L3_05.ipynb

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    {
      "cell_type": "markdown",
      "source": [
        "# L3-05\n",
        "## NEHAL MAHENDRA RANE\n",
        "### Problem Statement: Implement Quantum Phase Estimation to approximate eigenvalues."
      ],
      "metadata": {
        "id": "7z3aNiQneYeN"
      }
    },
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      ],
      "source": [
        "!pip install qiskit\n",
        "!pip install numpy\n",
        "!pip install matplotlib\n",
        "!pip install --upgrade qiskit\n",
        "!pip install qiskit-aer"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Imports\n",
        "from qiskit import QuantumCircuit\n",
        "from qiskit import transpile\n",
        "from qiskit import QuantumRegister, ClassicalRegister\n",
        "from qiskit_aer import Aer\n",
        "from qiskit_aer import AerSimulator\n",
        "from qiskit.visualization import plot_histogram\n",
        "import numpy as np\n"
      ],
      "metadata": {
        "id": "rdCNiAhAhTjd"
      },
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# Function to create a controlled unitary operation\n",
        "def controlled_unitary(circuit, theta, control_qubit, target_qubit):\n",
        "    circuit.ry(theta, target_qubit)\n",
        "    # Replace cu1 with cp\n",
        "    circuit.cp(-theta, control_qubit, target_qubit) # cu1 is deprecated, use cp instead\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "T4UzzGf4hluv"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Function to implement Quantum Phase Estimation\n",
        "def quantum_phase_estimation(theta, num_qubits):\n",
        "    circuit = QuantumCircuit(num_qubits + 1, num_qubits)\n",
        "\n",
        "    # Initialize the ancilla qubit to |+>\n",
        "    circuit.h(num_qubits)\n",
        "\n",
        "    # Apply controlled unitary operations\n",
        "    for i in range(num_qubits):\n",
        "        controlled_unitary(circuit, theta, num_qubits - i - 1, num_qubits)\n",
        "\n",
        "    # Apply inverse QFT\n",
        "    # Correct the inverse QFT implementation\n",
        "    circuit.append(QFT(num_qubits, inverse=True), range(num_qubits))\n",
        "\n",
        "    # Measurement\n",
        "    circuit.measure(range(num_qubits), range(num_qubits))\n",
        "\n",
        "    return circuit\n"
      ],
      "metadata": {
        "id": "yJE4kAx1hnbW"
      },
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit.circuit.library import QFT # Import QFT"
      ],
      "metadata": {
        "id": "aFT851-ThqIu"
      },
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Parameters\n",
        "theta = np.pi / 4  # Example angle\n",
        "num_qubits = 3\n"
      ],
      "metadata": {
        "id": "sMQii0wThsYd"
      },
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Create the circuit\n",
        "circuit = quantum_phase_estimation(theta, num_qubits)"
      ],
      "metadata": {
        "id": "KGMXmN9dhvQe"
      },
      "execution_count": 22,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Transpile the circuit for the simulator\n",
        "transpiled_circuit = transpile(circuit, basis_gates=['u1', 'u2', 'u3', 'cx'])\n"
      ],
      "metadata": {
        "id": "kq0plYW9hvmj"
      },
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Use the Aer simulator\n",
        "simulator = Aer.get_backend('qasm_simulator')\n",
        "result = simulator.run(transpiled_circuit).result()\n"
      ],
      "metadata": {
        "id": "0125178Eh0W2"
      },
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Get the counts\n",
        "counts = result.get_counts(circuit)\n",
        "print(counts)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZMGQz3ilh2Bl",
        "outputId": "4ed9da9d-3a7e-4caa-c2ab-6eb1977d794a"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "{'100': 119, '110': 126, '001': 124, '101': 143, '011': 115, '111': 133, '000': 131, '010': 133}\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot the histogram\n",
        "plot_histogram(counts)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 446
        },
        "id": "5zMtf6mAh3Pr",
        "outputId": "3d8dcb45-6462-47b7-f66f-b5458de6fcbf"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "WIAfk0TNh6uN"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}