Some tips on running experiments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since you need a lot of repetitions and calculations might take a long time, there are some tips how to make it go smoother:\n",
    "\n",
    "- personally, I prefer running such calculations from the terminal, not notebook. It's easier for me to run several processes then.\n",
    "- check how many processes you can run in parallel, so they don't steal resources from each other. If your code is using a single thread it usually depends on the number of cores you have.\n",
    "- use a different filename every time you run the code. Why? Because you can accidentally erase your results if you don't change the filename. How? You can manually change the name of the file every time - but at some point you will forget to do so. I usually add a timestamp to the filename.\n",
    "- if the execution of your code may stop in the middle (e.g. because you need internet connection) or you need as much data as you can, you can use random set of parameters every time you run it. In our case, instead of writing: `for steps in [1,2,3]` you can write: `while True: steps = random.choice([1,2,3])`. This will make your program run as long as it can (e.g. all night or until crash) and after enough repetitions you will get roughly the same number of results for each parameter set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analyzing results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, that we have gathered the measurements, we can analyze them to see which set of parameters gives us reasonable results in reasonable time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "filename = \"results_notebook_04.csv\"\n",
    "results = pd.read_csv(filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "for steps in results.steps.unique():\n",
    "    for tol in results.tol.unique():\n",
    "        subset = results[results.steps==steps]\n",
    "        subset = subset[subset.tol==tol]\n",
    "        count = len(subset)\n",
    "        time = subset.time.mean()\n",
    "        best_sol_valid_prob = subset.best_valid.sum() / len(subset)\n",
    "        valid_sol_perc = subset.valid_prob.mean() * 100\n",
    "        best_sol_prob = subset.best_prob.mean()\n",
    "        print(\"steps:\", steps, \"tol:\", tol, \"count:\", count)\n",
    "        print(\"Probability of best solution being valid:\", best_sol_valid_prob)\n",
    "        print(\"Mean percentage of valid solutions:\", valid_sol_perc)\n",
    "        print(\"Probability of best solution:\", best_sol_prob)\n",
    "        print(\"Mean calculation time\", time)\n",
    "        print(\"\\n\")\n",
    "            "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also do the following for a more compact representation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>steps</th>\n",
       "      <th>tol</th>\n",
       "      <th>count</th>\n",
       "      <th>time</th>\n",
       "      <th>best_sol_valid_prob</th>\n",
       "      <th>valid_sol_perc</th>\n",
       "      <th>best_sol_prob</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0.100</td>\n",
       "      <td>50</td>\n",
       "      <td>12.841700</td>\n",
       "      <td>0.14</td>\n",
       "      <td>2.7916</td>\n",
       "      <td>0.036282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.010</td>\n",
       "      <td>50</td>\n",
       "      <td>12.231217</td>\n",
       "      <td>0.16</td>\n",
       "      <td>3.6626</td>\n",
       "      <td>0.028970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0.001</td>\n",
       "      <td>50</td>\n",
       "      <td>10.992243</td>\n",
       "      <td>0.12</td>\n",
       "      <td>2.9140</td>\n",
       "      <td>0.026822</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>0.100</td>\n",
       "      <td>50</td>\n",
       "      <td>10.540390</td>\n",
       "      <td>0.16</td>\n",
       "      <td>2.7670</td>\n",
       "      <td>0.023370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>0.010</td>\n",
       "      <td>50</td>\n",
       "      <td>11.941149</td>\n",
       "      <td>0.18</td>\n",
       "      <td>3.1754</td>\n",
       "      <td>0.023816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2</td>\n",
       "      <td>0.001</td>\n",
       "      <td>50</td>\n",
       "      <td>10.634088</td>\n",
       "      <td>0.16</td>\n",
       "      <td>3.3540</td>\n",
       "      <td>0.027508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3</td>\n",
       "      <td>0.100</td>\n",
       "      <td>50</td>\n",
       "      <td>9.769331</td>\n",
       "      <td>0.10</td>\n",
       "      <td>3.1338</td>\n",
       "      <td>0.024058</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3</td>\n",
       "      <td>0.010</td>\n",
       "      <td>50</td>\n",
       "      <td>13.200291</td>\n",
       "      <td>0.16</td>\n",
       "      <td>3.1818</td>\n",
       "      <td>0.030872</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3</td>\n",
       "      <td>0.001</td>\n",
       "      <td>50</td>\n",
       "      <td>11.099619</td>\n",
       "      <td>0.14</td>\n",
       "      <td>3.0058</td>\n",
       "      <td>0.024244</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   steps    tol  count       time  best_sol_valid_prob  valid_sol_perc  \\\n",
       "0      1  0.100     50  12.841700                 0.14          2.7916   \n",
       "1      1  0.010     50  12.231217                 0.16          3.6626   \n",
       "2      1  0.001     50  10.992243                 0.12          2.9140   \n",
       "3      2  0.100     50  10.540390                 0.16          2.7670   \n",
       "4      2  0.010     50  11.941149                 0.18          3.1754   \n",
       "5      2  0.001     50  10.634088                 0.16          3.3540   \n",
       "6      3  0.100     50   9.769331                 0.10          3.1338   \n",
       "7      3  0.010     50  13.200291                 0.16          3.1818   \n",
       "8      3  0.001     50  11.099619                 0.14          3.0058   \n",
       "\n",
       "   best_sol_prob  \n",
       "0       0.036282  \n",
       "1       0.028970  \n",
       "2       0.026822  \n",
       "3       0.023370  \n",
       "4       0.023816  \n",
       "5       0.027508  \n",
       "6       0.024058  \n",
       "7       0.030872  \n",
       "8       0.024244  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "analysis_array = []\n",
    "for steps in results.steps.unique():\n",
    "    for tol in results.tol.unique():\n",
    "            subset = results[results.steps==steps]\n",
    "            subset = subset[subset.tol==tol]\n",
    "            count = len(subset)\n",
    "            time = subset.time.mean()\n",
    "            best_sol_valid_prob = subset.best_valid.sum() / len(subset)\n",
    "            valid_sol_perc = subset.valid_prob.mean() * 100\n",
    "            best_sol_prob = subset.best_prob.mean()\n",
    "            analysis_array.append([steps, tol, count, time, best_sol_valid_prob, valid_sol_perc, best_sol_prob])\n",
    "\n",
    "analysis_df = pd.DataFrame(analysis_array, columns=['steps', 'tol', 'count', 'time', 'best_sol_valid_prob', 'valid_sol_perc', 'best_sol_prob'])\n",
    "display(analysis_df)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_color_map(result_name):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.set_yscale('log')\n",
    "    scatter_plot = ax.scatter(analysis_df.steps, analysis_df.tol, s=200, c=analysis_df[result_name], cmap='plasma')\n",
    "    cbar = fig.colorbar(scatter_plot)\n",
    "    ax.set_xlabel(\"steps\")\n",
    "    ax.set_ylabel(\"tol\")\n",
    "    ax.set_title(result_name + \" for different parameters\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_color_map('time')\n",
    "plot_color_map('best_sol_valid_prob')\n",
    "plot_color_map('valid_sol_perc')\n",
    "plot_color_map('best_sol_prob')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, based on the results above, you can choose what parameters are the best :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Warning / I'm sorry"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These results are not as good as they have been with the previous version of this algorithm I was working on. Frankly, they are extremely crappy. I think this is due to a bug somewhere, but I was unable to find it. For one set of parameters the best solution was valid around 75% of the time, and for the same parameters here - well it's around 15%.\n",
    "\n",
    "I'm really sorry for that, but I decided that I prefer to publish this imperfect version, rather than wait until I find the bug."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fixing starting city"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is another thing we can do to hugely improve how well our algorithm works.\n",
    "If we know from which city we start (and we do), we can introduce that straight into our cost operators and hence reduce number of qubits we need to use from N^2 to (N-1)^2.\n",
    "\n",
    "Let's take look at the example. Let's say we have 4 cities and we know that we always start from city 0.\n",
    "\n",
    "Hence all the valid strings should start with [1,0,0,0,...].\n",
    "\n",
    "This allows us to use representation for 3 cities and simply include cost to the 1st city in the cost operator.\n",
    "\n",
    "So if we know that the first city is always the 0-th one, instead of having bitstring: [1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1], we get [1,0,0, 0,1,0, 0,0,1]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are three ways you can proceed now:\n",
    "\n",
    "1. Figure it out by yourself\n",
    "2. Follow my tips\n",
    "3. Take a look at my code and reproduce it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Figure it out by yourself"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make a copy of `scripts/forest_tsp_solver_naive.py` and solve it by yourself :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Follow my tips"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. You need to exclude the first city from all your calculations\n",
    "2. In `create_weights_cost_operators` you need to add costs of travelling to the first city.\n",
    "3. Make sure you decode your solution properly! I have created `binary_state_to_points_order_with_fixed_start` method for that."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Take a look at my code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "My approach to this problem is inside `scripts/forest_tsp_solver_improved.py`. Feel free to check it out if you get stucked, but remember - the more time you spend by trying to do it by yourself, the more you will learn out of it :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finally"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After you have finished, import your new class and "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: Fast method for expectation will be used. Noise\n",
      "                     models will be ineffective\n",
      "Solution: [0, 1, 2, 3, 3]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from scripts.forest_tsp_solver_improved import ForestTSPSolverImproved\n",
    "from scripts import utilities\n",
    "from scripts import plots\n",
    "\n",
    "steps = 3\n",
    "tol = 10e-3\n",
    "\n",
    "cities = utilities.create_cities(4)\n",
    "distance_matrix = utilities.get_distance_matrix(cities)\n",
    "tsp_solver = ForestTSPSolverImproved(distance_matrix, steps=steps, xtol=tol, ftol=tol, use_constraints=True)\n",
    "solution, _ = tsp_solver.solve_tsp()\n",
    "print(\"Solution:\", solution)\n",
    "\n",
    "states_with_probs = []\n",
    "for state in tsp_solver.sampling_results:\n",
    "    states_with_probs.append([''.join(map(str,state)), tsp_solver.sampling_results[state]/10000])\n",
    "states_with_probs = sorted(states_with_probs,key=lambda x: -x[1])\n",
    "plots.plot_state_histogram(states_with_probs[:10][::-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With all that you have already learned, it's time for you to experiment.\n",
    "Here are some propositions for that:\n",
    "- see how much better results you can get from the \"improved\" version - do a proper analysis, as we did!\n",
    "- for the analysis print out not only mean, but also standard deviation - this will give you a better picture.\n",
    "- try running it for different types and si"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary and next steps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we learned?\n",
    "- how to tune parameters for QAOA\n",
    "- how to use a more compact encoding for TSP\n",
    "- how to check if the changes we did are really valid\n",
    "\n",
    "What's next?\n",
    "- using ACADEMIC PAPERS to get really awesome results!\n",
    "\n",
    "**Update (2023):**\n",
    "\n",
    "After 4.5 years I found that some people still find this repo useful – that's great :)\n",
    "I have absolutely no intention of updating or fixing anything here, it's been way too long.\n",
    "However, in the meantime I've written a series of articles on the topic of variational quantum algorithms and QAOA specifically. You can find the first post here: https://www.mustythoughts.com/variational-quantum-eigensolver-explained :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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