quantum_sensor_training.ipynb

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      "name": "python3",
      "display_name": "Python 3"
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      "name": "python"
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        "outputId": "622e94f3-4539-4e78-cb68-63d855f4ccf3"
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        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
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            "Successfully installed dill-0.3.7 pbr-6.0.0 ply-3.11 qiskit-0.45.1 qiskit-terra-0.45.1 rustworkx-0.13.2 stevedore-5.1.0 symengine-0.11.0\n",
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            "Installing collected packages: qiskit-aer\n",
            "Successfully installed qiskit-aer-0.13.1\n"
          ]
        }
      ],
      "source": [
        "!pip install qiskit\n",
        "!pip install qiskit-aer"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit import QuantumCircuit, Aer, transpile, assemble, execute\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def create_quantum_circuit(theta):\n",
        "    circuit = QuantumCircuit(1, 1)\n",
        "    circuit.h(0)  # Hadamard gate\n",
        "    circuit.ry(theta, 0)  # RY gate with parameter theta\n",
        "    circuit.measure(0, 0)\n",
        "    return circuit\n",
        "\n",
        "def simulate_quantum_circuit(circuit, shots=1024):\n",
        "    simulator = Aer.get_backend('qasm_simulator')\n",
        "    compiled_circuit = transpile(circuit, simulator)\n",
        "    result = execute(compiled_circuit, simulator, shots=shots).result()\n",
        "    counts = result.get_counts(compiled_circuit)\n",
        "    return counts\n",
        "\n",
        "def parameter_shift(theta, target, shots=1024, delta=0.001, learning_rate=0.01):\n",
        "    forward_circuit = create_quantum_circuit(theta + delta)\n",
        "    backward_circuit = create_quantum_circuit(theta - delta)\n",
        "\n",
        "    forward_counts = simulate_quantum_circuit(forward_circuit, shots)\n",
        "    backward_counts = simulate_quantum_circuit(backward_circuit, shots)\n",
        "\n",
        "    forward_expectation = forward_counts.get('0', 0) / shots\n",
        "    backward_expectation = backward_counts.get('0', 0) / shots\n",
        "\n",
        "    gradient = (forward_expectation - backward_expectation) / (2 * delta)\n",
        "\n",
        "    return theta - learning_rate * gradient\n",
        "\n",
        "def train_quantum_sensor(target, epochs=200, convergence_threshold=0.01):\n",
        "    theta = -1.0\n",
        "    # Lists to store data for final plot\n",
        "    epochs_list = []\n",
        "    cost_values = []\n",
        "\n",
        "    for epoch in range(epochs):\n",
        "        circuit = create_quantum_circuit(theta)\n",
        "        counts = simulate_quantum_circuit(circuit)\n",
        "\n",
        "        # Evaluate the cost function (simple example)\n",
        "        cost = np.abs(counts.get('0', 0) / 1024 - target)\n",
        "\n",
        "        # Update theta using the parameter-shift rule\n",
        "        theta = parameter_shift(theta, convergence_threshold)  # Pass convergence threshold here\n",
        "\n",
        "        # Append data for final plot\n",
        "        epochs_list.append(epoch + 1)\n",
        "        cost_values.append(cost)\n",
        "\n",
        "        # Print numbers\n",
        "        print(f\"Epoch {epoch + 1}/{epochs}, Cost: {cost}, Theta: {theta}\")\n",
        "\n",
        "        # Check for convergence\n",
        "        if cost < convergence_threshold:\n",
        "            print(f\"Converged at epoch {epoch + 1} with cost {cost}\")\n",
        "            break\n",
        "\n",
        "    # Final plot\n",
        "    plt.plot(epochs_list, cost_values, marker='o', linestyle='-', color='b')\n",
        "    plt.title('Cost Function Over Epochs')\n",
        "    plt.xlabel('Epochs')\n",
        "    plt.ylabel('Cost')\n",
        "    plt.grid(True)\n",
        "    plt.show()\n",
        "\n",
        "    return theta\n",
        "# Example usage\n",
        "target_value = 0.9  # Replace with your target value\n",
        "trained_theta = train_quantum_sensor(target_value, convergence_threshold=0.0005\n",
        ")\n",
        "print(f\"Trained Theta: {trained_theta}\")"
      ],
      "metadata": {
        "id": "VwEnmFKZz-h4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 997
        },
        "outputId": "864d4f04-7b97-4f64-c18b-0b4bbb95e287"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/200, Cost: 0.025781249999999978, Theta: -0.970703125\n",
            "Epoch 2/200, Cost: 0.011132812499999978, Theta: -0.94140625\n",
            "Epoch 3/200, Cost: 0.011132812499999978, Theta: -0.98046875\n",
            "Epoch 4/200, Cost: 0.004296874999999978, Theta: -1.0830078125\n",
            "Epoch 5/200, Cost: 0.023828124999999978, Theta: -1.1123046875\n",
            "Epoch 6/200, Cost: 0.04726562499999998, Theta: -1.1513671875\n",
            "Epoch 7/200, Cost: 0.05800781249999998, Theta: -1.146484375\n",
            "Epoch 8/200, Cost: 0.04921874999999998, Theta: -1.17578125\n",
            "Epoch 9/200, Cost: 0.06386718749999998, Theta: -1.126953125\n",
            "Epoch 10/200, Cost: 0.05996093749999998, Theta: -1.09765625\n",
            "Epoch 11/200, Cost: 0.04531249999999998, Theta: -1.0830078125\n",
            "Epoch 12/200, Cost: 0.028710937499999978, Theta: -1.1513671875\n",
            "Epoch 13/200, Cost: 0.05898437499999998, Theta: -1.1513671875\n",
            "Epoch 14/200, Cost: 0.05410156249999998, Theta: -1.126953125\n",
            "Epoch 15/200, Cost: 0.04335937499999998, Theta: -1.1318359375\n",
            "Epoch 16/200, Cost: 0.05898437499999998, Theta: -1.0537109375\n",
            "Epoch 17/200, Cost: 0.03652343749999998, Theta: -1.01953125\n",
            "Epoch 18/200, Cost: 0.017968749999999978, Theta: -0.9853515625\n",
            "Epoch 19/200, Cost: 0.023828124999999978, Theta: -1.0927734375\n",
            "Epoch 20/200, Cost: 0.029687499999999978, Theta: -1.0\n",
            "Epoch 21/200, Cost: 0.014062499999999978, Theta: -1.0048828125\n",
            "Epoch 22/200, Cost: 0.027734374999999978, Theta: -1.0244140625\n",
            "Epoch 23/200, Cost: 0.030664062499999978, Theta: -0.9853515625\n",
            "Epoch 24/200, Cost: 0.009179687499999978, Theta: -0.90234375\n",
            "Epoch 25/200, Cost: 0.011328125000000022, Theta: -0.84375\n",
            "Epoch 26/200, Cost: 0.05332031250000002, Theta: -0.921875\n",
            "Epoch 27/200, Cost: 0.0003906249999999778, Theta: -1.0146484375\n",
            "Converged at epoch 27 with cost 0.0003906249999999778\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Trained Theta: -1.0146484375\n"
          ]
        }
      ]
    }
  ]
}