Collapse operators

Collapse.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Untitled3.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyOL9vngPXvFtTA0S340YAf4",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/amcdawes/1128458ce38e3a79b57ee759b0f88135/untitled3.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yE-q_jh4pLQz",
        "outputId": "16cc8d72-c13a-4ad7-c543-f18fcdbec411"
      },
      "source": [
        "!pip install qutip"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting qutip\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/a1/07/91f0b86db374bb93e4958834f5797a5b251ff7f6eff38f2a82451e3237d6/qutip-4.5.3.tar.gz (3.3MB)\n",
            "\u001b[K     |████████████████████████████████| 3.3MB 6.0MB/s \n",
            "\u001b[?25h  Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Getting requirements to build wheel ... \u001b[?25l\u001b[?25hdone\n",
            "    Preparing wheel metadata ... \u001b[?25l\u001b[?25hdone\n",
            "Requirement already satisfied: scipy>=1.0 in /usr/local/lib/python3.7/dist-packages (from qutip) (1.4.1)\n",
            "Requirement already satisfied: cython>=0.21 in /usr/local/lib/python3.7/dist-packages (from qutip) (0.29.22)\n",
            "Requirement already satisfied: numpy>=1.16.6 in /usr/local/lib/python3.7/dist-packages (from qutip) (1.19.5)\n",
            "Building wheels for collected packages: qutip\n",
            "  Building wheel for qutip (PEP 517) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for qutip: filename=qutip-4.5.3-cp37-cp37m-linux_x86_64.whl size=12454443 sha256=3e201124861fbb0716cc974f48cd0c779282f75b91798538e99fcfefe72c9429\n",
            "  Stored in directory: /root/.cache/pip/wheels/3a/c7/5a/78f98f4e9c897dead831832cb7ec31965937253aedeba86622\n",
            "Successfully built qutip\n",
            "Installing collected packages: qutip\n",
            "Successfully installed qutip-4.5.3\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BSNeAUpvpTep"
      },
      "source": [
        "from qutip import *"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CLsboX1n3bW4"
      },
      "source": [
        "import numpy as np"
      ],
      "execution_count": 171,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "juXGi3jD-EEt"
      },
      "source": [
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 184,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0ACFHYss3Jis"
      },
      "source": [
        "H = sigmaz()\n",
        "rho = sigmaz()\n",
        "d = np.sqrt(0.1)\n",
        "c_ops = [d * sigmax()]\n",
        "tlist = linspace_with(0,20,100)\n",
        "result = mesolve(liouvillian(H,c_ops), rho, tlist, e_ops=[sigmaz()])"
      ],
      "execution_count": 255,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "nHSnamNC3o4B",
        "outputId": "79385a6d-e0ae-4300-8aa6-1822b2353a7c"
      },
      "source": [
        "plt.plot(result.expect[0])"
      ],
      "execution_count": 256,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f20e831fe90>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 256
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kw1UQWe497_r"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}