{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note: This section is still in a draft form.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Section 4: Procedural generation with arbitrarily many qubits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Import standard things."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit, execute, Aer\n",
    "from math import pi\n",
    "from tools import plot_height"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We will use randomness at some point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We will be using real quantum devices.\n",
    "* They are currently not fault-tolerant, so there will be imperfections.\n",
    "* While designing our method, we'll simulate this 'noise'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.providers.aer.noise import NoiseModel\n",
    "from qiskit.providers.aer.noise.errors import pauli_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* To mitigate for it, we'll be using some maths!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.linalg as la\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* This function creates a noise model, in which outputs on each qubit lie with the given probability `p`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_noise(p):\n",
    "\n",
    "    error_meas = pauli_error([('X',p), ('I', 1 - p)])\n",
    "\n",
    "    noise_model = NoiseModel()\n",
    "    noise_model.add_all_qubit_quantum_error(error_meas, \"measure\")\n",
    "        \n",
    "    return noise_model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We'll have the lies happen 1/10th of the time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise_model = get_noise(0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The folloqing function takes a given list of circuits and runs it on the given backend (simulator by default).\n",
    "* The simulation uses a noise model if one is given.\n",
    "* In addition to the circuits given in `circuits`, two additional circuits are run: one for which all outputs should be `0`, and one for which all should be `1`.\n",
    "* The results from these are used to clean up the results from other circuits, using the same method as standard Qiskit measurement error mitigation.\n",
    "* For each circuit in `circuits`, the probability that each qubit outputs a `1` is calculated (and cleaned up).\n",
    "* These are compiled into a list `p` for each circuit, for which the probability `p[j]` refers to qubit `j`.\n",
    "* The output `probs` contains these lists for each circuit, with `probs[k]` containing the `p` for the `k`th circuit.\n",
    "* The output `raw_probs` contains the same lists of probabilities, but without the error mitigation. The results for the all `0` and all `1` circuits are also appended to this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_probs(circuits,backend=Aer.get_backend('qasm_simulator'),noise_model=None):\n",
    "    \n",
    "    def get_raw_p(counts):\n",
    "\n",
    "        n = len(list(counts.keys())[0])\n",
    "        shots = sum(counts.values())\n",
    "\n",
    "        p = [0]*n\n",
    "        for bitstring in counts:\n",
    "            for j in range(n):\n",
    "                if bitstring[::-1][j]=='1':\n",
    "                    p[j] += counts[bitstring]/shots\n",
    "\n",
    "        return p\n",
    "\n",
    "    n = circuits[0].n_qubits\n",
    "\n",
    "    qc0 = QuantumCircuit(n,n)\n",
    "    qc1 = QuantumCircuit(n,n)\n",
    "    for j in range(n):\n",
    "        qc0.measure(j,j)\n",
    "        qc1.x(j)\n",
    "        qc1.measure(j,j)\n",
    "\n",
    "    benchmarks = [qc0,qc1]\n",
    "\n",
    "    if noise_model:\n",
    "        result = execute(circuits+benchmarks,backend,noise_model=noise_model,shots=8192).result()\n",
    "    else:\n",
    "        result = execute(circuits+benchmarks,backend,shots=8192).result()\n",
    "        \n",
    "    p0 = get_raw_p(result.get_counts(-2))\n",
    "    p1 = get_raw_p(result.get_counts(-1))\n",
    "\n",
    "    Minv = []\n",
    "    for j in range(n):\n",
    "        Minv.append( la.pinv( [[1-p0[j],1-p1[j]],[p0[j],p1[j]]] ) ) \n",
    "\n",
    "    raw_probs = []\n",
    "    probs = []\n",
    "    raw_probs = []\n",
    "    for k in range(len(circuits)):\n",
    "        mitigated_p = []\n",
    "        raw_p = get_raw_p(result.get_counts(k))\n",
    "        for j in range(n):\n",
    "            p = np.dot( Minv[j], [1-raw_p[j],raw_p[j]] )[1]\n",
    "            p = min(max(p,0),1)\n",
    "            mitigated_p.append( p )\n",
    "        probs.append( mitigated_p )\n",
    "        raw_probs.append( raw_p  )\n",
    "    raw_probs.append( get_raw_p(result.get_counts(-2))  )\n",
    "    raw_probs.append( get_raw_p(result.get_counts(-1))  )\n",
    "        \n",
    "    return probs, raw_probs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Let's see it in action.\n",
    "* We will run circuits that should output all `0`s and all `1`s (`get_probs` will still run its own versions of these)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/scipy/linalg/basic.py:1321: RuntimeWarning: internal gelsd driver lwork query error, required iwork dimension not returned. This is likely the result of LAPACK bug 0038, fixed in LAPACK 3.2.2 (released July 21, 2010). Falling back to 'gelss' driver.\n",
      "  x, resids, rank, s = lstsq(a, b, cond=cond, check_finite=False)\n"
     ]
    }
   ],
   "source": [
    "n = 4\n",
    "\n",
    "qc0 = QuantumCircuit(n,n)\n",
    "qc0.measure(qc0.qregs[0],qc0.cregs[0])\n",
    "\n",
    "qc1 = QuantumCircuit(n,n)\n",
    "qc1.x(qc1.qregs[0])\n",
    "qc1.measure(qc1.qregs[0],qc1.cregs[0])\n",
    "\n",
    "probs, raw_probs = get_probs([qc0,qc1],noise_model=noise_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* For the first circuit, the probability that the four qubits will output `1` should be zero.\n",
    "* Let's see what we find from the raw results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.1014404296875, 0.0947265625, 0.099609375, 0.099365234375]\n"
     ]
    }
   ],
   "source": [
    "print(raw_probs[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Around 10% take the wrong value, due to the measurement errors.\n",
    "* Now let's see what they are after clean up."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.0009215174320381936, 0, 0, 0.006853487663722069]\n"
     ]
    }
   ],
   "source": [
    "print(probs[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Much closer to zero!\n",
    "* Now let's look at results for the second circuit, where the output should be `1` with certainty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.9005126953125, 0.90185546875, 0.9002685546875, 0.9005126953125]\n"
     ]
    }
   ],
   "source": [
    "print(raw_probs[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The correct result again comes out only around 90% of the time.\n",
    "* Again, let's look at the same after clean up."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 1, 1, 1]\n"
     ]
    }
   ],
   "source": [
    "print(probs[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* This error mitigation again gives us a result that is much closer to the value we'd find without noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We'll be using the 53 qubit *Rochester* device.\n",
    "* Each qubit will be used to encode a pixel,  so we need a mapping between qubits and positions.\n",
    "* The dictionary below defines the mapping we'll use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "rochester = {\n",
    "    (2,1):5,(6,1):6,(2,5):28,(6,5):29,(2,7):51,(6,7):52,\n",
    "    (0,3):16,(4,3):17,(8,3):18,(0,7):39,(4,7):40,(8,7):41}\n",
    "for j in range(0,5):\n",
    "    rochester[2+j,0] = j\n",
    "for j in range(7,16):\n",
    "    rochester[j-7,2] = j\n",
    "for j in range(19,28):\n",
    "    rochester[j-19,4] = j\n",
    "for j in range(30,39):\n",
    "    rochester[j-30,6] = j\n",
    "for j in range(42,51):\n",
    "    rochester[j-42,8] = j"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The probability for a `1` on each qubit will be used as the height for a height map.\n",
    "* A 9x9 grid is used, so some positions have no qubit.\n",
    "* To show this, here is a heightmap that has `height[x,y]=1` wherever there is a qubit, and has no entry otherwise (implying a height of zero)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "height = {}\n",
    "for x in range(9):\n",
    "    for y in range(9):\n",
    "        if (x,y) in rochester:\n",
    "            height[x,y] = 1\n",
    "    \n",
    "plot_height(height,color_map='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The following function takes a list of probabilities, `p`, from a device whose mapping between qubits and positions is specified by `device`.\n",
    "* To fill in the gaps, each pixel without a value is set to the average of its valued neighbours."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_height(p,device):\n",
    "    \n",
    "    L = max(max(device.keys()))+1\n",
    "    \n",
    "    height = {}\n",
    "    for pos in device:\n",
    "        height[pos] = p[device[pos]]\n",
    "    \n",
    "    all_full = False\n",
    "    while not all_full:\n",
    "        all_full = True\n",
    "        extra_height = {}\n",
    "        for x in range(L):\n",
    "            for y in range(L):\n",
    "                if (x,y) not in height:\n",
    "                    total = 0\n",
    "                    num = 0\n",
    "                    for (dx,dy) in [(0,1),(0,-1),(1,0),(-1,0)]:\n",
    "                        if (x+dx,y+dy) in height:\n",
    "                            total += height[x+dx,y+dy]\n",
    "                            num += 1\n",
    "                    if num==0:\n",
    "                        all_full = False\n",
    "                    else:\n",
    "                        extra_height[x,y] = total/(num)\n",
    "        for pos in extra_height:\n",
    "            height[pos] = extra_height[pos]\n",
    "                            \n",
    "    return height"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We can now take results from a device and display them as a height map.\n",
    "* The following function does the opposite: takes a height map and turns it into a quantum circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def height2circuit_temp_1(height,device,limit=np.Inf):\n",
    "    \n",
    "    n = min( len(device), limit )\n",
    "    \n",
    "    qc = QuantumCircuit(n,n)\n",
    "    \n",
    "    for pos in height:\n",
    "        if pos in device:\n",
    "            j = device[pos]\n",
    "            if j<limit:\n",
    "                qc.ry(2*np.arcsin(np.sqrt(height[pos])),j)\n",
    "                qc.measure(j,j)\n",
    "        \n",
    "    return qc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We will test it all with the following height map."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "height_initial = {}\n",
    "L = 9\n",
    "for x in range(L):\n",
    "    for y in range(L):\n",
    "        height_initial[x,y] = (1 + np.cos( np.sqrt( (x-(L-1)/2)**2 + (y-(L-1)/2)**2 )/(L/5) ) )/2\n",
    "        height_initial[x,y] = height_initial[x,y]*(1 + np.cos( ( abs(x+(L-1)/2) + abs(y-(L-1)/2) )/((L-1)/5) ) )/2\n",
    "        \n",
    "plot_height(height_initial)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We'll first simulate it.\n",
    "* Since 53 qubits is too many to simulate, we'll use a subset of 27.\n",
    "* This is what the `limit` keyword is for in the above function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xFfFZPY8+X7Q180x4WS/jCYL7EsF9LGtoz56zN8IzJ2j1rqSvVtFn62fN1fPV41rNPJ/1hyKsxqRbnOXx1tbnzhrckbtMzfza6uBGDu3b726i82X/x/I9smoabv26swnYevrteVyre8+Xac2sMekS3cII7n0E93he/9s2joa2hVaMZ0JsFeHR+IrkOPYbac1MdDFkt+CKtEV39+BqXZrT8zyWob2SMcRnj7c69tsTVatLj1rDq3HTDKILVVmCK+I75e4a3OihFdGP7RmNEHtFeDTA0aff6GvmkfByItWmll0zO4Dg2gRX80YTUUL7xa//75P/+8fv/9L1Wlev2xvie7/X1hD3nKB1dr/p4+9B74lXIh//7o2eeHX7uJbH3vva518zfbeqJPdmZtItxDq4EdfKBPf262pNtM9De2UmxPesmohPp1ujY79aJ171PDbrmnl20iW6RRDc+whum6yhvZI5xJeBDbx6bn1s5DUz0cVDBPc+gnuuamivRAtxS4QrT7+t4Z09m1nkfniJLrp4HMNteQ2Ce/1rEYIb5RKf3tC++vLp38G3311/FFsP7RCLjMf4LMIVp9/Ia+ae8BLdDewYXBGd6O4U3CihFemL7fPQXr+XWiG+moBHp9/Vlx21htfzs3eJLi6VC66I25S7Q3B3Ce0V7RCLrFlPV5p+H/1axDWzRXQ/bXkQYsl0WVAzgvv01waD+/bbH7uP1bYG9+13/9O9Ql4Z3OM5tZ+39/d1peX7evZnNPWpT6d/z8avnW69r3m0537O4mct0cVd0dbKWsdxR2QKbo8o021G3tOuxkcX3n/d8U9SOqN9z2av5/ZAdJMpOeU6GZ1yR0Q4aepMxOBarIItnjfa2c8zZzafP+/4mc29eo7p3vPwmO4dqz+BiOjihYpTrvdaeYTXMdyIwcVjM8dzz8wczz3TezzX7L7Phnenmhl+iG4iUU6eiiZacEen3FEE97HsU67VPZ5n1sraJ1DdMz3lBr4dJNFFt2hT7qhIwfU4jpshuJqRzB7cy68vulbWeOwjq1fLInzgQRo7TrmWa2WC+1jku0lVYX2Z0Plrx1grP7Jiyr36YHtNRDeBSMH1vhHGGYJ7rdLtG3tEnnJng3v5/BNBPuNxXW7Pc/ScPCUSY8oVYb2MDq2fkavBcq38SJbgtsoa3NlgWp0FrUHjAxNWTLnaa+VHem6GcVfgY7kHohtcpCm3hcaUu2qtPCLq3aayBjcirSm3NbgRT546Yz3l3tM75VoY/blJdDfHWnnu10ZcfQj96dduEtzRaTXyWllDtJOntI7jithOuVFWyyJEN7QoH9nnaXatnOE47pnZ47gVgjuqwlo52slTFmtlzxthaND+OUl0N9XzFynTlKv5fJGO4xJcf6yVz2lOudPPkeBY7oHoBhVxCrV2NeVqr5WzBLdFxeD2TK5R18pawa2yVl4x5V6tlj0vFxLhkqGQIq2VvaZc77VypuBq3nO5wl2mnou6VvYI7vV7iL1W1nhspilXhEl3O1kn6JG18i7B7flovh4ZgmtBY8rVuDSo6XWSr5Wz3+5x5Ocp0Q3GMoq9zx1lyp25t7IWgrvG1RQbda3caue1ssZjr0Q6a/lAdDeRdcK94rVWHhHl0qCswb3CWvnsPdjc6nHEo4hmn3JHEd1AIoUxw5Qb/TjuGa8TpyoE1yuunmvl2Q+lz/wJQmc0bvcYHdHdQKSY35pdK/eodBx3p+A+EnGtrBnc6mtlj9s9RlwtixDdMKzCOPK8ka7LfUTrNo/ZgtuK4PryCu71+4i/Vu5hPeV6Xy4kQnRLWzrhJlgrZwxuy5Tbew1uhuBahnZ2yvVaKYvUWCtXm3J7f84S3QAs4jj6nGpT7gSPy4MIbq7p9hBxrazJ6mP5Iq+VH6l2LPdAdBeLdLxV7aP7DG+E0XN50Ei8LYJ7heC22X2tPDrlRl8rV74Rxj1EtyDLkM9OuZ5r5ZHXGHEVXI8zlasH10KVtfKM1WvlR2amXIvVsubPVKK7UMm18sTJU1mP457xOHGK4PaLFtxot3r0uAlG9+MLTLkiRLcUy+BqmL2/cqvdjuO2Irg6vIO74laPI84CuuuNMO4huotoT7nWwc005fY+NnNwW6dcgvvRzJQbKbjXz73+g+lFHgdX83aPh57V8orLhUSI7ta8JlyR8ynX665T9xDcvUQ6W3n2OG3mtfIjWafcnqGH6C4QYcrtCe7slKu9VtY6jrviTOUWBDcm7xtgVF4r73C7x0eIrrMIwY1kZMrteR7v4EY6cYrgPhVlrTwb3OuvLbRW7phyo9728Tmim5jHiVOWU+7K47gjPIJ7NeUS3DFRgqthm7VyUUTXkeZUGuZMZYP7K0c9jnsm0pnKBFfPikuDIq2VR4PLlPsY0d1Ib3Atb4ShNYVGWCtHOnGK4L40OuVGC+711+pPuSN6Lg8S2WvKFSG6blZPuSZnKidbK68IbguCm5fHzS8+PEfytXKkG2GsulxIhOim43XilPWHGtxjuVZedaayxmfjEtxx1lNu03M1BrfyWvkRjSk302pZhOi60AplmOO4IiZTbs/jtY7vVjhTmeDeF2GtrBHc66/1WyuPBjfSlLsa0TWWMbhWU260y4NWB1fjxCmCq2vFmcqXd6UKtFYe8ej5st0IQ+tnOdFNINSEK6J+I4xVx3EfiRLcng8ywFMjU262E6cseK2VtWRbLYsQXVMrb1wxGtyZKXdkrWx9edAj0S8NYq08Lktwm57Hecod+ZqRtXK2KVcT0Q3OM9xWH2oQ7fIgzlTGrVXBnVkrn4lw16mz59vtEqHniK4RjViGWyufyLJWtgwuJ06tZ/WBBt7Bvf56vbOrRRZfHiQyNOVmXC2LEN2wvIPrPeWuuDxo5aVBIpw4Zc1yrdz0XIrBzb5WfiTClLvyGl0RomtidsoNGdwTj6bcSJcHZThT+WrKJbi6ol4aVHWt/NAmx3IPRLcI8+A+mHI118r3aN7m8Z4swcW53ik34qVBbc+Rd62sOeVmXS2LiHy2+g1Us2rKHTEb3DNaa+UevWvl2eC28Dxx6tWXT//uvP3um8uvqWB1cDUvDdpurbzZlCvCpKsq21p5Vva18vnX5Tpx6nlwj//fvf//zqJeGiSy4Vp5UOYpV4RJN4ywx3EVP7ovy1pZK7gan407GtxHv15t+rU4W3nFmcpXwS25Vt5wyhUhumpmptywwT3RO+VGujyo0pnKvZNspQBbrZWbnsvp0qD3z8FauRLWy0m5BLfz5KkMlwdVOnFqdnW80/o56pnKIqyVe8yulldfLiTCpKtixZQ7YsXH9T2y4jhupROnNGOZcfrtmXIjn6nMWjmXH968kV99M/dvhOguFPqTg4yn3J7n0Pwwg0c0juNWuMVjhgCvDK7Xmcrvn6fgWhmsl2eNhjPbmcoia47jPqK5Vq5wprKF7OvnzME9k3qtPDHlZj9r+cCkOyFLcLWmXA3R1speZyq3iBTcR6+5evrVPls56qVBJdfKEBEm3TRWnqksUnetfKXSiVMaVk6/2mvliJcGvX+eomvlxMdyNRFdZys/Y7fJginX0uzlQZE+ZHz1lHlY8T4sjuM2PZfjpUEzwq+VJ2msliOcuSxCdIeFj6fYn62sMeVqGb3zlIamy0wUQ7CSd3B//P4v25yp/P65xqbcR7RjfMZqyo10LHf2zGURousq/MlTih9qYMVzteytJS6rpt23332zJLgWoh7HPRNlrbxiytWgMeVqBFeE6A5hyu1neQJVFlmn3ejT7SH7Wnnk5CnPSfZM5Ck3ylr5QHSDWz3lPhJptRyB1roy0rSbabplrdwuy5QbKbhaU64I0XWT9c5TkVbLFWSZdrNMtz2irpVHLw+qPuVGoRlcEa7T7eYZz6hTbhUaN7yw8OP3f1l2V6roZybfk32tfMbz5CmmXB9MusV4HMtd8cEGK7X+gNVcXV7RjuOqVbJXcKutlbUjSHDv055yRYhuF887UEWYcletliPcFMNSSyisV623Msa2R7W18hnvlbP2arna5UH3EN1GJc9YXvQB9dAxG8tMJ0rdE3WtPHt5kAiXCM2IulY+EN0GGT66z+sSod6VsMcKeeWNMZ5rnqoWT7vZp9vIa+W258p98pRIzCk38lr5QHQDclktX0y51qvlLMdzo+uNZ/bptkfWtfKOJ09FCq41onuh5FpZGavlMd7Tbvbp9pB5rTxzHDfSqrfyJwlZTrkiRPfUbHDDnkA1eCzXYzrVfI3ZDzvI4iqmlabb7GvlKyWm3M7VcqQp1zq4IkT3oQwTrojNlKu1Wq60Qu75wdvzA99y2s16GdAjKz6UvpX1WjnCx/YdNKfcSMH1QnSNVJtyHxlZLY/EuMrlQlaex7VSbEX07+QVba08GlyLlbPXlBvp8iARnylXhDtS3VV2yp0IbqWpNZpXX/7y8kPuW+9SlfGOUmd6Y5t1rawtw5SrIdNa+cCk+8yq4LrdDOPCytVypbB73p3qsPt0u9taOdyU22HHtfKB6N7QCq5HuFfeCOMQ4azlSNfozlh93W4v6/di9cEQmdbKZyxOnprWuFqOFlzPKVeE9TIaaE6glabZHUWNrfda2eM2j9onT81+rcZqedfjuLeYdP9u5ZTbu1q2mnI5a1lXbwiif+xf9uBGO0brvVaOMOVqyLpWPhBdyXPilKXe4HqulqOcuRzhh/aKFbPHsVvr/+CoslY+M7NWzjLlZl4rH7aP7urgRplyH/GaWpmO34s07Xp8GtDs7zfjWvkquJHur1zVquCKEF1VqwP+gvNa+cqOYbU4i9lj2vWIrVdwI2woNFidPDU95TqtlrOvlQ9bR3d1JM2nXCNnq+Udw6pt5bSbYbrteq1ka+Wqk+zsarnCWvmwbXRXB9ecwpRLQOOyCKPHBK0VXNbKbb9WYcqtMuEetoyuRXCtIx75HssRRfqwg5FAeE6DXtOtd3A918qzlweNyjAZR7pMyGrK7XneLaMbgekdqAxuhHEYXS2P/trZmctVbowxSiOUmabbrtd0XitfWXHyVIQzlmdVWisftosuU+57V1Muq+X7XKcnw1hlm24PrJXbfs2F8Wo5y1q5N+ZbRTfKcdysUy7GWd2LuTecHrEVsfkPhoxrZYvrcVtEmXKjrJajTLkiG90GMkpwe3VNucaXCEW41/JuWj6BqFX12IrEWytfWXHylIpEU65lcEeee4tJ1zK4vc8d5dOEzmh/QhCraltXMd1huu2RYa1s8XVaX99qdMqtulY+bBHdrCJNuVZ2CvKKj/vzum1khOBqrZUjBHfl/ZVXnkClHdxIa+VD+fUyU+5HM8FdsVqOcs/l1UY+5H6n2PbQCPOqy4NEgky5jh9uMCPaWvlQetLNehxXxGbKbbH7h89XsGNwm1bGCS4Pavn1RyJNuSOr5Sxr5Vllo5s5uBZWrZWtgrzyGt2ZaWk4Ko0fcu917NbiUiDL4DY9T/C1cuUpN9Naefa5y0bXmuVqedWU+whnLeMQabrt4bFWtrw86CqY2adcTZGDK1L0mO42U67yyVPeq2XW0n00Lx8aeW1tGrGNtFa+snKtvNOUG125SdcjuGGmXEW7BfDtt3HuzRxd5uA2PU/xtXKLVWcs77RWPpSK7jYTrojbJUIzq+WZkFc+c3kmOK4fi2dw7FbE99KpCGtly2i6TbmNelbLu024h5Lr5UhWTrmWa+XIIn3CUFbRY+u1Vva4PCjFlJvgMqEMU65IoUnXa8oNMU0Hub9ytVhnYT3tVghu0/MkvjxIhCn3VsSbYDxSIrohQnhH9inX8qzl7MGe/cG/4u5UV6JdCjTj6s8n+nHcll93ozzlZlsrawc9fXQ9gxsi7kGm3CvZoxqddhyjT7cHrbXy9XOs/fQgjUuEWqId4TNzZ2VZKx84ptvIMrjNU26AS4Q0vnbW7h9er6lSbJufy+E47uq1srfW1fLOa+VD6kk3xOT5wOr7LF+5iubKG2JUPnP51mycZoNZMbgaa+UrGdbKalOu4mp597XyIe2kW2WtvGrKXYnV81pWJ2JpB7d3uo2wVrY+Dpt5ytWWccoVSRrd6MFdNeV6XSJ09fVE1U/vXaoqTrfNzxn88qCWX9d4DZH8lwlZB9fy+VOvl61Zx117ytXCvZZus9nRAAAPNElEQVT9uN4oonBwd1grR7tEqEem1bJ10NNNupGP44q0T7kRLxFCn1evvwhxO8mrabdybGe+7ulzxPxQeguaZyyvWC1nXSsfUk260dfKJpJcIoSYqge36bkn18rWlweJBJxyg55AlXmtfEgT3UrBjXyJ0NVqefZ47tWv73Lm8i2Vm/8/i2uW+ya/ev3FVHBn18oRLg/ynIKzT7kVpFsvW5sJbuTLhKqslblG91qG2IrMT7eW0/Fh9XFckdxTrqYKU65IkuiGWfUq2PESIU87f9hB1UuBhl/HeK3sMaFqXiK04u5TWU6g8jxOHH69nGWtHHnKbcVZy+tEvBezxX2T1T6sIMBa+YrXWnnFSVreq+XsJ0/dSjHpwseffvrpMrx//vnn01X17K//+9/+dnpc99XrX56umF99+UXTtHv80J49+/j2h//scx2B+6///O+p59F4D5q0J1vr4GpMuNHWys1TbsNqedUtH6sIP+l68ZhytS8TsqDxD332169+6F390Oy5JvM4kUfnshOd51nxyTxWU63qPZMbnm91cP/888+Xn49LcPfGpBtRgsuEqky8T58z1vR7G0GL6bfCVPvhcQrr5AgnTYkQ3OqIrtQ6UeuRq8jdalkza7xmxPC+f169lbFWyLVWz5VC++HxRdbJIgR3B0R3UqXV8i2N47stj4ka3o/Pn3/6rRjaD18XYJ088+uH1rOUCW5+oaPrMYHuMOWOIry3r5Fr+q0cWpH91sk9z6f5YQYEV1/o6FbRNeUaHs/tWTEfCO+914o7/Woz+bSf2ZtibLZO7nk+ghsf0Z0Q4drcn/76VYgbZIwEvfc5NMIroncDjYjTr5ZIU+2H52g4K331Orn1MT03vSC4tWwdXVbLbVpPrJqdZlseMxtekac/vKtOv7OvHen5NGIrkm+d3POcBDePraM7o+oJVI9UC++Hx24+/WYO7cfXnP+UIIL7HsG1Fza61lPorlPuzBq4anhFcky/WvGNeJxWZOyD5iuuk1ufU4TgZhQ2uhV0T7kJborRKmN4P3xd0Ol35nmihlZkLLbvX7/W5UC9z0twc9oyurNTboQTqFbpuXGGRnivWIVXpMb0W2F9/PI95Fgnj3xCEMGtb8voYo5neFvCbBneD8+hHGDL6bdiaD88R9F1cuvzihDc7LaLrteUG/kEKo0Jc8fwfnguo/Wz5pnPs1SfazK2rR/DV32dLEJwKwgZ3S1Pckp4PHfn8IrEnX613sPU8zhMtYcd1ski/sEltjZCRhc1eYT3yu0PcosAR5t+e15L5bmcptpD1nVy7wfPE9w6toouq2V9vZ9ItPojAW8dP+AzTL/a8Y0UWpH+2IrssU4WIbjVbBVdfKQxNR4yh1fEfvoVmQ+wxuq5QmhF8q6Te2MrQnAr+nT1G/BSecpt/hgvQ9o/gGZ/veUH8z2vXv/yw/80vfryC5VQibyPZ09Aex9/+lwKv4+Z72/LdEtwXyK4cYSbdDmJKq/sE+9z0dfPZ9Nvlan2EGW6FSG4mBMuuha4GUZc0cMrkuPkK5M7TiWJrUiddbIIwa1ui+h6yXYCleZx3UPvtNvyPiKE92ARYIs7X43KFFoRv8++DTPdihDc5MpHlynXX/XwHiwD7BlfvWPNfrEViblONp1uRQhuAeWj62V4yi1yPPe5qOEVEfX4iugf//WYfrNNtbeqrJO7ToIkuCUQ3RNMuf687lx1yDT9iiicfJV0qj1EXCebT7ciBLeQUNHVPnN55vl2Ca7Fcd3DyLQr4nvnqqwB7omvVmhFiO3Icz7XfYkfwS0lVHSzynYClacM4T1kCnDL9Jt9qhVpj1rJ6VaE4BZUNrpMuXFkCu/BI8AW62dNGWLb8tgIwR26gQ3BLalsdFMoehLVPaPhveLxIQlWAba6/neGxp24osS25TEhp1sRgltYyeh6TrkVVsuWx3Vntbw3j/AeqgZ45VQr0h+0stOtCMEtLkx0t7z9o6Kf/vqVfP6br1e/jVNWa+aWx1j8h4XVJUgWt588e50ZXlNtz9dpBtd1uhUhuBsIE90IdpxyvVULr0i+6bdqbFseE3a6FSG4mygXXSbm+CzD2/Ich50CvDq0ImtjK2I73XrEVoTgVlAuuqPcz1gOdhKV93HdVWc0P3/soWqAq8e29XEhg9sRWxGCW0Wp6HpOuayW17FYI2cP8G18tT4LOOoKuefxIWMrQnA3FiK6q1fCXJe7xsxlRJbHbzMGOEJoReLEViRocA1iK0JwMwkRXQ1MufNWXDoUNby3z3HIEuDZ9zHCK7YtXxMytiIEFyJSKLqjlky5wY7nrhY9vLfPdagQ4NnQisSKrUjQ4HbGVoTgVlYiuqvX05VEvlHGIysuFfIKsEV8V021o1+r+bm30adbEYJbXYnojhqZcquulm9lWzOLrLtG93jug9UNOETmA5xphdzzdVWmWxGCu4Pl0WVKxcEjvIddApxthdz7dVbB9Z5uRQjuLpZHd9ZotJlyz61aM1uH9/Zxh4oBrh5bkYDr5MHYihDcnaSPbjqGJ1Fp33+5enhvH3/IHuBZUY/X3tpxuhUhuFWkji5Trr2MJ1aJjL9v7wBbvk6PDLEVsZluV8RWhODuKnV0UZfG5+/O/geDR4A9X+fqtSN/Xbjp1im2IgS3mrTRZcr1k3XNLKL33qsFmNjGXiUfCG49S6O73ZnLiW+KQXifPt8hU4C9V8ijX9fz8Xsjr5FhuhUhuFWlnHSZctcgvPef9xA1wJWO1868TpbpVoTgVpYyulgn64lVIvbv3esEqdYAV43tyGtlmW5FCG5120SXKTc3jWlXxPekpVWXIlU7XjvzWpmmWxGCu4N00R1ZLfPRfboyr5lvVQ5w5K/ziK0I0y1iWhbd6CdRqU+5iU+iuqdKeA/VAtz7Pqy/biS0o6/FdIvIUk260UO9m8zHd8943rxiRYCjH6+deT2mW0SXKrq/+uabvOF9+1uXaff4oaN5O8gzxw9Hz/geP8gtJt57Mpyh3Pv8ll8jkii2Iky3m/vVN9+4vl6q6Hr67Lt/1l8xH/+4ia+K2x/slQM8+1pV18gHptvaLKPoHVyRRdH1nlZ//e23sU6mco6vV3hF1sRXxH/6FVm3hm59reqxFSG41VULrgiT7imTafeWU3y9p16RdScLrZh+D1GOBVc9G/kW6+T6KgZXZKPohpt2bxWOr8he0++t6PdRnv36FbEVyTXdihDcXtZBXBlckQXRzXYilPm0e2uT+IrsM/0eKn2cX7pVsgjr5CSqB1dko0lXJPi0e6t4fEXWT7+HCBHO8nF+KWMrwjo5iR2CK7JZdNPZKL4ia6a/CBFeeUJWi1WxFSG4u9gluCIin7x79079Sb/63R8ePqnGenn2OdLeh9nxrlYrAnyIsHo9rJqEb636WL8dYyvCOtlbleB+/cfff9LyONdJN9vx3HAKX+d7a/X0eyvaJOz1sX7pTpK6xXSbRpXg9thyvTxybNf1hKorC+Irstex30dWR7h1Fb1lbEUIbiI7Bldk0+iW4RhfEabfe+5FauUNOkbtGlsR1skr7BpcEcfoRlstp592by2KrwjT7z2rp+Eeac9IvsV0m8rOwRVh0u12/EMlvu8x/V6LGOESsRUhuMnsHlyRzaM7c93u7T/acAFeGF8Rpt8rKyO8e2xFYq+TM0Qjqizfu62jqyXs9LsgviJrA5xl+r3lEeEysRUpGdwswYgq0/fPJbrRjudaCTv9LoqvSIz1c5b4HrQjnO4DCc4UXCdnCkZE2b5/KSddzQ+zt7o1ZMjpN0B8RZh+e42eIV0mthOTrQjTbWUZv4cpo5tJyOl3YXxFYky/z2WL8dk0nOqD5M9MxlYkZnAzhiKirN9Hoit+H4QQbvp9+9tl4RVZf/LVrewxHg2tCLF9juDGl/n7aB7dXY7n9gg1/S6eeg8rp98zZ0HKEuRHKsZWJGZwM0cimuzfSybdv1v1sX9hpt/bH3hMv02yTsehYqsU2gPr5NoqfC+JbhBMvy9lCvCtqDEmtvcx3eZQ5ftpGt1sq+UoH3LP9PtS1PVzj1Wr6sqxFYkX3CpxiKTS95RJN7CQ068I62cDFtNx9diKxFsnV4pDFNW+p2mjq3mt7q0o0+5zBPilCtPvldEYjwY3wgcRtGC63UPF72va6O4szPpZJMTx36rT7xmtj/Q7ZImtCMHdRdXvq1l0sx3PvRV12n2O6felHaZfTZliKxJrnVw1ChFU/t4y6RYRcvoVWX7XKxECfE+m2M5MtiL6wa0chNV2+N4S3QeyTLvPhZp+RUIFmPgqxjZ4aA8EN49dvrcm0c28Wq4k1PQrsvz470hwqoSa2M7ZJQir7PT9ZdLdANPvuNFYRYl1hthqhfZAcHPZ7ftLdE9kXTGfCTv9ioQPcI8IU7VKcINdX3tFM7i7xWCFHb/HqaNrda3uDsJNvyLL18+raU3V07FNNNUeiG0+u36fU0fXQ8Vp97lwAS46/VqJvkK2Cu2B4Oaz8/eZ6OIJ1s8bCnY/5B5awd05At52/14T3QY7TLvPhZt+RQiwtsSxFSG4GfG9JrpoEDrAxLdP8tCK1I1ttPcDG0S30Y7T7j3hAsz026ZAbEUILvIjuhhGgBMI9GHxoyqfKBXt/cAe0e3AtPsYAQ6E0L4QLW7R3g/8pI+u97W6z38YEOGXwga4J74On5gTXdZjtc9FClyk94I10kd3tasfFLtHOVSACemlKqEViRW4SO8FaxFdY0T5o1ABxgcZL/O5EiVyUd4H4iC6i+0aZQK8XrYbWLSIErko7wPxEN3gdogyAfZTMbQisSIX6b0gHqKbXLUoE2B9VUN7iBK5KO8DsRHd4jJHmQDP8YjtqtCKxIlclPeBHIju5u790IwYYgLcpnpoDxFCF+E9IB+iixduf6gS4PVW3JziuQihFYkRugjvAXmViC4fZm8nS4CzxTdCSK8Q2qeivA/kViK68BE5wBGm3wwhvUJoX4r0XpAf0cWQXQJcIaRXCO190d4PaiC6mJYtwDuE9AqhPRf1fSG/T969e7f6PQAAsIVPV78BAAB2QXQBAHBCdAEAcEJ0AQBwQnQBAHBCdAEAcEJ0AQBwQnQBAHBCdAEAcEJ0AQBwQnQBAHBCdAEAcEJ0AQBwQnQBAHBCdAEAcEJ0AQBwQnQBAHBCdAEAcEJ0AQBwQnQBAHBCdAEAcEJ0AQBwQnQBAHDy/wEckJoRgU3vkgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "limit = 27\n",
    "qc = height2circuit_temp_1(height_initial,rochester,limit=limit)\n",
    "\n",
    "probs,raw_probs = get_probs([qc])\n",
    "p = probs[0] + [0]*(53-limit)\n",
    "height = make_height(p,rochester)\n",
    "plot_height(height)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Here we put half the image in (due to only using half the qubits), and got half the image out.\n",
    "* Here are some results from running the circuit with no limit, using the 53 qubit *Rochester* device as the backend."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p=[0.10919456219850923, 0.16044568245125349, 0.09048625792811826, 0.11478420569329661, 0.01750400855157675, 0.17499999999999982, 0.11574979056129564, 0.007768721344880438, 0.08535402521823476, 0.3501374885426216, 0.5677950594693499, 0.7200184501845022, 0.5024050422955714, 0.3711212246586675, 0.10785066830542339, 0.01569726699369308, 0, 0.799728813559322, 0.07532605802502002, 0.03544720311097811, 0.0007676560900716691, 0.07124372050540444, 0.3079360506985453, 0.6212898497618173, 0.8309606258817493, 0.7347986312187418, 0.4237070807807376, 0.18767772511848335, 0.20848918523337134, 0.6287630189756027, 0.061037913417585465, 0.100013194352817, 0.34700485698866695, 0.6118154842190453, 0.7705248990578735, 0.6120502817511918, 0.3511696692659317, 0.1114186851211074, 0.022350530825107295, 0.010901728702694527, 0.43033920512447255, 0.005681818181818239, 0.0005247966413016135, 0.02600000000000008, 0.12480810561866737, 0.16719559044596638, 0.11907040328092963, 0.07396630934150084, 0.01814696485623008, 0.008415147265077194, 0, 0.31355697255336856, 0.11640714014432188]\n",
    "height = make_height(p,rochester)\n",
    "plot_height(height)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The image does not come out perfectly, as we'd expect due to noise.\n",
    "* It comes out pretty nicely, though!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Now we'll define a new circuit to convert height maps to circuits\n",
    "* This differs by adding in an implementation of every `cz` gate on the device, just before measurement.\n",
    "* In theory, this will have no effect. In practice we can expect to see effects from noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def height2circuit_temp_2(height,device,limit=np.Inf):\n",
    "    \n",
    "    red = [(0, 1), (2, 3), (4, 6), (13, 12), (11, 10), (9, 5), (21, 22), (23, 24), (25, 29), (36, 35), (34, 33), (32, 28), (44, 45), (46, 47), (48, 52), (7, 16), (30, 39), (18, 27), (41, 50)]\n",
    "    green = [(7, 8), (9, 10), (11, 17), (22, 23), (21, 20), (16, 19), (30, 31), (32, 33), (34, 40), (45, 46), (43, 44), (39, 42), (15, 14), (13, 6), (25, 26), (38, 37), (36, 29), (48, 49), (2, 1)]\n",
    "    blue = [(0, 5), (9, 8), (19, 20), (21, 28), (32, 31), (42, 43), (44, 51), (11, 12), (13, 14), (15, 18), (27, 26), (25, 24), (23, 17), (34, 35), (36, 37), (38, 41), (50, 49), (48, 47), (46, 40), (4, 3)]\n",
    "    \n",
    "    n = min( len(device), limit )\n",
    "    \n",
    "    qc = QuantumCircuit(n,n)\n",
    "    \n",
    "    for pos in height:\n",
    "        if pos in device:\n",
    "            j = device[pos]\n",
    "            if j<limit:\n",
    "                qc.ry(2*np.arcsin(np.sqrt(height[pos])),j)\n",
    "    \n",
    "    for pairs in [red,green,blue]:\n",
    "        for pair in pairs:\n",
    "            if pair[0]<limit and pair[1]<limit:\n",
    "                qc.cz(pair[0],pair[1])\n",
    "    \n",
    "    for pos in height:\n",
    "        if pos in device:\n",
    "            j = device[pos]\n",
    "            if j<limit:\n",
    "                qc.measure(j,j)\n",
    "        \n",
    "    return qc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The results from a simulated run come out as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "qc = height2circuit_temp_2(height_initial,rochester,limit=limit)\n",
    "\n",
    "probs,raw_probs = get_probs([qc])\n",
    "p = probs[0] + [0]*(53-limit)\n",
    "height = make_height(p,rochester)\n",
    "plot_height(height)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Results from a real run are noisier than before, as expected.\n",
    "* Still pretty good, though!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = [0.009271721250186687, 0.12571347031963487, 0, 0.11378687537627952, 0.11220366379310348, 0.16896345116836464, 0.19807037457434734, 0.1080806799441838, 0.0542184607246759, 0.4533512464546947, 0.6510054501033639, 0.6864168271367205, 0.49212417800886976, 0.41575859178541497, 0.12443894134034998, 0.039715719063544874, 0.31570404436629257, 0.7955108785458552, 0.09762639131017838, 0.026998961578400885, 0.0476251114223862, 0.12394067796610185, 0.21739753511034693, 0.5995431382885258, 0.7080310551100926, 0.6775725593667545, 0.33528404224950037, 0.08964501881236696, 0.26531620553359686, 0.5159870250231695, 0.13996763754045305, 0.0779101741521539, 0.3371308016877635, 0.5970209884901827, 0.7207501019160213, 0.4394103620203772, 0.39190687361419063, 0.1193887297039159, 0.06800556770729752, 0.10569610429923938, 0.3264977296030467, 0.028944911297852392, 0.04038814581694213, 0.052019278710320804, 0.13344441078461078, 0.3722366710013004, 0.11908528692650666, 0.11099187490418526, 0.06481123566550703, 0.05513666352497655, 0.03586081142683477, 0.2545377796538624, 0.27651361235270205]\n",
    "height = make_height(p,rochester)\n",
    "plot_height(height)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The final version of `height2circuit` will have some random single qubit rotations after the `cz` gates.\n",
    "* These will have the effect of perturbing the image using quantum intereference effects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def height2circuit(height,device,limit=np.Inf,theta=np.pi/2):\n",
    "    \n",
    "    red = [(0, 1), (2, 3), (4, 6), (13, 12), (11, 10), (9, 5), (21, 22), (23, 24), (25, 29), (36, 35), (34, 33), (32, 28), (44, 45), (46, 47), (48, 52), (7, 16), (30, 39), (18, 27), (41, 50)]\n",
    "    green = [(7, 8), (9, 10), (11, 17), (22, 23), (21, 20), (16, 19), (30, 31), (32, 33), (34, 40), (45, 46), (43, 44), (39, 42), (15, 14), (13, 6), (25, 26), (38, 37), (36, 29), (48, 49), (2, 1)]\n",
    "    blue = [(0, 5), (9, 8), (19, 20), (21, 28), (32, 31), (42, 43), (44, 51), (11, 12), (13, 14), (15, 18), (27, 26), (25, 24), (23, 17), (34, 35), (36, 37), (38, 41), (50, 49), (48, 47), (46, 40), (4, 3)]\n",
    "    \n",
    "    n = min( len(device), limit )\n",
    "    \n",
    "    qc = QuantumCircuit(n,n)\n",
    "    \n",
    "    for pos in height:\n",
    "        if pos in device:\n",
    "            j = device[pos]\n",
    "            if j<limit:\n",
    "                qc.ry(2*np.arcsin(np.sqrt(height[pos])),j)\n",
    "    \n",
    "    for pairs in [red,green,blue]:\n",
    "        for pair in pairs:\n",
    "            if pair[0]<limit and pair[1]<limit:\n",
    "                qc.cz(pair[0],pair[1])\n",
    "    \n",
    "    for pos in height:\n",
    "        if pos in device:\n",
    "            j = device[pos]\n",
    "            if j<limit:\n",
    "                rand_theta = theta*2*(random.random()-0.5)\n",
    "                if random.random()<0.5:\n",
    "                    qc.rx(rand_theta,j)\n",
    "                else:\n",
    "                    qc.ry(rand_theta,j)\n",
    "                qc.measure(j,j)\n",
    "        \n",
    "    return qc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Here are three examples from a simulation.\n",
    "* Remember, there is no noise here.\n",
    "* The effects are induced on purpose by `height2circuit`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HP96DZpgtl5k1p92po1spuJuI8GaZdnujO2NwI08JqhzcN6+/O/X5D8+e9n9OkgCfiWnGEN9y5lrUnsvMy0a3YmwvrRjebMEVOf4Zz7RhKlNwzwb0rGwBjthUVSHGt0JsucxMdO+oHlyR4xd8hvBqRtc9uCKnp9xZgusR2+iInkGA7R5PQ2t4PZeZNcJbJrozBHdT4VQijfBqB1fEfll55eBWDuhZlQM88vHRj9vi3rJz5DLzEtE9fWWRoOB+9eTJ7rGKFcKbbVk5U3AjTwmaKa5vXu3/tzw874+pSH+EMwV49HMyPPa1isvMpaNbdbq9fFM2Ca/TObxnoktwc+5Qrhbco6j2WDXAZz4vw9fItsw8bXQrBvfeG7J3eKOn3RmD23Pd24zBzRhbzaD2WjnAZz/X+2t5LzMvF93Ky8l7qoa3N7orBzfrKUFRwY2Maq+RCBPgcRrXlz67zCwSE95U0Z01uCLH56LNEt6e6BLcts/NGtyMUb18TsPTbPEAi9SLcMvXzrTMXD66KrdhShzczezhJbj9/z7rhqmMQb3U+/wI8Lgsk/DpZWaRrvCemXZTR3fm6faW0WVmkdjwHkW3UnBFjn/Oswc3e1RF7J7jygEWqRPh1vBGLTOXjO4n//v/nXvQYsHdZDuVSGPabY1uhYtfRO9QFrELbsbYltxQ5bARq0KAtR6j53E9TyMiupeKBneT7VSiM+HVCq5I/LJydHAtTwmKDm7012+RdQq2vh3hJluEsy8zj4S3ZnSTB/fy8Xo3BrR8XmR4r19IlZaVZw5upuVkz6/1r//y74cf87vf/3rosQlwjms9m4RXaZl5jegWCu4mU3g1j++uFtyqpwRZRDBiam0J7JHZAvz+a8wfYa/ju5rTbv3oFozt5uhFVjW8bsdxiwc38pSgs3GsGtcWBPi9yAC3PtbZ47uWy8xzRrdwcDej0+7R50afSnSE4NbYoTxzXFt4B3jkcz1uyiCSN8LRy8zrRHeC4G4slplFbMKrEV2Cm3OH8oyBffP69vfr4Vl/dETyT8GZAyxid1pS1mXmnvDmju5Ewd2sEt7Zg1v1lCDr4HpMr/cCe2TWAIvkjrDmTRqyLjPXj26SOwRpPeY1941VIq7hjQ6uyPnoZtyhLJInuJnj2oIAX3+dse+HdYRbw5t1mflMdH/V8kHVeQT3jL2v2/oHSK+Wc2uzyRrcI9mD+6//8u8//2Plzevvf/7H0ujjj/63j37/Rz7vzevvui8B+ubV94evv1uO/oi8xeL98/T1ExoHPRG/90Tf6B6ca7o5nO5+0vqX1dGGpt7H03Zq0t15Ualc+/on0VOuZXCPzHodZevQiohLaDGv1vdub713XbvkP+lOGl6rY7qwdybIIxPBJurCF8S2rhmO8WZ4z+sZSM4E9pYllpetWb2IWv/w2LP34mpdTpl5yo1cVt7/XP0grxDbmY/pwp7HEnNMdCeddnu/5qll5Usdxy3QbqZl5dlju4IZplyrz48wOgHHTbqThHf2ZWWVuwftyDzl7qmyrOw13QJeIt47NZeYTaJ7dFWknxUPb+Zl5UsaS8zDkk7hkacH7X+uTpBXWEq+NvPS8sxT7j1qm6juvAfde1+0fk+MP6ZbPLwjj6+2rHwpadzOiNqxHHV60PFjH3/uirFFHVVW+FqNTMBm0W2edkVKhvfMNZezufeXXfQGqjNGl5XP3sRgj/WyMrH1w5T7Xrb79FrSWmI2nXRnDe+ZF4nJlLtxOmfXg9Y9cnsfd0/kXYOO/r3HhS0y815aBkaZLy/PFt6Q2/kFmHHKzXp60PFj+9/IQKRGbCthym3ntVqocVy3dwJ2OaY7U3itH8NS6IaqDlZT7pmvmeVWfbdYTLnE9j7OsR1TZRl5j8YSs9tGqlXCO/IcVKdchQ1V0acJnTE65e6JPI7rvaxccbqddWl51Sl3dq67l2cO7wzLymrT7onwZ5xy92Q4PUhDxdhWsvp03HMf3VHaf8xbLTG7nzI0Y3jTLSsn3lB15hdj9BShjDek16Ax5RLbPl7xZMpVlug9MeQ83a7wFldlyt1Yb6DaY3knoBEzLyvPEtsKS8tMuX2Rzn4lv7PHdcMujjHLVatmWFb2Yjnl3jM65Va46tTQ154kthEyT7kjlplyT7DYYBp/RaoWScObbln5ksFyykxTbtarTrUYvuE6sXXnFuqBpWUPe++1qwV8ExrdGY/vtjw+U24f7Sk381WnLJaVmW4/lH3Xsgem3A/1DiLpbmL/+atXzR9bNbzVl5V7X2SWmw0sptzRx8x81ales8d29Hju0NdKvLRcccqtRHuJ2WzSnTm8qZeVL3neBMHoa2mfIpT1qlMtWqfc2WNbRdYNVB5TrsWNYmZhurw8Y3iPXhQVplxve0vLnlNu5qtOaUy5xPZY5qXlmabcIzNMwfVuYn9DhfCOPkZYcBU2VFluoNqzN+VqnyKU+TiuiP0dhKrJvrTMlJvQwfuU12VyzaPbM+2K1A8vPmQ15fY+5uzLyky4ta005a7OZdJdIbwpp9wGR1Ps6lNulWVlHBtZWs46sY7IPuVWPJ6b6ib212YOb/oJ2XND1YUKUy7LyvV4Li2P6A01U26b6PdZrSVm12O6M4f37NfLKOo6zSNT7kjELa86pYFlZUSyGj6i47nH4z3PfSNVb3izq7qsfGn4hbYzQY9OuVlOEWJZeS5eS8sey9FeNzZAm5Q3sb82y6lEmf9i+0jQErMmzVOEWFauKfvSci+v6yz3mu4QmxKNJeawU4ZmCe/Zx8/qzAYqiylX8xiw5VWnNLCsXBNT7ji3TVQJho/Q83Qrh7fksnKie0pq0T5F6OxxXJaV7Xjexs8loAtOuRUm4pH3wtQ3sb9WMbwVXjhnrDzl7jm7rNyCZWXcM+uUW83ZJWaT6P7m5UuLhxWR+PAeBTftlNug2rTbO+VGLytr3EFo1SnXk8cGqhWnXLxnNun2hLfSqUTWj2HuxKXQjnhOudrn+VZYVl6Z59LyLKpMuRUvinGG6fLyiuGdXoKNCHtGplzr04NaMOXWlXUDVS/rKbfSVHw0fJxZYjY/prtKeEsF2zmcXlOuxVWuKi0rP/38t/L08982P68qst/coPtrOCwtV5lyW1UK9pHwjVTXKoa3VHDPGNxANcJr89Qsy8qXsZ0xvCNmWVpmyp2LS3R7N1ZVDC9u0776lObmqZmXlWedei3NsoFqtilXndJK3+gSs9ukax3eLorhLRvn3hde0Sl3lMeyctvzaFtWHvl3Fay+gWr2KTfzJiqrszlcl5ctw9s17SopG1wnVafcluBmudRjS1SrhzcrplyMcD+mmya8LDOr8JpyNadf6+O4Lbx3K1dcbp5tA1Wv2afcGYwsMYdspJohvFPEuHWJeeAYiNedhEYvhHHPLMvKmp9TjcfScsZIM+XWELZ7ufJVq6YIroKRKTf6FKGVlpX3Pjd7fFe/m9AKU27m47kbi+O6oacMVTyHd7rgHk2xylOuh3tT7orLynuyh9dLxqm1F1NunN4l5vDzdKuFF+9lnXKtlpVbgpt5WdnjsTLIuLTMlHvObMeFU9zwgPAm5TTlekzG0TczEIlfVt57zEzxXX0DVS+m3AGBl7NNccODXoRXWecLUHvKvUdrymVZuU2m8GbFlKv/8TPoWWJOc8ODiletwoc0p1yv48KrLitHfo09Z6bcWS6I0aPqlFthE9VGezNVqhseVLxq1bQUl18iTxGaZVm5xcOzFyqPk2252Uq2pWWm3DWku/ZymnN4RdYKb2Nk7y0te0y5qhfIUDg9qIXmHYRaPDx7oRpfT9lPE8p2BaqqU+7qUl57mfAGSzrl3mNxLNdrWblFS/yuQ1s1vKNWXFruxZSbQ/gpQ/ekCu8qDmKbccodOUUo07Kyxuape4Flufm+7qk12QYqplxfmsd1U9/woNpVq6bgMOVGniI067LyPVWWm7MvLVeXacpNs4kq6LSh9Dc84BzeHDSn3HsynCJUfVn57McdyTj19i4tM+Ui0qcRX/Q3L1/Kty/a3wR6Pv7zV6+6zpn69PUf2pcOzoY38IRsb71Trsv0q7Cs3CLrObkPz17Im9c6q0dPP/+tfPfNv6k8FlOurUxTbq8ZjxOHRFekP7w9esPrJuO03PCHgPbt+2b3u9//2u00oR5awRWRssFlyq3li8ePpwtv2o1UcHBy8r43nXrsWLbS8ibb8jFHS54Pzz47DE5L2FpC+ub1S5XgfvfNv/38z1kt//0tLHctZwvuiJFg9a46Rd/gpBqiu6qFlro3rW+KXuF9/5zswqsd27O20GpNt9bHcrseO2Fws6r8R7kGoruijuBqLi17/UW894bWE96jN2nP8B5Fb4vrFtqMsdWUbfOUh96l5TPLsktMu0GH+4juapQm3JK/ZD/pmUqyhFfkeOqddQn5WrbgzjrlLhHeAGHRtdpEhR0OS8pVlo4enj1VW25umYq9wjsq6xLypd/9/tfLBtdzysXHNC+oxKS7ioHgrrBr2fM4b8bwZp9qRcZiKzJPcCNZTbtV/ji3QHRlgctCKk+4sy0jeYe3ZWfzkTOhrLKEPBpbkbmCu/qUO9v7DdGFmr2/Xvd+cUZ/qTTPWcy2s9kivLMuIV+bKbgZcGxXF9Gd3eCUu8LS8rWM4T17StEKU+0lgovsiO7MDDZOVfkrdvTNruopRbf+t8xTrWZoNzMGN8vSssW0W+W4bsvhx6673J15MkjM+eIXVX6BWmxvri3Xan54/nT3BghH/16k7bKRD88+271es/auZstNURZmDC7mxKQ7o4muNhU5WVc8peisKlPtpVmDm2XK3XBsVwfRnY1CcLVv41f5l6/iKUW9rJeQLc0a3FlU/t23QnRnEjThzrS0fEvFU4paVJxqL80c3GxT7kY7ojO8d/Tex53ozmKiJeWMMu5sHqUdW8/QbrIFdyURy8ytj9F81kXjdZctruFAdGegGFztpeVI2kt9lcNrsYTsHdpNxuCyrIxWRBenHC0PHcW6Wsxbr9mc5VzeGabaSysEN+vS8iU2VY0jutU5TLn4WGt4I87lnWmq3bR8L299TtfHJwguauk9nitCdGtzCm7mv1I1LwXZS/OUoiOt4Z1tqh2J7fa5XR+fJLgVptyN1rQ7w2aqHlwco6oEE+5qvyy3PDx7qnYRDRHZ/ZiWi2icFT3NVsGEOz+rG+Ew6VaUILj4RbZzeUdEbooanWb3HrPr45Oci1tpyt1kXgWzNrK0LMKkW49zcM/8Uq30C6k18bZ8zBbHs1Nvlc1Qlo9dNbgr+uLx4xR/aJzFpFsJ5+J281wGzLazee/zvM+ptZhob32dro8nuCp6/rjmuC6Tbh3KwT27rLzSL0mvlqlXY+IVaT/O6z3Veh+fXS24M0x8q2LSrSAouCstD2vLMPF67z72mGbvfd2ujy8e3IxWe68YPZ4rQnTzSzbhtmr5JZz9FzXqXF7Pax9HhfbyOXR9fJLgnpF1ym39fa7we2+1c1mE6C5FK7gsLbfzPpfX464+kZG9fi5dH5/oesozTbla3N5XGq+7bIVjupkFnhpU4a/RKjzP5dWWIa63VL34hci54Gadcjez7DC2FDLpfvviRcSXrYVzcdVkWCL03tl8RqZp9pZVg4scw8CZ47kiLC/nlDi4LC2fkzW82UO7WTm4VSZI9nPsY3k5mwTBPfsL4f0L9fW7d/Llo0euX/MMz1OK9j63gjPPc6bgruKrJ0/kz2/fhj6HkU1Uv3n5UkT+a9vjdz867CQILnxEhDd7aFUvBUlwQ816bPfs0rII0c2jQHBZWtblEd6soTW9MlWi4GqZMWCrIroZJAqu19Lwysd0LrWGV2R/13LWuIr4PrdswV1xyt0cTbuzTsNHSmykmnq3c6LgzizzJKN5l6IMoi6aMWtwVwtTtRW198dz2zHpTsI6uK2/CEywY7ZgaCw3e8ryh8Cswa3OYpq1nJD3NlFpHM8VIbqxlKZcreASzHhax3ktZAnstZmDO8OUu+oy8j1ENwrBxR0Zwps1sBqqBHcFKwa5xDHd6RQLbrVjLDPQuohG09e6OgZbKbhcT7mG3j/qzd5zlK+73Hs8V4RJ11+x4EY9Fuwm3kpR3ZNtWVnbahNgZlrHc0WIrq+JgwvhuzInAAAQoklEQVQbZ08pmiWw17IFlyn3WPalZMvb+X3wdVy+CtTvi3vWbMFtuRTk9qb75tX3Hk9JTc/O5hWsENzMcdKWPcb3jCwti3BM10eyc3F7gmtxbCU6+A/PPyu1zLjJdPzS23aXphWCi/dm3UvCpGutcHBnV3Hybb03bzVWf1BUDG7Fqc+b53SseTxXhOjaShZcS5Vj/vD8M8JrLGJKrxjc2VVdStZEdAuI2jg16/LOLdWm3kzhzbjsTXBriY5x7yaq0eO5IkTXDjuVS6oUX6/wZozqnorH6zerT4HXou+vq720LEJ0bRDc8qrEt3Vnc8tjzMA6uEy5OIvoapskuCstLe+pFN9b4Z0pqEeqB3eVKTd6KTka0dU0SXCzfp1IFeK7UmCvEdz6qsT4zPFcEc7T1bNocFdT9RxfjCO4se6tunW/x9257vK9TVQWx3NFiK6OyYJrubQ8yx8DxDePyjuVVw2u5ftAxOmVPdMv0T1rsuCiD/GNRXBRjXt0v33xwvtLYhGRO0uJr7/K32+CW9PZ47kibKSCs7/88EPXNN778Zhb5Q1ThPYXGt+Le4/x9m9/PP3YVsdzRSZdXv7m+XOfL5TszkEiOi/m3pPRe7+m5ZsP51HOyyK4X79798E/2v7yww8//4MxlhfH8Lqd36Upowt/lm8qvY8dvcwMfZrfV8vIihDaURrfr7tT7p2dyxFYXk4g480M/vz2rekuZpaZ0UojuGyKysNyabkCJl0R+fuzv/Z/UsKl5U3UC9J6mbnn41lmBhNtHfe+h5HXXbbCpIu7RqbdTBPs1+/eyZePHpk8Nnz0TrkVJ1qLx8y6KhSygarzohjWiO6kZl2O7f3vighvtfvzZtUaXELr9/ie7ylRU67lzmWRAtFNeV5v4qVlbRmn3Vn/oMAvjoJLaGNk/b5onCbkJX10UVOmkLLMXMtecKudRztDaCPcm3K7v5+Ku5Y1LowhwkaqqWn9wnst8/Q830qnEaGdZ3AvN0JpxpENVu1W/B5NN+maXxhjoaXls6yXgTMf3+W4ri6t4Fq9ya8YD2+aV6CK2kQlwqQ7drqQIutzdKOn3UynESG3e1Pu2eBaTZ7aj7vaa3ml04QuTTfpIh+O7+KIdnAzXSGt57HuPfbqGweHvucDx3Otdy6LEF10sL5K1aWe8LKbuTatSzxWDe2Zz5ntdd875Vbatbwhuj2KHs/NEKVMx3eZdvM4u3GqSmgtHm/vMaN/349ELqVHHs8VIbrodGbazXT+rkd42Uw1bi+4q4f2zNfNHOPe04R2p9xENzi4RnQXkWHaHVH1eeNY73HcKjuPM2+IyhDjzN8fD0tHN3rnclWe067l47PMHMdqp3KrlULbIkOMb6n+fb1l6egixmrLzPjQSHAz3g5O8/Eul1a9Niu28Iqx6gaqnaXlveO5HjuXRSaLrvmFMYrTnDI9dzKL5DrtqAfHdT80slP5TNwyX9rxXmiu//dMEd6MxtjyqnOWtC4BKTJZdE0Z7FzOePN6LyNRtAop066PkZ3KmqfXnGE11fZ+fMYAXxqJ8ewXw7hGdDHs7LTL8V2I6AR3ttC2PE72AF/S/F5W3bW8SR3dlLf1Ky7LsuuoqsvMHt68/k4enj2Nfho3WexUXiW0rY9fKcJHLH62Vufn9i49p44u8ouYdqstM3se180YXs2dytlDKxK3XFpxCl7hClTXlo3uyqcLZZv+rMOb7b93JZo7lavsPs6g8hQcsYHKa+eyyMLR7VL08o9evHcyj2gNb9Vju29efxf9FD6iuVM54518tEJ7/Zws/kDMOAWr/6FS4HiuCNFFEh7LzLOHNxOvncotsi4ft/yBsUqAW8ywtCxCdJelveSqMe1mOr6rjfN13xsJbobThqxDe/TxVq/xqGXo3ussnxV9k4NL00S32oUxVj5HNxLTrj3NncqRpw1pLn+efW7W0++m6hRcZWlZRORX0U8AcTK+SXlMNa0f73Ud4LOuj+dGHt+N2Kn8lx9+UD9Wq/Va1n5ul49rbfs+aH0/juz9N82ytCwy0aTbY+WdyxXMvMw8M8+dyhn/YBTx3XlrvfR8TWsKzrbT+4jmJSBFmHSPsXO5S+QvlMVSpOa0O7KbtwqvncqaU57mFKfxvEanOauJeo/2BHxqyj1YWj46nut5upDIopMufpF1Qsz0vDIf381wqlC1aypnmmqvg7L9/0f3fHhPvyJ9m7GqTbkWiC7UaZ23y0UzatPcOHU2cJk2RYkcT29a8RXxvydu2c1YTlyjy7WUc8ocnyzhzTztRvLYOHUmcpmn2p7POXO2Q8T0u2n5/lsuLWfEpAsT0VepyvqHhNf5uh7XYPbYODUSu2pTbc9jVI1vlEzn527SRjfFVMwmqhSy3AIw27Sb8dSgPZaXeMwWWhGb01w04ysSH+BVThO6NMXu5Z4LY2Q4XSjjhTEsdj5GvxFm381clebGqbMXxtDeQauxA3n7x5LW1/He9ZyN985lkcSTLqAh6zJzVRl2Kkf/MXfL6cheHpvsXGGbbfptVvB4rgjRxQWLQGke2x19fq2f57XMPON1mD12KmeLrWpob/3vAfEV8Tv2a720nPF4rgjRRTEc330v4nhu9p3Ko1+zl1ls733c5PFdDdG9h01UaqJ3MousucysuYM5eqfymSm3XGzvfV5wfEX0Anz6Z+K0tKx9CUgRoosrFeI0yzJzFdE7lUeCWz60e48VFF8Rn+l31l3Lm6Wim2Hn8qq0p90KfxzsqXJcN3qncm9wp4ztvccuGt8su6Ujdi6LLBZdtKketD0zTLsZrrfssVO5NbhLhHbv6yWIr4jO9Nv0M2j4PmfdRCVCdN1lPEfXS5Zpd4bwevC4Gf2Z4M4S21uB6FqVSxBfETZetSof3Z4LY6BdlWm3yvOsJutO5ZlDe+vfD8VXpCvAVvEV+TjAWZaWI5WPrgl2LpvJsJNZJMe0m/W4btadyqnPrW3Uu+w5FF+Roen38nsTMf1qLS1nN8VlIGGjyl+lo8+z9fMyXSKy93hu78dn3amsdXnGYW/+8dQb/qev/3DqOOPw5w8+b+1LWXpebjLz8VwRJl0EsJh2WWY+r9pO5SPVptqex/SYfEX0l56ziNq5LLLQpMvpQmOqTLujKk673qJ3Kvd+nepTrenXSDL53nr8VaScdFPc1g+mZp52e47vZjmuG7lTeU/r51SfarfJq3dj6FKT7wTHc0WSRjcUm6g+kiVmLUaeq/amKitW5+dG71Q+cxx3lthe//9Xiq/mlKu5wmBxCUiR4tGtcrrQbMdDsssQ3irn7nrsVN4zGtzI2GqHdu9jVorvKtyi27pk3PpxJjeuV5hyZ3vxWU12GU4bWoXmjQ8irjh1KXqyFXn/fnImvN88fx66kcfC27/90fa9L2Bp+dsXL5qm3daP27hEd9bgzhbYaxbBJbYIo/jG7RHe0ZW84U2jJ4cO8/A2aP25RP7hY757ebbgPvmHP/38z6y+ePy4fHBn33U9s3s/u9M7kpWdPSOiyuExS9l3LVts6jWN7ozBnR3LyRiR+o+cgrteq025FWn+0dMTZ7PlZe3g9iC4bTx24hJbHRnuLFSScXAtlpkJbi69x2yPmEy6FsFtfSES3Nu2JePLf6xFBzf19LWI0J+B04SrucxcPbjZl4szCLsiFcG1ExHYS189eRIe3Co0L4zx5lWdabj3VKHuN3PnJWWO7+bR87OI+L6HnKdLcHVkvGAFsUW4oGO4GkvNo193SPCycqWpWHOJ2X3SJbhjoqfXFhmD27O8yXL0BII3TXlf471qcDPxnnZdJ12C2yZjUPdkjO2q3rz6Th6e61wIo5REO5TPTrw9X2eIcXAznK9rQWvaTXkZSPXgdvB+sVQL7DWCC2uHy5CJgouaPC+Wke4ykCbBbfzLzjq41QN7qVJso29UcFbL6UIzb6LalTS41tNu1il3dhrTbqrLQM4S3Mpv8C0qBRdxzI+RJw3uxiq8FYIbvcTstcQ/wjy6swd39sBeIra4JWQDWvLgbrTf/CsEt0XGncteS8wpLgNZKbjZdxBbqR5c7zBUuK1fBTffnIsEd+O9oxm2zl5F0Sy6FYLba6XIXqoeXOS/jGTzH0XFgrvRCO8sU243x5+5x+lDoZeBNPkPNDo1aMXgcmWpGiptolrZmfBWDG7GJWQtZ6bdsMtAVrpj0KrBnU22i19oXgLSg8b3r+fG9TO/afeoGNwMsi7rh0SX4ObFdJvLyLLwtJNv0aXlS24hSBzc7H9MWS8xu18cg+DmQmBhgctv3tezoznrtIbxc3Zdo0tw/RFVIJ+W8M6wrBx9vu4oy9OH3KJLcG0QVczooyXICZaWr+2Fd4bgrmBk2k137WWC+zHC6qfaJSMrHb/t2US1CtWLZxDcj5z5/lpNuy7RrXLHoKg3W6KKqlY7HmvhOgyzHce9XGLOvolqRO+0ax5dgvseYQU+RrTf28LLsvL8TKO7UnCJKrR5XEXqzavv5eH5Z+Zfp8cKx3NvIbj5WCwxm0W3SnB7Edfaqh2zrYjp1RHBTaHnClUmF8eodBP6njdggotM2ESFKiofy9W+WEbYZSCz3DGoFcHFRmOSs74EZIUgMxGfVGzKjQpvto1pIdEluIC/7HcaEln3eG63YsHFL9yjW+0WfQQXQCorBTfJH12aS8yu0bUKrtVOZYILANDkFl2CC7Q7WgqucMy2V8sxP7WrN1W10pSbjNa0G7aR6i6CC5R1a3PUrZ3LTZuorpYWt+AuG16COyzTZiqXy0BGn4tLcPddf3/YVYoWka+TLbyZ3kxNEdwUNC6WYR5dgutH66IP2+PMGl8ukNEv62vh1KUTgQCm0SW4Y7IEYfb43kOU/Z05VWj68DLlTsUsugS3/3lktWp8q3vz6jt5eP40+ml8ZOR1dHQcd9rwEtx0zi4xm0S3UnB7zRDRUcQ3h0o7lz0v/zhdeAmuKtV7F58Qt3s5SXB7ptyVg3vpi8eP+V4YqnDlqKw+ff2HFG+smNuZ04dioktwp0B8x1hfdznK6ArI0fHckYiWDy9T7rT8o0twp0N80crz0ETZ8BLcqflGt+A9cYlJO+KLbMqFl+CWMbrE7Bddw+Ba7VQmIGNWj++Xjx6ZPfbZTVQrHi/mOC8y8YkuwV1S5viyA/u+r9+9O/yYlu9fy85li+O596QPL1PuhwzuMKS9u31k2k117WWCO6fM8Z1JpVOJoqQNL8Fdhn10i90TlzjYIb7HZl7+zbK6kC68BLe03mnXNroJdioT3HyIrx+v6XckqC238rt29mLzmzThJbjLsYsuwcUB4quv9BLzwfHcLbia4Q2NL8Fdkk10iwUXsTLGN8tS6KVKQbW+/KNWeEWCpl6CG8biUqE9S8wu99O9J0twex47WxysRESHazuPyx5ki5/pFt4zl+TbuF63meAuLWz3MsHNLXL6zDj5apn1EpC9ztzK71qp47wEd3kh0SW4dRBfRKw83Duee0+J47wEFxIQ3Yq36OONPz6+FrItY898upCH1Md5CS5+8smPP/4Y/RwAAFhCqitSAQAwM6ILAIATogsAgBOiCwCAE6ILAIATogsAgBOiCwCAE6ILAIATogsAgBOiCwCAE6ILAIATogsAgBOiCwCAE6ILAIATogsAgBOiCwCAE6ILAIATogsAgBOiCwCAE6ILAIATogsAgBOiCwCAE6ILAICT/wAylZAmNTNAswAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for j in range(3):\n",
    "    qc = height2circuit(height_initial,rochester,limit=limit)\n",
    "\n",
    "    probs,raw_probs = get_probs([qc])\n",
    "    p = probs[0] + [0]*(53-limit)\n",
    "    height = make_height(p,rochester)\n",
    "    plot_height(height)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Below are 70 samples of real runs.\n",
    "* A random selection of 3 are shown."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "probs = [[0, 0.19980438731311997, 0.1119966442953022, 0.21462029808374739, 0.21212121212121224, 0.24343083787803665, 0.2839741708247726, 0.25150698986789777, 0.20750605326876514, 0.4778840406455469, 0.6301094890510947, 0.5461853259280911, 0.5143323926927077, 0.5697781885397412, 0.5143587430461585, 0.10184799221898017, 0.5930624915643137, 0.7625086147484492, 0.1973737103041672, 0.045274725274725036, 0.1667731629392972, 0.3367891446866902, 0.33649683649683637, 0.640562597673207, 0.5971293199554069, 0.5477222003413416, 0.369032258064516, 0.16890783863561826, 0.3180645161290323, 0.5593991807009557, 0.6222222222222223, 0.40617608409986855, 0.39308893176635673, 0.5183673469387756, 0.7164975974372665, 0.5398078975453575, 0.4958256686005375, 0.27778591301801153, 0.4005019720329868, 0.3007471980074722, 0.46801444043321316, 0.2579929531515073, 0.20536663124335813, 0.0476190476190477, 0.24824026278742387, 0.42695278969957084, 0.3217508417508419, 0.13518770667185356, 0.07979341510652026, 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0.16073260073260048, 0.07463258785942499, 0.40859887177923476, 0.2733932733932733, 0.5143254037159227, 0.6020066889632106, 0.6587895496914794, 0.4516129032258063, 0.13315841259429323, 0.29403225806451616, 0.6206190259444697, 0.48058902275769755, 0.19789750328515116, 0.49938607261883877, 0.6136054421768709, 0.716230646022424, 0.5237993596584846, 0.37144474317249176, 0.20866891199297127, 0.10953746862674793, 0.5794935657949358, 0.3878700361010832, 0.15437818086911131, 0.28134962805526037, 0.03864970645792573, 0.1345221335836072, 0.16240343347639494, 0.2404040404040405, 0.37327368216300316, 0.11155584247901865, 0.10414052697616065, 0.16275903796702448, 0.26329603536400054, 0.0948071536306831]]\n",
    "\n",
    "for _ in range(3):\n",
    "    j = random.randint(0,69)\n",
    "    height = make_height(probs[j],rochester)\n",
    "    plot_height(height)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We will use these in much the same way as we used the 'tartans' of the last section.\n",
    "* The tartans were given that name because the interference effects in that case induced a tartan-like pattern.\n",
    "* In this case the results are more blobby, so we'll call them 'blobs'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "blobs = []\n",
    "for p in probs:\n",
    "    blobs.append(make_height(probs[j],rochester))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* In the last section, we took a large island, and used the smaller tartans to provide texture.\n",
    "* Here we'll use the same except that we will use the blobs to provide texture.\n",
    "* Again we use the base island from Section 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from island import island\n",
    "\n",
    "plot_height(island)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The `quantum_island` below is made using the second method from the last section, in which the texture is positioned randomly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = max(max(island))+1\n",
    "\n",
    "quantum_island = {}\n",
    "for xx in range(size):\n",
    "    for yy in range(size):\n",
    "        quantum_island[xx,yy] = 0\n",
    "\n",
    "for _ in range(int(20*size**2/L**2)):\n",
    "    chosen = False\n",
    "    while not chosen:\n",
    "        x0 = random.randint(0,size-1)\n",
    "        y0 = random.randint(0,size-1)\n",
    "        chosen = (random.random()<island[x0,y0])\n",
    "    blob = random.choice(blobs)\n",
    "    for (x,y) in blob:\n",
    "        xx = x-int(L/2)+x0\n",
    "        yy = y-int(L/2)+y0 \n",
    "        if (xx,yy) in quantum_island:\n",
    "            quantum_island[xx,yy] += blob[x,y]\n",
    "        else:\n",
    "             quantum_island[xx,yy] = blob[x,y]  \n",
    "                \n",
    "max_height = max(quantum_island.values())\n",
    "\n",
    "for (xx,yy) in quantum_island:\n",
    "    quantum_island[xx,yy] = quantum_island[xx,yy]/max_height\n",
    "    \n",
    "plot_height(quantum_island)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We'll use this in the combined terrain generation procedure of [Section 5](5_A_Combined_Approach.ipynb)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('quantum_island.py', 'w') as file:\n",
    "    file.write('quantum_island='+str(quantum_island))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}