{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "42c975c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit.transpiler import generate_preset_pass_manager\n",
    "from qiskit_ibm_runtime import QiskitRuntimeService\n",
    "from qiskit_ibm_runtime import SamplerV2 as Sampler\n",
    "from scipy.optimize import curve_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "866fa483",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using backend: ibm_marrakesh\n"
     ]
    }
   ],
   "source": [
    "# ----------------------------------------------------------------------\n",
    "# Connect to IBM Quantum\n",
    "# ----------------------------------------------------------------------\n",
    "service = QiskitRuntimeService()\n",
    "\n",
    "backend = service.least_busy(\n",
    "    simulator=False,\n",
    "    operational=True\n",
    ")\n",
    "\n",
    "print(\"Using backend:\", backend.name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "72aac1ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ----------------------------------------------------------------------\n",
    "# Build preset pass manager (works normally)\n",
    "# ----------------------------------------------------------------------\n",
    "pm = generate_preset_pass_manager(\n",
    "    backend=backend,\n",
    "    optimization_level=1\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "66572313",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ----------------------------------------------------------------------\n",
    "# Create T1 circuits (X — delay — X — measure)\n",
    "# ----------------------------------------------------------------------\n",
    "def make_T1_circs(delays_ns, qubit=0):\n",
    "    circuits = []\n",
    "    for t in delays_ns:\n",
    "        qc = QuantumCircuit(1, 1)\n",
    "        qc.x(qubit)                    # prepare |1>\n",
    "        qc.delay(int(t), qubit, 'ns')  # use ns delays\n",
    "        qc.x(qubit)                    # flip back\n",
    "        qc.measure(qubit, 0)\n",
    "        qc.name = f\"T1_{int(t)}ns\"\n",
    "        circuits.append(qc)\n",
    "    return circuits\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "b66d8bf5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[     0.  16000.  32000.  48000.  64000.  80000.  96000. 112000. 128000.\n",
      " 144000. 160000. 176000. 192000. 208000. 224000. 240000. 256000. 272000.\n",
      " 288000. 304000. 320000. 336000. 352000. 368000. 384000. 400000.]\n"
     ]
    }
   ],
   "source": [
    "# Delay times: 0 to 400 us\n",
    "delays_ns = np.linspace(0, 400000, 26)\n",
    "raw = make_T1_circs(delays_ns)\n",
    "print(delays_ns)\n",
    "\n",
    "# Transpile using your preset pass manager\n",
    "T1_transpiled = [pm.run(circ) for circ in raw]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "6ad9bcaf",
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler = Sampler(mode=backend)\n",
    "\n",
    "# sampler supports only positional args in run()\n",
    "job = sampler.run(T1_transpiled)\n",
    "\n",
    "result = job.result()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "ba8d175a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ----------------------------------------------------------------------\n",
    "# Extract P(1) from counts\n",
    "# ----------------------------------------------------------------------\n",
    "p1 = []\n",
    "\n",
    "for res in result:\n",
    "    counts = res.data.c.get_counts()\n",
    "    shots = sum(counts.values())\n",
    "    p1.append(counts.get('1', 0) / shots)\n",
    "\n",
    "p1 = np.array(p1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "5b169ef3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Estimated T1 = 402.0 µs\n",
      "\n"
     ]
    }
   ],
   "source": [
    "delays_s = delays_ns * 1e-9\n",
    "def model(t, T1):\n",
    "    return (1-np.exp(-t / T1))\n",
    "\n",
    "params, cov = curve_fit(model, delays_s, p1, p0=[100e-6])\n",
    "T1_seconds = params[0]\n",
    "T1_us = T1_seconds * 1e6\n",
    "\n",
    "print(f\"\\nEstimated T1 = {T1_us:.1f} µs\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "5732cb3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ----------------------------------------------------------------------\n",
    "# Plot\n",
    "# ----------------------------------------------------------------------\n",
    "plt.figure(figsize=(8,5))\n",
    "plt.scatter(delays_ns/1000, p1, label='data')\n",
    "\n",
    "tfit = np.linspace(0, max(delays_ns), 200)\n",
    "plt.plot(tfit/1000, model(tfit*1e-9,T1_seconds), 'r', label=f\"fit: T1={T1_us:.1f} µs\")\n",
    "\n",
    "plt.xlabel(\"Delay (µs)\")\n",
    "plt.ylabel(r\"$P_1$($\\tau$)\")\n",
    "plt.title(r\"$T_1$ Relaxation\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "08219644",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWMAAACuCAYAAADjw2w/AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy88F64QAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAYkElEQVR4nO3deVhTV/4G8DcQCLsILhERFAQFd8WFVkWtKEqtdWltbWs7o3Xsoo5161htnVrrUnWmtjNWW9epdfRXHetCrXul1g0RpaKisgxLEBeEhC0kub8/GGmpEEgM5BDfz/P4GO5y7vd6ry8nJzf3yiRJkkBERFZlZ+0CiIiIYUxEJASGMRGRABjGREQCYBgTEQmAYUxEJACGMRGRABjGREQCYBgTEQmAYUxEJACGMRGRABjGREQCYBgTEQmAYUxEJACGMRGRABjGREQCYBgTEQmAYUxEJACGMRGRABjGREQCYBgTEQmAYUxEJACGMRGRABjGREQCYBgTEQmAYUxEJACGMRGRABjGREQCYBgTEQmAYUxEJACGMRGRABjGREQCYBgTEQmAYUxEJACGMRGRABjGREQCYBgTEQlAbu0CbJkkSSgq1lm7DJO4OMshk8lMWkeSJOiKS+uoIrHInRUm/fs8LueAMZIkQa/XW6y9umZvb2/R/a8thnEdKirWwa3PFmuXYRLN6QlwdXEwaR1dcSm2Br5cRxWJ5aWbX8PBxanWyz8u54Axer0eO3futFh7dW3MmDGQy+s/GjlMQUQkAIYxEZEAGMZERAJgGBMRCYBhTEQkAIYxEZEAGMbUYCnDO+A11bdo+/wAa5dC9Mh4nTHVGWV4B0Tt+mvFzwa9HmXqYhTl3MPdSylI3f0Tso4lWK9AIoEwjKnOpeyKRebReEAmg4OrMxq19YFfVC+0fX4Asn+8iOOTV0JbUGTtMomsimFMde5uYipSdsZWmnbug83oseBldJzyDPqvmYHDLy22UnVEYmAYk1VIBgPi/roFTbsFwXdQNzTr1R65Z68CABzcXdB52mj4R/eGq08TlGmKkH0iEfFLv4Hmv7nGG5bJ0HnaKPgM6IpGAS3g6OmG4tv3kXk4HheWbUNpngYA4OTtgefi1yJt32nEvvXpQ830/ngS2r86BDt7vwVN5m2L7z9Zj1arRVFRETw9Pa1dSiUMY7Kq698cQfPeIfAd3B25Z6/Cwd0Fw/cuhlvLJrj+76O4fy0Dzs0ao/1rQ/F0zBLsjZqLwsw71bZn7yhHxzdGIm3/aWQcOAddcSm8uwQi6MVBaN6rPfYOnQtDmQ4ldwuQcTAO/sN64YyHS6VhEnuFAwJG9UV2bCKDWBAlJSW4efMmUlNTkZKSgvz8fOh0Osjlcnh7e6NNmzYICAhAQEAAHByqv6+GVqvFypUrcfv2bSxYsACNGzeux70wjmFMVnXvSjoAwCPABwDQbc44uPs1w/6n5yEvKb1iuRs7jmHk0VXoNmscfvrzP6ptT19ahu1dX4e+RFtp+u24a3hy1Zvwi+qJtL2nAADJXx9G66fD0WZUP1zb/EPFsv7RfaDwdMP1rYcttp9knoyMDBw6dAixsbEoLi6udrkTJ04AANzd3TFw4EAMHjwYzZo1q7TMgyC+ePEiAOCTTz7B4sWLrXKHtqrY3KVtd+7cwZw5c9C2bVs4OTmhVatWmD59OgoLCzFx4kTIZDJ8/vnn1i6T/qdMXf4fzNHNGQAQMLofbp25gqKce1B4uVf80RWV4nb8dfhEdKmxzQdBLLOzg6OHCxRe7lD99AsAoEn3oIrlsn+8CHX6LQSNH1Rp/aAXB6HkXgH+e+CcRfaRTFdQUIDVq1dj9uzZOHjwoNEg/i21Wo09e/Zg+vTpWL9+PUpKSgA8HMROTk6YMGGCMEEM2FjPOCEhAcOGDUNOTg5cXV0RGhqK7OxsrF69Gjdv3sS9e/cAAF27drVuoWZYPK0H5k3qij++fwIbd19/aP6x9cMR3qUZerzwHS7fyLNCheZxcC8PYa2mGE7eHnDy8kDLAV3x4uWNVS5vqMV9cVuPCEeHKc/Aq2Nr2DtWfsuqaORW6efkb46gx1/Gw6tDa9y7nAY3v2ZQPtEBSV/FwFAmzn2IbfX4VyUuLg5ffvkl8vPzK6YpFAr06dMH7dq1Q2BgIJo3bw65XA6tVguVSoWUlBQkJSXh7Nmz0Ov1kCQJhw4dwsWLFzFp0iTs37+/UhC/++67aN++vbV2sUo2E8Z37tzBiBEjkJOTg5kzZ+KDDz6Au7s7AGD58uWYO3cu5PLym2Z37tzZytWabuE/L2BEhB9WzeqNg6eykHXr1zHOP7/cAQN6tsC7fz/X4P4jeoX4AwAKbmYD/+ulZP94EYn/2G1We37De2PAupm4HX8dZxdsRGH2XehLtZDZ22HItgWQ2VXuCd3YdhTdZj2PoBcH4cz8DQh6cRBkdnbCDVHY6vH/vZiYGGzZ8uv9n11dXTFmzBhERETA1dX1oeXlcjkCAwMRGBiIyMhI3L9/H0eOHMGePXtQWlqK3NxcfPzxxxXLixrEgA0NU0ybNg2ZmZl4++23sWLFioogBoA5c+agS5cu0Ol0aN26NTw8PKxYqXnKdAa8Ov8EXJ0dsH5hv4rpwa0bYfHUMJy+lItPNiVasULzBI1/CgCQefg8Su4WoPS+Bg7uLlDFJlb7x5jAsf2hKy7FgbEf4NqWg8g8fB6q2EQUVvNBXPHt+8g4dB4Bo/tB7qxA2+cH4vb5ZNxPzrT4vj4KWz3+v/X9999XCuIePXpgxYoVGD58eJVBXBVPT0+MGTMGy5YtQ7t27SrNc3BwEDaIARsJ4ytXrmD79u1o0qQJlixZUuUyPXr0AAB06VLzmKOoLly5iyXrL2Lok754fUw72NnJsGVxf8hkwKvzT8BgkKxdYq3J7OwQ9v4ENO8dgozD55F77hogSUjZFYum3YPgH92nyvWcvI3/IpX0hvL2ZZVP7c5/HlvtOslbD0PR2B3hyyfD1ccbyd8cMXFv6octHf/fS0xMxObNmyt+Hjt2LGbNmmX21Q5eXl5QKBSVpun1ejg7Oz9SnXXJJoYptm3bBoPBgJdeeglubm5VLvPgIDTkMAaAResu4JkBflgxsxe6tvdG707N8M4nZ5Ccll/zylbi3akNAsaU9+Z++w08t1bNkHU8ASfe/PU63/il29CsZ3sMWPcO0vacwu34ZOi1Orj5NoXvU91w91KK0asp0vedRuunwzH02w9w8/9+hJ2DHH5RPSF3VlS7TtaxBGgychE4NgJlmmKk7j5puZ23sIZ4/GtSXFyMtWvXVvw8atQojB1b/S/Pmjz4sO7SpUsAyp9pp9frYTAYsGbNGnz00UdWeaxSTcSryAxHjx4FAAwcOLDaZTIzy992NvQw1ukkvDr/BM5tewZvjgtBbHwO/v71L9Yuy6iA0f0QMLofDHo9dIUlKFTdQ86pJKTOXffQvSnK1EWIGfkeOkx5Bm1GhKPV0DBIegMKVXeRe/Yqkrca77WmfncScjdndJgcjZ7vT0BpfiEyDsXh/OKtGH9lU9UrSRKStx1F9zkvIHXPz9AVlVhmx+tAQzz+Ndm2bRvu3Cm/djw0NBTPPfec2W1VddXErFmzsGnTJmRmZiItLQ179+7FqFGjLFK7JdlEGKenl1+P6u/vX+V8nU6HkyfLezuPEsZhYWHIycmp9fIGOABe883eXnXyNVqUavVwdLBHTGwGJAu+Ow0KDoYdykxax0Gywwfo9dD0nFOXsamF6T0cfbEWl/72LS797Vujy1XX/vWth6v8AM5YLYbS8n2+XsMQRXBQMMpkBqPLVGq3Ds6Bujz+gHnngDGOjo7VDh/m5+dXdKYUCgWmTJkCOzvzRk+rCuIHY8RvvPEGFixYAIPBgJiYGERHR8PR0bHKdoKDg6HVaqucVxtKpRJxcXEmr2cTYVxYWAgA1V6LuH37dty5cwfu7u5o06aN2dvJyclBVlZW7VeQOQJeZm+uWhs/7AdHB3sk3czD/MldseOHVKRkqi3Stio7G5BMOxEdZfZAc4ts3ipk9nYIfiUS95LScft8stFls1XZ0EomPHa+Ds6Bujz+gHnngDG/H7v9rePHj0OnK7+EMDIy8qEvatSWsSAGgMDAQISHh+PkyZNQq9U4ffo0+vfvX2Vb2dnZKC0tNauOR2ETYaxUKpGXl4f4+HiEh4dXmqdSqTB79mwAQOfOnR/pIm+lUmnS8gY4QGX21qo2dXwoBvbywbzVcfjuWDritz+LDR/2w4A/xlik/RY+Pmb1jFH7zqIw3Fo1Q9OwYPgN7QmP1kr8OOVvNa7j08LH5J6xJc+Buj7+gHnngDHV9UAlScKRI+XvRGQyGQYPHmxW+zUF8QNDhgypeId85MiRasPYx8fnkXvG5rCJMB48eDCuXLmCZcuWITIyEsHBwQCAc+fO4ZVXXqkYj3rUL3uY+tajsKgMbn221LxgLbX188CS6WE4m3gbyzZcgsEgYeGaeCyZ3hNTx4fis2+SHnkb15OT4epS/Xf7q1JWVIKtgS8/8rbrmzI8FH0/fRsld/ORsHIHUr+r+YO75OvJcHBxqvU2LHkO1MfxB8w7B4zR6XTYuXPnQ9Pz8vKQm1t+46f27dubFWK1DWKgfPhBqVQiJycHN27cQFlZWZX3sUhOTrbKB3w2cWnbnDlz4O3tjYyMDHTo0AGdOnVCUFAQevXqhYCAAAwaVP5114b84Z1MBmxa1B/2djK8Ov/HisuYlm9MxLlfbmPJ9DAE+LrX0Ar91o0dx7GpxVj8u+NEJKzYYe1yjLLF45+SklLxOigoyMiSVTMliIHy3nfbtm0BlF/mlpGRYUbVdccmwtjX1xexsbGIjo6Gk5MT0tLS4OXlhbVr12L//v1ITi4fB2zIYTzz1U54sltzvP/PeFxN/fUyJoNBwmsLTkBub4cNH/Yz0gI1ZLZ4/NPS0ipeBwQEmLSuqUFc1XZSU1NN2mZds4kwBoCQkBDs27cParUaarUaZ86cweTJk1FYWIi0tDTY2dmhY8eO1i7TLO3bNMKit7rj1MVcrNz88GVMSTfvY+GaeESEtcDU8aFWqJDqkq0ef41GU/Ha29u71uuZG8QA0KRJk4rXDz74F4VNjBkbc/nyZUiShODgYLi4uFi7HLNcTc2Hc8/NRpdZuv4Slq6/VE8VUX2y1eMfFRWFsLAwlJWVwcfHp9br3bx5E7/8Uv5LydR7TQQHB2Pu3LlwdHRE8+ZiXQJk82GcmFj+ff2GPERBZIuUSqVZH9qFhIRgxowZ+OKLLzBr1iyT7jXh6emJbt26mbzN+sAwJqIGJywsDKtXr26w73arwjCmetFr0R/hNzQMbq2aYc/gWbh3OQ0A4N5GiX6fToXCyx1l6iL8NP3zijumGZv3mupb5F1JR9xHXyPr6AWzagqd/DTavzYUusIS7ImcbZH9pPpjS0EM2NAHeNU5evQoJElCdHS0tUt5rKXvP4WYkfOhyaj8QNEnlv8JyV8fwn/6TkPi57vR99O3azUPAL5/doHZQQwASev24eeZX5i9PpEl2XzPmMRw6/SVh6Y5eXvAu0sgDr6wCACQvv80+nw8Ee6tlShTF1U7T5328P1Bus58Ho2CWkLurIB76+Yozr2PY6+vhPa+Bk27B6H3kkmws7ODTG6PqxsP4NqWg3W7w0QmYhiT1bi2bILiW3kV9yAGAE3WHbi2bIIydVG186oKYwBo2j0Ie4fOQWmeBhFrZqDdK5FI/Ow/6DR1NC6v2VNxa0zHRrW7UTlRfWIYk83IOpaA0rzya1dzz19D4/Z+AICcn39Blxlj4dGmBVQnf0Hu2avWLJOoSjY/ZkziKsy6A+fmjSGz//U0dGvZBIVZd4zOq46+9Nebu0h6A+zk9gCApC/34/DLS1CUex/d/zIefZZMqoO9IXo0DGOympK7BbiXmIrAMeV3z/KP7oNC1T2o03KMzjOVR6APNBm5uL71MBJX70LTHsEW3Q8iS+AwBdWL8OWT4ftUDzg380Tktvko0xRj1xNT8fOctej797fQadpolGmKKz1Sydg8U4T8IQrKvp1g0OogGQw4t9D4t9mIrIFhTPXi1Jx1VU4vuJmNmBHvmTzv9xJWVr7r2tWNBypen5m/oZZVElkPhymoQSrOzUPUrg/RcpD5X20Nnfw0+iydhJJ7lntKBpG52DOmBml7l9cfuY2kdfuQtG6fBaohenTsGRMRCYBhTEQkAJkkWfpB3/SAJEkoKtZZuwyTuDjLTX5oqyRJ0BXX/9N0rUHurDDp3+dxOQeMkSQJer0JT9Q24pO126EuLIS7qytm/2lctdMehb29vUX3v7Y4ZlyHZDKZRR/sKCqZTGbSQzofJ4/LOWCMTCaz2AM+JQAGqfzvB21WNa0h4jAFEZEAGMZERAJgGBMRCYBhTEQkAIYxEZEAGMZERAJgGBMRCYBhTEQkAIYxEZEAGMZERAJgGBMRCYBhTEQkAIYxEZEAGMZERAJgGBMRCYBhTEQkAIYxEZEAGMZERAJgGBMRCYBhTEQkAIYxEZEAGMYWduLECYwcORL+/v6QyWT46KOPrF0SEdUgJiYGXbt2hUKhQOvWrbFq1ap6r4FhbGEajQahoaFYvnw5lEqltcshohrExcVh5MiRGDZsGBISErBw4ULMmzcPX3zxRb3WIa/XrT0Ghg8fjuHDhwMA5s6da+VqiKgmq1atQs+ePbFkyRIAQEhICC5fvoylS5diypQp9VYHe8ZE9Fg7efIkoqKiKk2LiopCeno6MjMz660O9oyJSEjpmTkoLdNVmqbT6yv+Tk7NrHYaALg4K+CrbFrjdlQq1UNDig9+VqlU8PX1NX8nTMAwJiIh5d69j50HTlQ5r6i4BBt2xBid9oexUb9fTWgcpiAiIYV1boeQtn5mrdu7awjaBdZu3RYtWiAnJ6fStFu3blXMqy8MYyISkkwmw+io/nB1cTJpPe/GHoge2KfWyz/55JP44YcfKk07cOAA/P39622IAmAYW5xGo0FCQgISEhKg1WqRk5ODhIQE3Lhxw9qlETU47q4uGB3Vv9bLy2QyjIseCEdHh1qvM2PGDJw9exbvvfcerl69is2bN+Ozzz7Du+++a07JZpNJkiTV6xZt3PHjxzFw4MCHpkdEROD48eP1XxCRDfg25kfEJV6rcblBT3THkH5hJre/f/9+zJs3D1evXoVSqcT06dPxzjvvmFOq2RjGRCS8klItPt24E3n56mqXaalsgjdffhb29g3zDX/DrNoGpPw3Gzqd3tplEDUITgpHPB89ALJq5svl9hgXPbDBBjHAMLaKvHw11m+PwSfr/g1NUbG1yyFqENq0aoH+vbtUOW9YRG80a9K4niuyLJsMY71ej3/9618YMmQImjZtCoVCAT8/P0RFReGrr76CXm/dHunx0wnQGwxo6uUJNxdnq9ZC1JBE9g2DsqlXpWlt/VsivEcHK1VkOTYXxgUFBYiMjMSECRNw6NAhODo6okuXLjAYDDh48CBef/11qNXVjzvVtbx8NeIulX8Q8dST3a1WB1FDJJfb44URgyqGI5wUjnhueATsZNUNYDQcNhfGEydOxLFjx+Dr64ujR48iKysLZ8+eRWZmJlQqFRYvXgwHh9pf9mJpD3rFbf1bok2r+rugnMhWKJt6YWi/ngCAZ4f0RSMPNytXZBk2dTXF+fPnERYWBrlcjgsXLqBjx44Wbf+zzbug1pg/xmuQDNAUlq/v6uwEe3t7S5VG9FiRJAnaMh0UJlxPXF/c3Zwx9dXRJq9nU/em2L17NwAgOjra4kEMAGpNMQo0hRZpq7C4xCLtED3OSrVaa5dgMTYVxklJSQCA8PDwOmnf3c38D9vYKyZ6PJibEzYVxgUFBQCARo0a1Un75rz1eOA/P8TiTMIVtPVviUkvRFuwKiKyBTYVxh4eHgCA/Pz8Omnf3DHj3/aKVbl38fE/tlq6NCISBMeMAXTo0AG7du3CqVOn6qR9S4wZc6yYiKpiU2E8atQoLFq0CDExMUhKSkJoaKhF2zdnLIhjxUSPF3PHjG3q0jYAGDduHHbs2AE/Pz9s2bIFERERFfNu3bqFDRs2YNq0aXB1da2XejhWTES1YXNhXFBQgJEjR1bcrrJly5bw8fGBSqVCVlYWJElCXl4ePD0967yWvHw1VqzbDr3BgD+NH8EveRBRtWzuG3geHh44fPgw1q9fjwEDBqCoqAgXL16EnZ0dhg4divXr18Pd3b1eauG37YiotmyuZyySwz+dR+y5S3htbBTDmIiMYhjXsZJSLZwUjtYug4gExzAmIhKAzY0ZExE1RAxjIiIBMIyJiATAMCYiEgDDmIhIAAxjIiIBMIyJiATAMCYiEgDDmIhIAAxjIiIBMIyJiATAMCYiEgDDmIhIAAxjIiIBMIyJiATAMCYiEgDDmIhIAAxjIiIBMIyJiATAMCYiEgDDmIhIAAxjIiIBMIyJiATAMCYiEgDDmIhIAAxjIiIBMIyJiATAMCYiEgDDmIhIAAxjIiIBMIyJiATAMCYiEgDDmIhIAAxjIiIBMIyJiATAMCYiEgDDmIhIAAxjIiIBMIyJiATw//KfGO12ORvjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 436.286x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(1,1)\n",
    "qc.x(0)                    # prepare |1>\n",
    "qc.delay(100, 0, 'ns')  # use 100ns delays\n",
    "qc.x(0)                    # flip back\n",
    "qc.measure(0, 0)\n",
    "qc.name = f\"T_1 circuit\"\n",
    "qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "5c1be3a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ----------------------------------------------------------------------\n",
    "# Create T2 circuits (H — delay — H — measure)\n",
    "# ----------------------------------------------------------------------\n",
    "def make_T2_circs(delays_ns, qubit=0):\n",
    "    circuits = []\n",
    "    for t in delays_ns:\n",
    "        qc = QuantumCircuit(1, 1)\n",
    "        qc.h(qubit)                    # prepare |1>\n",
    "        qc.delay(int(t), qubit, 'ns')  # use ns delays\n",
    "        qc.h(qubit)                    # flip back\n",
    "        qc.measure(qubit, 0)\n",
    "        qc.name = f\"T2_{int(t)}ns\"\n",
    "        circuits.append(qc)\n",
    "    return circuits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "7ece054a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[     0.   4000.   8000.  12000.  16000.  20000.  24000.  28000.  32000.\n",
      "  36000.  40000.  44000.  48000.  52000.  56000.  60000.  64000.  68000.\n",
      "  72000.  76000.  80000.  84000.  88000.  92000.  96000. 100000.]\n"
     ]
    }
   ],
   "source": [
    "# Delay times: 0 to 100 us\n",
    "delays_ns = np.linspace(0, 100000, 26)\n",
    "raw2 = make_T2_circs(delays_ns)\n",
    "print(delays_ns)\n",
    "\n",
    "# Transpile using your preset pass manager\n",
    "t2_transpiled = [pm.run(circ) for circ in raw2]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "0bcbd4ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler2 = Sampler(mode=backend)\n",
    "\n",
    "# sampler supports only positional args in run()\n",
    "job2 = sampler2.run(t2_transpiled)\n",
    "\n",
    "result2 = job2.result()\n",
    "\n",
    "# ----------------------------------------------------------------------\n",
    "# Extract P(1) from counts\n",
    "# ----------------------------------------------------------------------\n",
    "p12 = []\n",
    "\n",
    "for res in result2:\n",
    "    counts = res.data.c.get_counts()\n",
    "    shots = sum(counts.values())\n",
    "    p12.append(counts.get('1', 0) / shots)\n",
    "\n",
    "p12 = np.array(p12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "09625bed",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated $T_2^*$ = 21.9 µs\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def model2(t, T2):\n",
    "    return .5*(1-np.exp(-t / T2))\n",
    "\n",
    "\n",
    "\n",
    "delays_s = delays_ns*1e-9\n",
    "params2, cov = curve_fit(model2, delays_s, p12, p0=[100e-6])\n",
    "T2_seconds = params2[0]\n",
    "T2_us = T2_seconds * 1e6\n",
    "\n",
    "print(f\"Estimated $T_2^*$ = {T2_us:.1f} µs\\n\")\n",
    "\n",
    "# ----------------------------------------------------------------------\n",
    "# Plot\n",
    "# ----------------------------------------------------------------------\n",
    "plt.figure(figsize=(8,5))\n",
    "plt.scatter(delays_ns/1000, p12, label='data')\n",
    "\n",
    "t2fit = np.linspace(0, max(delays_ns), 200)\n",
    "plt.plot(delays_s*1e6, model2(delays_s,T2_seconds), 'r', label=f\"fit: $T_2^*$={T2_us:.1f} µs\")\n",
    "\n",
    "plt.xlabel(r\"Delay $\\tau$ ($\\mu$s)\")\n",
    "plt.ylabel(r\"$P_1(\\tau)$\")\n",
    "plt.title(r\"$T_2^*$ Relaxation\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "10c5849c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWMAAACuCAYAAADjw2w/AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy88F64QAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAW6UlEQVR4nO3de1xUZf4H8M/AwHAXuTkiglwDNK+YkhfURFFyXS9pV2t/Wmu7pWt5aSvXtjTLyv1l7cu0rHQzV3/pul7IK6JmmqKBJCoq4HIbEUVguA0zc35/sFLEMDDjwDwMn/fr5UvmnOc88z3j8cMzz5w5RyZJkgQiIrIqO2sXQEREDGMiIiEwjImIBMAwJiISAMOYiEgADGMiIgEwjImIBMAwJiISAMOYiEgADGMiIgEwjImIBMAwJiISAMOYiEgADGMiIgEwjImIBMAwJiISAMOYiEgADGMiIgEwjImIBMAwJiISAMOYiEgADGMiIgEwjImIBMAwJiISAMOYiEgADGMiIgEwjImIBMAwJiISAMOYiEgADGMiIgEwjImIBMAwJiISAMOYiEgADGMiIgEwjImIBMAwJiISAMOYiEgAcmsXYMskSQJqa61dhmkUCshkMpM2kSQJ2uoOtp9mkjub9vp0lmPAGEmSoNPpLNZfW7O3t7fo/rcWw7gt1dZCO+Npa1dhEvm2jYCTk0nbaKtrsTn0yTaqSCxPXPsKDi4mvD6d5BgwRqfTYfv27Rbrr61NmzYNcnn7RyOnKYiIBMAwJiISAMOYiEgADGMiIgEwjImIBMAwJiISAMOYOixlbG88U/QNwmaMsnYpRPeM5xlTm1HG9kbCjr82PNbrdKirqEaV6jZunc9Gzs7vUHAkzXoFEgmEYUxtLnvHceQnnwNkMji4OqNLmD8CEx5A2IxRKDyajpTnPoCmvMraZRJZFcOY2tytjBxkbz/eaNmZZRsxaOmT6DP3Nxi5dgEOPbHCStURiYFhTFYh6fVI/esm+A4IR8CYAfB7IBLFpy8BABzcXdB33lQEJQ6Bq78P6tRVKDyWgXPvfA31f4qNdyyToe+8KfAf1R9dQrrD0dMN1TfvIP/QOfz47hbUlqoBAE7eHnjk3Drk7jmF43/8sEk3Q96eg8inx2H7kD9CnX/T4vtP1qPRaFBVVQVPT09rl9IIw5is6srXh9FtSBQCxg5E8elLcHB3wcTdK+DWwwdX/pmMO5fz4OzXFZHPjMfDSSuxO2EJKvNLmu3P3lGOPs9PRu7eU8jbdwba6lp49wtF+GNj0O2BSOwevwT6Oi1qbpUj70AqgiY8gB88XBpNk9grHBAyZTgKj2cwiAVRU1ODa9euIScnB9nZ2SgrK4NWq4VcLoe3tzeCg4MREhKCkJAQODg4NNuPRqPBBx98gJs3b2Lp0qXo2rVrO+6FcQxjsqrbF68DADxC/AEAAxbPhHugH/Y+/CpKM683tLu67QgmJ6/GgIUz8d2f/t5sf7raOmzt/yx0NZpGy2+mXsaw1X9AYMJg5O4+CQDI+uoQej0ci+ApI3B54/6GtkGJQ6HwdMOVzYcstp9knry8PBw8eBDHjx9HdXV1s+2OHTsGAHB3d8fo0aMxduxY+Pn5NWpzN4jT09MBAO+99x5WrFhhlSu0GWJzp7aVlJRg8eLFCAsLg5OTE3r27In58+ejsrISs2fPhkwmw8cff2ztMum/6irq/4M5ujkDAEKmjsCNHy6iSnUbCi/3hj/aqlrcPHcF/nH9WuzzbhDL7Ozg6OEChZc7ir77CQDgMzC8oV3h0XRUXL+B8MfHNNo+/LExqLldjv/sO2ORfSTTlZeXY82aNVi0aBEOHDhgNIh/qaKiArt27cL8+fOxYcMG1NTUAGgaxE5OTpg1a5YwQQzY2Mg4LS0NEyZMgEqlgqurK6Kjo1FYWIg1a9bg2rVruH37NgCgf//+1i3UREdLihF/MgXvRPfFS6GRBts47t6GiX7dsXPIiHau7t44uNeHsEZdDSdvDzh5eaDHqP547MIXBtvrW3Fd3F6TYtF77m/g1acX7B0bv2VVdHFr9Djr68MY9OfH4dW7F25fyIVboB+UD/ZG5mdJ0Ndpzdwry7PlY+DXUlNT8emnn6KsrKxhmUKhwNChQ3HfffchNDQU3bp1g1wuh0ajQVFREbKzs5GZmYnTp09Dp9NBkiQcPHgQ6enpmDNnDvbu3dsoiF955RVERhp+Ha3FZsK4pKQEkyZNgkqlwssvv4xly5bB3d0dALBq1SosWbIEcrkcMpkMffv2tXK1dJdXVBAAoPxaIfDfUUrh0XRk/H2nWf0FThyCUetfxs1zV3B66ReoLLwFXa0GMns7jNuyFDK7xiOhq1uSMWDhDIQ/NgY/vP45wh8bA5mdHacorCQpKQmbNm1qeOzq6opp06YhLi4Orq6uTdrL5XKEhoYiNDQU8fHxuHPnDg4fPoxdu3ahtrYWxcXFePvttxvaixrEgA2F8bx585Cfn48XXngB77//fqN1ixcvxtdff4309HQEBwfDw8PDSlXSr4U//hAAIP/QWdTcKkftHTUc3F1QdDzDrP5Cp4+EtroW+6Yvg67653njLmH+BttX37yDvINnETJ1BM6u2IywGaNx82wW7mTlm/X8ZL5vv/22URAPGjQIc+bMMelDNk9PT0ybNg3Dhg3D2rVrcfny5YZ1Dg4OwgYxYCNzxhcvXsTWrVvh4+ODlStXGmwzaNAgAEC/fi3POVLbk9nZIeYvs9BtSBTyDp1F8ZnLgCQhe8dx+A4MR1DiUIPbOXkb/0Uq6fT1/csaH9p9/zS92W2yNh+Coqs7Ylc9B1d/b2R9fdjEvaF7lZGRgY0bNzY8nj59OhYuXGj22Q5eXl5QKBSNlul0Ojg7O99TnW3JJkbGW7ZsgV6vxxNPPAE3NzeDbe7+I3TkMK7S6VDS0e6nBsD7/mCETKufx/zlN/DcevqhICUNx/7w83m+597ZAr/BkRi1/iXk7jqJm+eyoNNo4Rbgi4CHBuDW+WyjZ1Nc33MKvR6OxfhvluHa/x2FnYMcgQmDIXdWNLtNwZE0qPOKETo9DnXqauTsPGG5nbewjnoMGFNdXY1169Y1PJ4yZQqmT2/+l2dL7n5Yd/78eQD197TT6XTQ6/VYu3Ytli9fbpXbKrVEvIrMkJycDAAYPXp0s23y8+vfdnbkMH7z8gW8efmCtcswWcjUEQiZOgJ6nQ7ayhpUFt2G6mQmcpasb3JtirqKKiRNfg295/4GwZNi0XN8DCSdHpVFt1B8+hKyNhsfteb8+wTkbs7o/VwiBv9lFmrLKpF3MBVnV2zG4xe/NLyRJCFrSzIGLn4UObu+h7aqxjI73gY66jFgzJYtW1BSUn/ueHR0NB555BGz+zJ01sTChQvx5ZdfIj8/H7m5udi9ezemTJlikdotySbC+Pr1+vNRg4KCDK7XarU4caJ+tHMvYRwTEwOVStXq9s52dsjsH2v28/3anMAQTPPvaXDdhFNHLfIcERERqNbrTdrGQbLDMjzQZLnq5AV82d30EY6uWoPzf/sG5//2jdF2zfV/ZfMhgx/AGatFX1tXv20LUxQR4RGok7X+9eksx4Axjo6OzU4flpWVNQymFAoF5s6dCzs782ZPDQXx3Tni559/HkuXLoVer0dSUhISExPh6OhosJ+IiAhoNBqD61pDqVQiNTXV5O1sIowrKysBoNlzEbdu3YqSkhK4u7sjODjY7OdRqVQoKChodXsXe3ugv9lP10SYmxse8u1muQ4NKCwsRJWJt1V3lNkDbVtWm5LZ2yHiqXjczryOm2ezjLYtLCqERmr969NZjgFjfj13+0spKSnQautPIYyPj2/yRY3WMhbEABAaGorY2FicOHECFRUVOHXqFEaOHGmwr8LCQtRaYSrIJsJYqVSitLQU586dQ2xs41FIUVERFi1aBADo27fvPZ3krVQqTWrvbOZveGvy9/c3a2QMyw2k2o1bTz/4xkQgcPxgePRS4ujcv7W4jX93f5NHxh2NOceAMc2NQCVJwuHD9e9EZDIZxo4da1b/LQXxXePGjWt4h3z48OFmw9jf3/+eR8bmsIkwHjt2LC5evIh3330X8fHxiIiIAACcOXMGTz31VMN81L1+2cPUtx5STQ20M56+p+dsb1lZWZA5OZm0TV1VDTaHPtlGFbUdZWw0hn/4AmpulSHtg23I+XfLH9xlXcmCg0vrX5/OcgwYo9VqsX379ibLS0tLUVxcf+GnyMhIs0KstUEM1E8/KJVKqFQqXL16FXV1dQavY5GVlWWVD/hsIozvnkecl5eH3r17IzIyEjU1Nbh69SomTJiAXr16Yf/+/R36wzuyvKvbUnB1W4q1y+i0srOzG34ODw830tIwU4IYqB99h4WFQaVSQafTIS8vDyEhIeYV3wY63nsoAwICAnD8+HEkJibCyckJubm58PLywrp167B3715kZdXPAzKMicSRm5vb8LOpoWhqEBt6npycHJOes63ZxMgYAKKiorBnz54my9VqNXJzc2FnZ4c+ffpYoTIiMkStVjf87O3t3ertzA1iAPDx8Wn4+e4H/6KwmTBuzoULFyBJEiIiIuDi4mLtcswS5+MHzaQZRtu0tJ46Nls8BhISEhATE4O6ujr4+xv+uroh165dw08/1V+Fz9RrTURERGDJkiVwdHREt25inQJk82GckVF/jQNOURCJRalUmvWhXVRUFBYsWIBPPvkECxcuNOlaE56enhgwYIDJz9keGMZE1OHExMRgzZo1HfbdriEMY2oXD7z1PwgcHwO3nn7YNXYhbl/IBQC4Bysx4sMXofByR11FFb6b/3HDFdOMrXum6BuUXryO1OVfoSD5R7Nqin7uYUQ+Mx7ayhrsil9kkf2k9mNLQQzYyNkUxiQnJ0OSJCQmJlq7lE7t+t6TSJr8OtR5jW8o+uCq3yPrq4P41/B5yPh4J4Z/+EKr1gHAt79danYQA0Dm+j34/uVPzN6eyJJsfmRMYrhx6mKTZU7eHvDuF4oDj74FALi+9xSGvj0b7r2UqKuoanZdRW7T64P0f3kGuoT3gNxZAfde3VBdfAdHnv0Amjtq+A4Mx5CVc2BnZweZ3B6XvtiHy5sOtO0OE5mIYUxW49rDB9U3ShuuQQwA6oISuPbwQV1FVbPrDIUxAPgODMfu8YtRW6pG3NoFuO+peGR89C/c/+JUXFi7q+HSmI5dmt4xgsjaGMZkMwqOpKG2tP7c1eKzl9E1MhAAoPr+J/RbMB0ewd1RdOInFJ++ZM0yiQyy+TljEldlQQmcu3WFzP7nw9Cthw8qC0qMrmuOrvbni7tIOj3s5PYAgMxP9+LQkytRVXwHA//8OIaunNMGe0N0bxjGZDU1t8pxOyMHodPqr54VlDgUlUW3UZGrMrrOVB6h/lDnFePK5kPIWLMDvoMiLLofRJbAaQpqF7GrnkPAQ4Pg7OeJ+C2vo05djR0PvojvF6/D8P/9I+6fNxV16upGt1Qyts4UUb9LgHL4/dBrtJD0epx5Y2PLGxG1M4YxtYuTi9cbXF5+rRBJk14zed2vpX2wrdHjS1/sa/j5h9c/b2WVRNbDaQrqkKqLS5Gw4030GGP+V1ujn3sYQ9+Zg5rbFRasjMg8HBlTh7S137P33Efm+j3IXN/0Sn9E1sCRMRGRABjGREQCkEmSJFm7CFslSRJghbvM3hOFwuSbtkqSBG11B9tPM8mdTXt9OssxYIwkSdBZ6G7T763biorKSri7umLR72c2u+xe2NvbW3T/W4tzxm1IJpMBFryxo6hkMplJN+nsTDrLMWCMTCaz2A0+JQB6qf7vu30aWtYRcZqCiEgADGMiIgEwjImIBMAwJiISAMOYiEgADGMiIgEwjImIBMAwJiISAMOYiEgADGMiIgEwjImIBMAwJiISAMOYiEgADGMiIgEwjImIBMAwJiISAMOYiEgADGMiIgEwjImIBMAwJiISAMOYiEgADGMLO3bsGCZPnoygoCDIZDIsX77c2iURUQuSkpLQv39/KBQK9OrVC6tXr273GhjGFqZWqxEdHY1Vq1ZBqVRauxwiakFqaiomT56MCRMmIC0tDW+88QZeffVVfPLJJ+1ah7xdn60TmDhxIiZOnAgAWLJkiZWrIaKWrF69GoMHD8bKlSsBAFFRUbhw4QLeeecdzJ07t93q4MiYiDq1EydOICEhodGyhIQEXL9+Hfn5+e1WB0fGRCSk6/kq1NZpGy3T6nQNf2fl5De7DABcnBUIUPq2+DxFRUVNphTvPi4qKkJAQID5O2EChjERCan41h1s33fM4Lqq6hp8vi3J6LLfTU/49WZC4zQFEQkppu99iAoLNGvbIf2jcF9o67bt3r07VCpVo2U3btxoWNdeGMZEJCSZTIapCSPh6uJk0nbeXT2QOHpoq9sPGzYM+/fvb7Rs3759CAoKarcpCoBhbHFqtRppaWlIS0uDRqOBSqVCWloarl69au3SiDocd1cXTE0Y2er2MpkMMxNHw9HRodXbLFiwAKdPn8Zrr72GS5cuYePGjfjoo4/wyiuvmFOy2WSSJEnt+ow2LiUlBaNHj26yPC4uDikpKe1fEJEN+CbpKFIzLrfYbsyDAzFuRIzJ/e/duxevvvoqLl26BKVSifnz5+Oll14yp1SzMYyJSHg1tRp8+MV2lJZVNNumh9IHf3jyt7C375hv+Dtm1TYg+z+F0Gp11i6DqENwUjhiRuIoyJpZL5fbY2bi6A4bxADD2CpKyyqwYWsS3lv/T6irqq1dDlGHENyzO0YO6Wdw3YS4IfDz6drOFVmWTYaxTqfDP/7xD4wbNw6+vr5QKBQIDAxEQkICPvvsM+h01h2RppxKg06vh6+XJ9xcnK1aC1FHEj88Bkpfr0bLwoJ6IHZQbytVZDk2F8bl5eWIj4/HrFmzcPDgQTg6OqJfv37Q6/U4cOAAnn32WVRUND/v1NZKyyqQer7+g4iHhg20Wh1EHZFcbo9HJ41pmI5wUjjikYlxsJM1N4HRcdhcGM+ePRtHjhxBQEAAkpOTUVBQgNOnTyM/Px9FRUVYsWIFHBxaf9qLpd0dFYcF9UBwz/Y7oZzIVih9vTB+xGAAwG/HDUcXDzcrV2QZNnU2xdmzZxETEwO5XI4ff/wRffr0sWj/H23cgQq1+XO8ekkPdWX99q7OTrC3t7dUaUSdiiRJ0NRpoTDhfOL24u7mjBefnmrydjZ1bYqdO3cCABITEy0exABQoa5GubrSIn1VVtdYpB+izqxWo7F2CRZjU2GcmZkJAIiNjW2T/t3dzP+wjaNios7B3JywqTAuLy8HAHTp0qVN+jfnrcdd/9p/HD+kXURYUA/MeTTRglURkS2wqTD28PAAAJSVlbVJ/+bOGf9yVFxUfAtv/32zpUsjIkFwzhhA7969sWPHDpw8ebJN+rfEnDHnionIEJsK4ylTpuCtt95CUlISMjMzER0dbdH+zZkL4lwxUedi7pyxTZ3aBgAzZ87Etm3bEBgYiE2bNiEuLq5h3Y0bN/D5559j3rx5cHV1bZd6OFdMRK1hc2FcXl6OyZMnN1yuskePHvD390dRUREKCgogSRJKS0vh6enZ5rWUllXg/fVbodPr8fvHJ/FLHkTULJv7Bp6HhwcOHTqEDRs2YNSoUaiqqkJ6ejrs7Owwfvx4bNiwAe7u7u1SC79tR0StZXMjY5Ec+u4sjp85j2emJzCMicgohnEbq6nVwEnhaO0yiEhwDGMiIgHY3JwxEVFHxDAmIhIAw5iISAAMYyIiATCMiYgEwDAmIhIAw5iISAAMYyIiATCMiYgEwDAmIhIAw5iISAAMYyIiATCMiYgEwDAmIhIAw5iISAAMYyIiATCMiYgEwDAmIhIAw5iISAAMYyIiATCMiYgEwDAmIhIAw5iISAAMYyIiATCMiYgEwDAmIhIAw5iISAAMYyIiATCMiYgEwDAmIhIAw5iISAAMYyIiATCMiYgEwDAmIhIAw5iISAAMYyIiATCMiYgEwDAmIhIAw5iISAD/D06F/GB/R0mnAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 436.286x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(1,1)\n",
    "qc.h(0)                    # prepare |+>\n",
    "qc.delay(100, 0, 'ns')  # use 100ns delays\n",
    "qc.h(0)                    # flip back\n",
    "qc.measure(0, 0)\n",
    "qc.name = f\"T_2^* circuit\"\n",
    "qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "574da2cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ----------------------------------------------------------------------\n",
    "# Create T2 Hahn echo (H — delay/2 - X — delay/2 - H — measure)\n",
    "# ----------------------------------------------------------------------\n",
    "def make_T2hahn_circs(delays_ns, qubit=0):\n",
    "    circuits = []\n",
    "    for t in delays_ns:\n",
    "        qc = QuantumCircuit(1, 1)\n",
    "        qc.h(qubit)                    # prepare |1>\n",
    "        qc.delay(int(t/2), qubit, 'ns')  # use ns delays\n",
    "        qc.x(qubit)\n",
    "        qc.delay(int(t/2), qubit, 'ns')  # use ns delays\n",
    "        qc.h(qubit)                    # flip back\n",
    "        qc.measure(qubit, 0)\n",
    "        qc.name = f\"T2hahn_{int(t)}ns\"\n",
    "        circuits.append(qc)\n",
    "    return circuits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "409884c5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[     0.   8000.  16000.  24000.  32000.  40000.  48000.  56000.  64000.\n",
      "  72000.  80000.  88000.  96000. 104000. 112000. 120000. 128000. 136000.\n",
      " 144000. 152000. 160000. 168000. 176000. 184000. 192000. 200000.]\n"
     ]
    }
   ],
   "source": [
    "# Delay times: 0 to 200 us\n",
    "delays_ns = np.linspace(0, 200000, 26)\n",
    "raw2_hahn = make_T2hahn_circs(delays_ns)\n",
    "print(delays_ns)\n",
    "\n",
    "# Transpile using your preset pass manager\n",
    "t2_hahn_transpiled = [pm.run(circ) for circ in raw2_hahn]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "32a39688",
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler2_hahn = Sampler(mode=backend)\n",
    "\n",
    "# sampler supports only positional args in run()\n",
    "job2_hahn = sampler2_hahn.run(t2_hahn_transpiled)\n",
    "\n",
    "result2_hahn = job2_hahn.result()\n",
    "\n",
    "# ----------------------------------------------------------------------\n",
    "# Extract P(1) from counts\n",
    "# ----------------------------------------------------------------------\n",
    "p12_hahn = []\n",
    "\n",
    "for res in result2_hahn:\n",
    "    counts = res.data.c.get_counts()\n",
    "    shots = sum(counts.values())\n",
    "    p12_hahn.append(counts.get('1', 0) / shots)\n",
    "\n",
    "p12_hahn = np.array(p12_hahn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "9f9ffbfd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Estimated $T_2$ = 53.2 $\\mu$s\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def model2h(t, T2):\n",
    "    return .5*(1-np.exp(-t / T2))\n",
    "\n",
    "\n",
    "\n",
    "delays_s = delays_ns*1e-9\n",
    "params2_hahn, cov = curve_fit(model2h, delays_s, p12_hahn, p0=[100e-6])\n",
    "T2_hahn_seconds = params2_hahn[0]\n",
    "T2_hahn_us = T2_hahn_seconds * 1e6\n",
    "\n",
    "print(f\"\\nEstimated $T_2$ = {T2_hahn_us:.1f} $\\mu$s\\n\")\n",
    "\n",
    "# ----------------------------------------------------------------------\n",
    "# Plot\n",
    "# ----------------------------------------------------------------------\n",
    "plt.figure(figsize=(8,5))\n",
    "plt.scatter(delays_ns/1000, p12_hahn, label='data')\n",
    "\n",
    "t2fit = np.linspace(0, max(delays_ns), 200)\n",
    "plt.plot(delays_s*1e6, model2(delays_s,T2_hahn_seconds), 'r', label=f\"fit: $T_2$ echo ={T2_hahn_us:.1f} $\\mu$s\")\n",
    "\n",
    "plt.xlabel(r\"$\\tau$ ($\\mu$s)\")\n",
    "plt.ylabel(r\"$P_1(\\tau)$\")\n",
    "plt.title(r\"$T_2$ Relaxation Hahn echo\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "00535034",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 603.508x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(1,1)\n",
    "qc.h(0)                    # prepare |+>\n",
    "qc.delay(50, 0, 'ns')  # use 50ns delays\n",
    "qc.x(0)                    # invert\n",
    "qc.delay(50, 0, 'ns')  # use 50ns \n",
    "qc.h(0)                    # flip back\n",
    "qc.measure(0, 0)\n",
    "qc.name = f\"T_2 circuit\"\n",
    "qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c1e4e6f4",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.11.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}