notebooks/tally-alpha.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "98d0ce36",
   "metadata": {},
   "source": [
    "# Tally α"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af3e2f8b",
   "metadata": {},
   "source": [
    "## Composition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7af9e23f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from tally import H, V, e\n",
    "\n",
    "composition = V(e, e, e) | e & H(e, e & e)\n",
    "\n",
    "composition.draw()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d518f4c9",
   "metadata": {},
   "source": [
    "## Tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1aef5f4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diagram = composition.to_diagram()\n",
    "diagram.draw()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f07d08d3",
   "metadata": {},
   "source": [
    "## Circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bde8af70",
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.random import rand, seed; seed(42)\n",
    "\n",
    "from discopy.monoidal import PRO\n",
    "from discopy.markov import Box, Functor, Category\n",
    "from discopy.quantum import qubit, Ty, Circuit, Discard, Measure, IQPansatz, Bits\n",
    "\n",
    "DEPTH = 1\n",
    "\n",
    "def ansatz(n_qubits, params):\n",
    "    return IQPansatz(n_qubits, params)\\\n",
    "        >> Discard((n_qubits - 1) // 2) @ qubit @ Discard(n_qubits // 2)\n",
    "\n",
    "params0 = rand(6)\n",
    "\n",
    "F = lambda params: Functor(\n",
    "    ob={PRO(1): qubit},\n",
    "    ar={Box('H', 3, 1): ansatz(3, params[0:2].reshape(1, 2)),\n",
    "        Box('V', 3, 1): ansatz(3, params[2:4].reshape(1, 2)),\n",
    "        Box('H', 2, 1): ansatz(2, params[4:5].reshape(1, 1)),\n",
    "        Box('V', 2, 1): ansatz(2, params[5:6].reshape(1, 1))},\n",
    "    cod=Category(Ty, Circuit))\n",
    "\n",
    "F0 = F(params0)\n",
    "\n",
    "circuit = F0(diagram) >> Measure() >> Bits(0)[::-1]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7e050140",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐                                                                                       \n",
       "q_0: ┤ H ├───────■───────────────────────────────────────────────────────────────────────────────\n",
       "     ├───┤ ┌─────┴──────┐                   ┌───┐                                             ┌─┐\n",
       "q_1: ┤ H ├─┤ Rz(4.5993) ├──────■────────────┤ H ├─────────────────────────────────────■───────┤M├\n",
       "     ├───┤ └────────────┘┌─────┴──────┐     └───┘                                     │       └╥┘\n",
       "q_2: ┤ H ├───────────────┤ Rz(3.7615) ├───────────────────────────────────────────────┼────────╫─\n",
       "     ├───┤               └────────────┘                                   ┌───┐┌──────┴──────┐ ║ \n",
       "q_3: ┤ H ├────────────────────────────────────────────────────────■───────┤ H ├┤ Rz(0.98029) ├─╫─\n",
       "     ├───┤                                            ┌───┐┌──────┴──────┐└───┘└─────────────┘ ║ \n",
       "q_4: ┤ H ├────────────────────────────────────■───────┤ H ├┤ Rz(0.98014) ├─────────────────────╫─\n",
       "     ├───┤                   ┌───┐     ┌──────┴──────┐└───┘└─────────────┘                     ║ \n",
       "q_5: ┤ H ├───────■───────────┤ H ├─────┤ Rz(0.98029) ├─────────────────────────────────────────╫─\n",
       "     ├───┤┌──────┴──────┐    └───┘     └─────────────┘                                         ║ \n",
       "q_6: ┤ H ├┤ Rz(0.98014) ├──────────────────────────────────────────────────────────────────────╫─\n",
       "     └───┘└─────────────┘                                                                      ║ \n",
       "c: 1/══════════════════════════════════════════════════════════════════════════════════════════╩═\n",
       "                                                                                               0 </pre>"
      ],
      "text/plain": [
       "     ┌───┐                                                                                       \n",
       "q_0: ┤ H ├───────■───────────────────────────────────────────────────────────────────────────────\n",
       "     ├───┤ ┌─────┴──────┐                   ┌───┐                                             ┌─┐\n",
       "q_1: ┤ H ├─┤ Rz(4.5993) ├──────■────────────┤ H ├─────────────────────────────────────■───────┤M├\n",
       "     ├───┤ └────────────┘┌─────┴──────┐     └───┘                                     │       └╥┘\n",
       "q_2: ┤ H ├───────────────┤ Rz(3.7615) ├───────────────────────────────────────────────┼────────╫─\n",
       "     ├───┤               └────────────┘                                   ┌───┐┌──────┴──────┐ ║ \n",
       "q_3: ┤ H ├────────────────────────────────────────────────────────■───────┤ H ├┤ Rz(0.98029) ├─╫─\n",
       "     ├───┤                                            ┌───┐┌──────┴──────┐└───┘└─────────────┘ ║ \n",
       "q_4: ┤ H ├────────────────────────────────────■───────┤ H ├┤ Rz(0.98014) ├─────────────────────╫─\n",
       "     ├───┤                   ┌───┐     ┌──────┴──────┐└───┘└─────────────┘                     ║ \n",
       "q_5: ┤ H ├───────■───────────┤ H ├─────┤ Rz(0.98029) ├─────────────────────────────────────────╫─\n",
       "     ├───┤┌──────┴──────┐    └───┘     └─────────────┘                                         ║ \n",
       "q_6: ┤ H ├┤ Rz(0.98014) ├──────────────────────────────────────────────────────────────────────╫─\n",
       "     └───┘└─────────────┘                                                                      ║ \n",
       "c: 1/══════════════════════════════════════════════════════════════════════════════════════════╩═\n",
       "                                                                                               0 "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import warnings; warnings.filterwarnings(\"ignore\")\n",
    "from pytket.extensions.qiskit import AerBackend, tk_to_qiskit\n",
    "\n",
    "tk_to_qiskit(circuit.to_tk()).draw(fold=-1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7dd69b6e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4228515625"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = AerBackend()\n",
    "\n",
    "evaluate = lambda F, composition: float((\n",
    "    F(composition.to_diagram()) >> Measure() >> Bits(0)[::-1]).eval(\n",
    "        backend=backend, compilation=backend.default_compilation_pass()))\n",
    "\n",
    "evaluate(F0, composition)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4e25104",
   "metadata": {},
   "source": [
    "## Repeat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "10844ddb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def flip(composition):\n",
    "    for X, Y in [(H, V), (V, H)]:\n",
    "        if composition.label is X:\n",
    "            return Y(*map(flip, composition.terms))\n",
    "    return composition\n",
    "\n",
    "flip(composition).draw()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d7f8f53d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rotate(composition).to_diagram().draw()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "105a3fd3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐                                                                                       \n",
       "q_0: ┤ H ├───────■───────────────────────────────────────────────────────────────────────────────\n",
       "     ├───┤ ┌─────┴──────┐                   ┌───┐                                             ┌─┐\n",
       "q_1: ┤ H ├─┤ Rz(2.3533) ├──────■────────────┤ H ├─────────────────────────────────────■───────┤M├\n",
       "     ├───┤ └────────────┘┌─────┴──────┐     └───┘                                     │       └╥┘\n",
       "q_2: ┤ H ├───────────────┤ Rz(5.9735) ├───────────────────────────────────────────────┼────────╫─\n",
       "     ├───┤               └────────────┘                                   ┌───┐┌──────┴──────┐ ║ \n",
       "q_3: ┤ H ├────────────────────────────────────────────────────────■───────┤ H ├┤ Rz(0.98014) ├─╫─\n",
       "     ├───┤                                            ┌───┐┌──────┴──────┐└───┘└─────────────┘ ║ \n",
       "q_4: ┤ H ├────────────────────────────────────■───────┤ H ├┤ Rz(0.98029) ├─────────────────────╫─\n",
       "     ├───┤                   ┌───┐     ┌──────┴──────┐└───┘└─────────────┘                     ║ \n",
       "q_5: ┤ H ├───────■───────────┤ H ├─────┤ Rz(0.98014) ├─────────────────────────────────────────╫─\n",
       "     ├───┤┌──────┴──────┐    └───┘     └─────────────┘                                         ║ \n",
       "q_6: ┤ H ├┤ Rz(0.98029) ├──────────────────────────────────────────────────────────────────────╫─\n",
       "     └───┘└─────────────┘                                                                      ║ \n",
       "c: 1/══════════════════════════════════════════════════════════════════════════════════════════╩═\n",
       "                                                                                               0 </pre>"
      ],
      "text/plain": [
       "     ┌───┐                                                                                       \n",
       "q_0: ┤ H ├───────■───────────────────────────────────────────────────────────────────────────────\n",
       "     ├───┤ ┌─────┴──────┐                   ┌───┐                                             ┌─┐\n",
       "q_1: ┤ H ├─┤ Rz(2.3533) ├──────■────────────┤ H ├─────────────────────────────────────■───────┤M├\n",
       "     ├───┤ └────────────┘┌─────┴──────┐     └───┘                                     │       └╥┘\n",
       "q_2: ┤ H ├───────────────┤ Rz(5.9735) ├───────────────────────────────────────────────┼────────╫─\n",
       "     ├───┤               └────────────┘                                   ┌───┐┌──────┴──────┐ ║ \n",
       "q_3: ┤ H ├────────────────────────────────────────────────────────■───────┤ H ├┤ Rz(0.98014) ├─╫─\n",
       "     ├───┤                                            ┌───┐┌──────┴──────┐└───┘└─────────────┘ ║ \n",
       "q_4: ┤ H ├────────────────────────────────────■───────┤ H ├┤ Rz(0.98029) ├─────────────────────╫─\n",
       "     ├───┤                   ┌───┐     ┌──────┴──────┐└───┘└─────────────┘                     ║ \n",
       "q_5: ┤ H ├───────■───────────┤ H ├─────┤ Rz(0.98014) ├─────────────────────────────────────────╫─\n",
       "     ├───┤┌──────┴──────┐    └───┘     └─────────────┘                                         ║ \n",
       "q_6: ┤ H ├┤ Rz(0.98029) ├──────────────────────────────────────────────────────────────────────╫─\n",
       "     └───┘└─────────────┘                                                                      ║ \n",
       "c: 1/══════════════════════════════════════════════════════════════════════════════════════════╩═\n",
       "                                                                                               0 "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit2 = F0(flip(composition).to_diagram()) >> Measure()\n",
    "tk_to_qiskit(circuit2.to_tk()).draw(fold=-1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d1803ced",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.435546875"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evaluate(F0, flip(composition))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4995bbf",
   "metadata": {},
   "source": [
    "### Both compositions have scores around 50%: Tally has no opinion...\n",
    "\n",
    "### Time to do some learning!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da41c40b",
   "metadata": {},
   "source": [
    "## Learn"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b498f6e2",
   "metadata": {},
   "source": [
    "### Say that we like our first example, but not its rotation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "59486ee6",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = {composition: 1, flip(composition): 0}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5285e39b",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step 1: [0.37572392 0.95189811 0.73081014 0.59984229 0.15483483 0.15481071]\n",
      "Step 2: [0.34239453 0.98522751 0.69748074 0.63317168 0.12150544 0.12148132]\n",
      "Step 3: [0.28645697 0.92928994 0.64154318 0.57723412 0.06556788 0.06554376]\n",
      "Step 4: [0.26130525 0.90413823 0.66669489 0.60238584 0.09071959 0.04039204]\n",
      "Step 5: [0.21265488 0.9527886  0.71534527 0.65103621 0.13936997 0.08904241]\n",
      "Step 6: [0.14466666 0.88480038 0.64735705 0.58304799 0.07138175 0.15703063]\n",
      "Step 7: [0.11398004 0.85411376 0.67804366 0.55236137 0.10206836 0.12634402]\n",
      "Step 8: [0.04309363 0.92500017 0.74893007 0.48147497 0.03118196 0.05545761]\n",
      "Step 9: [0.02639453 0.90830106 0.73223096 0.46477586 0.01448285 0.07215672]\n",
      "Step 10: [-0.01016455  0.94486014  0.69567188  0.42821678 -0.02207623  0.03559763]\n",
      "Step 11: [ 0.02232081  0.91237478  0.72815724  0.39573142 -0.05456159  0.00311228]\n",
      "Step 12: [ 0.05091347  0.88378212  0.75674991  0.36713876 -0.02596892 -0.02548039]\n",
      "Step 13: [0.01150605 0.84437469 0.79615733 0.32773133 0.0134385  0.01392703]\n",
      "Step 14: [0.01446326 0.8473319  0.79911455 0.33068854 0.01639571 0.01688424]\n",
      "Step 15: [ 0.06980626  0.9026749   0.85445755  0.27534554 -0.03894729  0.07222724]\n",
      "Step 16: [ 0.06036946  0.8932381   0.84502074  0.26590874 -0.04838409  0.06279044]\n",
      "Step 17: [ 0.08109239  0.87251517  0.86574367  0.24518581 -0.02766116  0.08351337]\n",
      "Step 18: [ 0.09431834  0.85928922  0.87896962  0.23195986 -0.04088711  0.09673932]\n",
      "Step 19: [ 0.10204125  0.85156631  0.88669253  0.22423695 -0.04861002  0.10446223]\n",
      "Step 20: [ 0.07078238  0.88282518  0.85543366  0.19297808 -0.07986889  0.1357211 ]\n",
      "Step 21: [ 0.06987818  0.88192099  0.85452947  0.19207388 -0.08077309  0.13481691]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       " message: terminated after reaching max number of iterations\n",
       " success: True\n",
       "     fun: 0.015497207641601562\n",
       "       x: [ 6.988e-02  8.819e-01  8.545e-01  1.921e-01 -8.077e-02\n",
       "            1.348e-01]\n",
       "     nit: 21\n",
       "    nfev: 42"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from time import time\n",
    "import numpy as np\n",
    "import noisyopt\n",
    "\n",
    "i, start, losses = 0, time(), []\n",
    "\n",
    "def callback(params):\n",
    "    global i\n",
    "    i += 1\n",
    "    losses.append(loss(params))\n",
    "    print(\"Step {}: {}\".format(i, params))\n",
    "\n",
    "def loss(params):\n",
    "    return np.mean(np.array([\n",
    "        (value - evaluate(F(params), composition)) ** 2\n",
    "        for composition, value in data.items()]))\n",
    "\n",
    "experiment = noisyopt.minimizeSPSA(\n",
    "    loss, params0, paired=False, callback=callback, niter=21)\n",
    "experiment\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f81e50b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.draw(-np.array(losses))\n",
    "plt.xlabel('step')\n",
    "plt.ylabel('loss')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "64a4aace",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(V(e, e, e) | e & (e | e & e)): 0.828125,\n",
       " H(e, e, e) & (e | e & (e | e)): 0.0576171875}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{c: evaluate(F(experiment.x), c) for c in data}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0035b6fc",
   "metadata": {},
   "source": [
    "### Tally's score have come close enough to our human judgement..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3888bff8",
   "metadata": {},
   "source": [
    "### Our first quantum drawing experiment is a success!"
   ]
  }
 ],
 "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}