0_Hamiltomians-executed.ipynb

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  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "#0.- HAMILTONIANS\n",
        "\n",
        "### Setup"
      ],
      "metadata": {
        "id": "vh5qNW1XFcqO"
      }
    },
    {
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      "execution_count": 1,
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        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
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          ]
        }
      ],
      "source": [
        "pip install qiskit"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##0.1- Statevectors"
      ],
      "metadata": {
        "id": "QG2m_FT3GgQ6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit.quantum_info import Statevector\n",
        "zero = Statevector([1,0])\n",
        "print(\"zero is\", zero)"
      ],
      "metadata": {
        "id": "GvoF1FgEFl3_",
        "outputId": "cfee4904-a4ec-452f-958d-e286948d317a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "zero is Statevector([1.+0.j, 0.+0.j],\n",
            "            dims=(2,))\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "one = Statevector([0,1])\n",
        "print(\"one is\",one)"
      ],
      "metadata": {
        "id": "1uKKAuf2FxZX",
        "outputId": "0c3b7b2b-1e44-4235-9eb0-0d615043ddf5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "one is Statevector([0.+0.j, 1.+0.j],\n",
            "            dims=(2,))\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "zero = Statevector.from_int(0, dims = 2)\n",
        "one = Statevector.from_int(1, dims = 2)\n",
        "print(\"zero is\",zero)\n",
        "print(\"one is\",one)"
      ],
      "metadata": {
        "id": "h6GDC6mzF1RD",
        "outputId": "5d643acc-6793-4e4f-cd15-c75330860ead",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "zero is Statevector([1.+0.j, 0.+0.j],\n",
            "            dims=(2,))\n",
            "one is Statevector([0.+0.j, 1.+0.j],\n",
            "            dims=(2,))\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "psi = one.tensor(zero.tensor(zero))\n",
        "print(\"psi is\",psi)"
      ],
      "metadata": {
        "id": "sbAtXwKrF5Wy",
        "outputId": "d929f81e-3dfd-4f8d-fe13-2c8ac30019d1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "psi is Statevector([0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j,\n",
            "             0.+0.j],\n",
            "            dims=(2, 2, 2))\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "psi = one^zero^zero\n",
        "psi.draw(\"latex\")"
      ],
      "metadata": {
        "id": "nYZQFxuWF-C5",
        "outputId": "4fc7ae15-9047-4ca0-80a2-0b527cf96190",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        }
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.Latex object>"
            ],
            "text/latex": "$$ |100\\rangle$$"
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "psi = Statevector.from_int(4, dims = 8)\n",
        "print(psi)\n",
        "psi.draw(\"latex\")"
      ],
      "metadata": {
        "id": "x1kG7llVGGI_",
        "outputId": "ca258b45-81b1-4e30-c2c3-f085ccef3042",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 91
        }
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Statevector([0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j,\n",
            "             0.+0.j],\n",
            "            dims=(2, 2, 2))\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.Latex object>"
            ],
            "text/latex": "$$ |100\\rangle$$"
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from numpy import sqrt\n",
        "ghz = 1/sqrt(2)*(zero^zero^zero) + 1/sqrt(2)*(one^one^one)\n",
        "ghz.draw(\"latex\")"
      ],
      "metadata": {
        "id": "Xt4vnSoIGJ_I",
        "outputId": "40148c22-a8ef-444e-8d1a-0e8676489615",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 40
        }
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.Latex object>"
            ],
            "text/latex": "$$\\frac{\\sqrt{2}}{2} |000\\rangle+\\frac{\\sqrt{2}}{2} |111\\rangle$$"
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##0.2- Hamiltonians"
      ],
      "metadata": {
        "id": "Zvmgs6GrGnQT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit.quantum_info import Pauli\n",
        "Z0Z1 = Pauli(\"ZZI\")\n",
        "print(\"Z0Z1 is\",Z0Z1)\n",
        "print(\"And its matrix is\")\n",
        "print(Z0Z1.to_matrix())"
      ],
      "metadata": {
        "id": "biZDbIE_GYoX",
        "outputId": "efe1344d-ea9a-47e9-c366-54105ce506fc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Z0Z1 is ZZI\n",
            "And its matrix is\n",
            "[[ 1.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j]\n",
            " [ 0.+0.j  1.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j]\n",
            " [ 0.+0.j  0.+0.j -1.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j]\n",
            " [ 0.+0.j  0.+0.j  0.+0.j -1.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j]\n",
            " [ 0.+0.j  0.+0.j  0.+0.j  0.+0.j -1.+0.j  0.+0.j  0.+0.j  0.+0.j]\n",
            " [ 0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j -1.+0.j  0.+0.j  0.+0.j]\n",
            " [ 0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  1.+0.j  0.+0.j]\n",
            " [ 0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  1.+0.j]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"The sparse representation of Z0Z1 is\")\n",
        "print(Z0Z1.to_matrix(sparse=True))"
      ],
      "metadata": {
        "id": "lZzT7H3WGqmx",
        "outputId": "b0b9a2cd-7d9b-4f50-a486-cc8de0674d29",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The sparse representation of Z0Z1 is\n",
            "  (0, 0)\t(1+0j)\n",
            "  (1, 1)\t(1+0j)\n",
            "  (2, 2)\t(-1+0j)\n",
            "  (3, 3)\t(-1+0j)\n",
            "  (4, 4)\t(-1+0j)\n",
            "  (5, 5)\t(-1+0j)\n",
            "  (6, 6)\t(1+0j)\n",
            "  (7, 7)\t(1+0j)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "Z0Z1 = Pauli(([0,1,1],[0,0,0]))\n",
        "print(Z0Z1.to_matrix(sparse=True))"
      ],
      "metadata": {
        "id": "YCmGdR7cG-wk",
        "outputId": "b8f57055-8da4-43e5-a6d3-cb78d163fb26",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "  (0, 0)\t(1+0j)\n",
            "  (1, 1)\t(1+0j)\n",
            "  (2, 2)\t(-1+0j)\n",
            "  (3, 3)\t(-1+0j)\n",
            "  (4, 4)\t(-1+0j)\n",
            "  (5, 5)\t(-1+0j)\n",
            "  (6, 6)\t(1+0j)\n",
            "  (7, 7)\t(1+0j)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit.opflow.primitive_ops import PauliOp\n",
        "H_cut = PauliOp(Pauli(\"ZZI\")) + PauliOp(Pauli(\"ZIZ\"))\n",
        "print(\"H_cut is\")\n",
        "print(H_cut)\n",
        "print(\"The sparse representation of H_cut is\")\n",
        "print(H_cut.to_spmatrix())"
      ],
      "metadata": {
        "id": "JZsGLF0lIQQr",
        "outputId": "e219248f-d6c0-412e-d4cf-b5588dce4d4a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "H_cut is\n",
            "1.0 * ZZI\n",
            "+ 1.0 * ZIZ\n",
            "The sparse representation of H_cut is\n",
            "  (0, 0)\t(2+0j)\n",
            "  (3, 3)\t(-2+0j)\n",
            "  (4, 4)\t(-2+0j)\n",
            "  (7, 7)\t(2+0j)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit.opflow import I, Z\n",
        "H_cut = (Z^Z^I) + (Z^I^Z)\n",
        "print(\"H_cut is\")\n",
        "print(H_cut)"
      ],
      "metadata": {
        "id": "zMMEIKWNIT9R",
        "outputId": "b53e5e7e-b7a6-4fb5-c6d4-56eac0ee542a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "H_cut is\n",
            "1.0 * ZZI\n",
            "+ 1.0 * ZIZ\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "H_ising = -0.5*(Z^Z^I) + 2*(Z^I^Z) -(I^Z^Z) + (I^Z^I) -5*(I^I^Z)\n",
        "print(H_ising)"
      ],
      "metadata": {
        "id": "ywsiH4UIItUj",
        "outputId": "73874a9e-b5b7-431d-c073-660d4f20d69c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-0.5 * ZZI\n",
            "+ 2.0 * ZIZ\n",
            "- 1.0 * IZZ\n",
            "+ 1.0 * IZI\n",
            "- 5.0 * IIZ\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##0.3- Expectation values"
      ],
      "metadata": {
        "id": "N0l09joRI1qB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"The expectation value is\", psi.expectation_value(H_cut))\n"
      ],
      "metadata": {
        "id": "NRMwPowaIyrE",
        "outputId": "2c8c393f-3826-4d5e-d412-8600af379d7d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The expectation value is (-2+0j)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for x in range(8): # We consider x=0,1...7\n",
        "    psi = psi = Statevector.from_int(x, dims = 8)\n",
        "    print(\"The expectation value of |\",x,\">\", \"is\", \n",
        "        psi.expectation_value(H_cut))"
      ],
      "metadata": {
        "id": "GJXfu1ffJBq2",
        "outputId": "782e19c7-e00a-4d67-f6a6-dde19f8805c2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The expectation value of | 0 > is (2+0j)\n",
            "The expectation value of | 1 > is 0j\n",
            "The expectation value of | 2 > is 0j\n",
            "The expectation value of | 3 > is (-2+0j)\n",
            "The expectation value of | 4 > is (-2+0j)\n",
            "The expectation value of | 5 > is 0j\n",
            "The expectation value of | 6 > is 0j\n",
            "The expectation value of | 7 > is (2+0j)\n"
          ]
        }
      ]
    }
  ]
}