quantum_repetition_code.ipynb

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   "source": [
    "Author : Richard A. Wolf  \n",
    "Last update : April 2024  \n",
    "Sources : this notebook is based on [Craig Gidney's \"getting started\" notebook](https://github.com/quantumlib/Stim/blob/main/doc/getting_started.ipynb) introducing the [Stim library](https://github.com/quantumlib/Stim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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   "source": [
    "import numpy as np\n",
    "import stim"
   ]
  },
  {
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   "execution_count": 5,
   "metadata": {},
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    "# Step 1\n",
    "stim_code = stim.Circuit.generated(\"repetition_code:memory\", rounds=1, distance=2)\n",
    "stim_code.diagram('timeline-svg')"
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    "# Step 2\n",
    "def make_repetition_code() -> stim.Circuit:\n",
    "    \"\"\"Creates a repetition code circuit.\"\"\"\n",
    "    code = stim.Circuit()\n",
    "\n",
    "    for qb in range(3):                  #An R gate... \n",
    "        code.append(\"R\", [qb])           # ... on each qubit\n",
    "\n",
    "    code.append(\"CNOT\", [0, 1])          #A CNOT between qubit 0 and qubit 1\n",
    "    code.append(\"CNOT\", [2, 1])          #A CNOT between qubit 1 and qubit 2\n",
    "\n",
    "    return code\n",
    "\n",
    "our_code = make_repetition_code()\n",
    "our_code.diagram('timeline-svg')"
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       "<text dominant-baseline=\"central\" text-anchor=\"middle\" font-family=\"monospace\" font-size=\"30\" x=\"288\" y=\"64\" fill=\"white\">M</text>\n",
       "<text text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"288\" y=\"44\">rec[1]</text>\n",
       "<rect x=\"272\" y=\"176\" width=\"32\" height=\"32\" stroke=\"black\" fill=\"black\"/>\n",
       "<text dominant-baseline=\"central\" text-anchor=\"middle\" font-family=\"monospace\" font-size=\"30\" x=\"288\" y=\"192\" fill=\"white\">M</text>\n",
       "<text text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"288\" y=\"172\">rec[2]</text>\n",
       "</svg>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Step 3\n",
    "def make_repetition_code() -> stim.Circuit:\n",
    "    \"\"\"Creates a repetition code circuit.\"\"\"\n",
    "    code = stim.Circuit()\n",
    "\n",
    "    for qb in range(3):\n",
    "        code.append(\"R\", [qb])\n",
    "    code.append(\"CNOT\", [0, 1])\n",
    "    code.append(\"CNOT\", [2, 1])\n",
    "\n",
    "    code.append(\"MR\", [1])    #A Z-basis measurement + reset on qubit 1\n",
    "    code.append(\"M\", [0, 2])  #Simple Z-basis measurements on qubits 0 and 2\n",
    "                              # no resets here\n",
    "    return code\n",
    "\n",
    "our_code = make_repetition_code()\n",
    "our_code.diagram('timeline-svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "<text text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"480\" y=\"44\">D1 = rec[2]*rec[1]*rec[0]</text>\n",
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       "<text text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"288\" y=\"108\">rec[0]</text>\n",
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       "<text text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"480\" y=\"44\">D1 = rec[2]*rec[1]*rec[0]</text>\n",
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     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Step 4A\n",
    "def make_repetition_code() -> stim.Circuit:\n",
    "    \"\"\"Creates a repetition code circuit.\"\"\"\n",
    "    code = stim.Circuit()\n",
    "\n",
    "    for qb in range(3):\n",
    "        code.append(\"R\", [qb])\n",
    "    code.append(\"CNOT\", [0, 1])\n",
    "    code.append(\"CNOT\", [2, 1])\n",
    "\n",
    "    code.append(\"MR\", [1])           # First measurement\n",
    "    code.append(\"M\", [0, 2])         # Second and third measurements\n",
    "    \n",
    "    #Measurement of interest for that detector is the 3rd \n",
    "    # most ancient stored in the record, so the first one here\n",
    "    # [1,0] is a side annotations which could be ignored here\n",
    "    code.append(\"DETECTOR\", [stim.target_rec(-3)], [1,0])\n",
    "\n",
    "    #Measurements of interest for that detector are the latest, \n",
    "    # second latest and 3rd most ancient measurements stored\n",
    "    # in the record, so all of them here\n",
    "    # Again, [1,1] is just an annotation that we could ignore\n",
    "    code.append(\"DETECTOR\", [ stim.target_rec(-1), \n",
    "                              stim.target_rec(-2),\n",
    "                              stim.target_rec(-3)], \n",
    "                            [1,1])\n",
    "\n",
    "    return code\n",
    "\n",
    "our_code = make_repetition_code()\n",
    "our_code.diagram('timeline-svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "<circle cx=\"160\" cy=\"64\" r=\"12\" stroke=\"none\" fill=\"black\"/>\n",
       "<circle cx=\"160\" cy=\"128\" r=\"12\" stroke=\"black\" fill=\"white\"/>\n",
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       "<text text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"288\" y=\"172\">rec[2]</text>\n",
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       "<text dominant-baseline=\"hanging\" text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"416\" y=\"148\">coords=(1,0)</text>\n",
       "<text text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"416\" y=\"108\">D0 = rec[0]</text>\n",
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       "<text text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"416\" y=\"172\">L0 *= rec[2]</text>\n",
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       "<text dominant-baseline=\"hanging\" text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"480\" y=\"84\">coords=(1,1)</text>\n",
       "<text text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"480\" y=\"44\">D1 = rec[2]*rec[1]*rec[0]</text>\n",
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     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Step 4B\n",
    "def make_repetition_code() -> stim.Circuit:\n",
    "    \"\"\"Creates a repetition code circuit.\"\"\"\n",
    "    code = stim.Circuit()\n",
    "\n",
    "    for qb in range(3):\n",
    "        code.append(\"R\", [qb])\n",
    "    code.append(\"CNOT\", [0, 1])\n",
    "    code.append(\"CNOT\", [2, 1])\n",
    "\n",
    "    code.append(\"MR\", [1])\n",
    "    code.append(\"M\", [0, 2])\n",
    "    \n",
    "    code.append(\"DETECTOR\", [stim.target_rec(-3)], [1,0])\n",
    "    \n",
    "    # Here too, think of the pile of books, -1 is the most recent\n",
    "    code.append(\"OBSERVABLE_INCLUDE\", [stim.target_rec(-1)], 0)\n",
    "\n",
    "    code.append(\"DETECTOR\", [ stim.target_rec(-1),\n",
    "                            stim.target_rec(-2),\n",
    "                            stim.target_rec(-3)],\n",
    "                            [1,1])\n",
    "\n",
    "    return code\n",
    "\n",
    "our_code = make_repetition_code()\n",
    "our_code.diagram('timeline-svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 5\n",
    "depolarisation_probability = 0.03\n",
    "flip_probability = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
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   "source": [
    "stim_code = stim.Circuit.generated(\n",
    "              \"repetition_code:memory\",\n",
    "              rounds=1,\n",
    "              distance=2,\n",
    "              before_round_data_depolarization=depolarisation_probability,\n",
    "              before_measure_flip_probability=flip_probability\n",
    "             )\n",
    "stim_code.diagram('timeline-svg')"
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  {
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   "execution_count": 13,
   "metadata": {},
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       "<svg viewBox=\"0 0 800 288\"  version=\"1.1\" xmlns=\"http://www.w3.org/2000/svg\">\n",
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       "<text text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"544\" y=\"108\">D0 = rec[0]</text>\n",
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       "<text text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"544\" y=\"172\">L0 *= rec[2]</text>\n",
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       "<text dominant-baseline=\"hanging\" text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"608\" y=\"84\">coords=(1,1)</text>\n",
       "<text text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"608\" y=\"44\">D1 = rec[2]*rec[1]*rec[0]</text>\n",
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     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def make_repetition_code(depolarisation_proba:float, flip_proba:float) -> stim.Circuit:\n",
    "    \"\"\"Creates a repetition code circuit.\"\"\"\n",
    "    code = stim.Circuit()\n",
    "\n",
    "    for qb in range(3):\n",
    "        code.append(\"R\", [qb])\n",
    "\n",
    "    #depolarisation errors\n",
    "    code.append_operation(\"DEPOLARIZE1\", 0, depolarisation_proba)\n",
    "    code.append_operation(\"DEPOLARIZE1\", 2, depolarisation_proba)\n",
    "\n",
    "    code.append(\"CNOT\", [0, 1])\n",
    "    code.append(\"CNOT\", [2, 1])\n",
    "\n",
    "    for qb in range(3): # flip errors\n",
    "        code.append(\"X_ERROR\", qb, flip_proba)\n",
    "        \n",
    "    code.append(\"MR\", [1])\n",
    "    code.append(\"M\", [0, 2])\n",
    "    \n",
    "    code.append(\"DETECTOR\", [stim.target_rec(-3)], [1,0])\n",
    "    code.append(\"OBSERVABLE_INCLUDE\", [stim.target_rec(-1)], 0)\n",
    "    code.append(\"DETECTOR\", [ stim.target_rec(-1), stim.target_rec(-2), stim.target_rec(-3)], [1,1])\n",
    "\n",
    "    return code\n",
    "\n",
    "our_code = make_repetition_code(depolarisation_probability, flip_probability)\n",
    "our_code.diagram('timeline-svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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       "<text text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"544\" y=\"108\">D0 = rec[0]</text>\n",
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       "<text dominant-baseline=\"central\" text-anchor=\"middle\" font-family=\"monospace\" font-size=\"16\" x=\"544\" y=\"192\">OBS_INCLUDE(0)</text>\n",
       "<text text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"544\" y=\"172\">L0 *= rec[2]</text>\n",
       "<rect x=\"464\" y=\"48\" width=\"288\" height=\"32\" stroke=\"black\" fill=\"lightgray\"/>\n",
       "<text dominant-baseline=\"central\" text-anchor=\"middle\" font-family=\"monospace\" font-size=\"16\" x=\"608\" y=\"64\">DETECTOR</text>\n",
       "<text dominant-baseline=\"hanging\" text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"608\" y=\"84\">coords=(1,1)</text>\n",
       "<text text-anchor=\"middle\" font-family=\"monospace\" font-size=\"8\" x=\"608\" y=\"44\">D1 = rec[2]*rec[1]*rec[0]</text>\n",
       "<path d=\"M324,40 L324,32 L764,32 L764,40 \" stroke=\"black\" fill=\"none\"/>\n",
       "<path d=\"M324,248 L324,256 L764,256 L764,248 \" stroke=\"black\" fill=\"none\"/>\n",
       "</svg>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Wrapping up\n",
    "def make_repetition_code(depolarisation_proba:float=0.1, flip_proba:float=0.1) -> stim.Circuit:\n",
    "    \"\"\"Creates a repetition code circuit.\"\"\"\n",
    "    code = stim.Circuit()\n",
    "\n",
    "    for qb in range(3):\n",
    "        code.append(\"R\", [qb])\n",
    "\n",
    "    ############################## Tick start\n",
    "    code.append(\"TICK\")\n",
    "\n",
    "    code.append_operation(\"DEPOLARIZE1\", 0, depolarisation_proba)\n",
    "    code.append_operation(\"DEPOLARIZE1\", 2, depolarisation_proba)\n",
    "\n",
    "    code.append(\"CNOT\", [0, 1])\n",
    "\n",
    "    code.append(\"TICK\")\n",
    "    ############################## Tick end\n",
    "\n",
    "    code.append(\"CNOT\", [2, 1])\n",
    "\n",
    "    ############################## Tick start\n",
    "    code.append(\"TICK\")\n",
    "\n",
    "    for qb in range(3):\n",
    "        code.append(\"X_ERROR\", qb, flip_proba)\n",
    "        \n",
    "    code.append(\"MR\", [1])\n",
    "    code.append(\"M\", [0, 2])\n",
    "    \n",
    "    code.append(\"DETECTOR\", [stim.target_rec(-3)], [1,0])\n",
    "    code.append(\"OBSERVABLE_INCLUDE\", [stim.target_rec(-1)], 0)\n",
    "    code.append(\"DETECTOR\", [ stim.target_rec(-1), stim.target_rec(-2), stim.target_rec(-3)], [1,1])\n",
    "    \n",
    "    code.append(\"TICK\")\n",
    "    ############################## Tick end\n",
    "\n",
    "    return code\n",
    "\n",
    "our_code = make_repetition_code(depolarisation_probability, flip_probability)\n",
    "our_code.diagram('timeline-svg')"
   ]
  }
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