Special_Topics_Pt2.ipynb

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   "source": [
    "### Special Topics - Part 2\n",
    "\n",
    "Introduction to QuTiP - The Quantum Toolbox in Python\n",
    "====================================="
   ]
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   "source": [
    "QuTiP is a python package for calculations and numerical simulations of quantum systems.\n",
    "\n",
    "It includes facilities for representing and doing calculations with quantum objects such state vectors (wavefunctions), as bras/kets/density matrices, quantum operators of single and composite systems, and superoperators (useful for defining master equations).\n",
    "\n",
    "It also includes solvers for a time-evolution of quantum systems, according to: Schrodinger equation, von Neuman equation, master equations, Floquet formalism, Monte-Carlo quantum trajectors, experimental implementations of the stochastic Schrodinger/master equations.\n",
    "\n",
    "For more information see the project web site at https://qutip.org/, and the documentation at https://qutip.org/docs/latest/index.html. Follow the instructions there in order to download and install QuTiP.\n",
    "\n",
    "\n"
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   "source": [
    "To use QuTiP in a Python program, first inlude the `qutip` module:"
   ]
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   "source": [
    "import numpy as np\n",
    "from qutip import *"
   ]
  },
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   "source": [
    "### Creating and inspecting quantum objects\n",
    "\n",
    "We can create a new quantum object using the `Qobj` class constructor, like this:"
   ]
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      "text/latex": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
       "Qobj data =\n",
       "[[1.]\n",
       " [0.]]"
      ]
     },
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   "source": [
    "q = Qobj([[1], [0]])\n",
    "\n",
    "q"
   ]
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    "Here we passed python list as an argument to the class constructor. The data in this list is used to construct the matrix representation of the quantum objects, and the other properties of the quantum object is by default computed from the same data.\n",
    "\n",
    "We can inspect the properties of a `Qobj` instance using the following class method:"
   ]
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       "[[2], [1]]"
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   "source": [
    "# the dimension, or composite Hilbert state space structure\n",
    "q.dims"
   ]
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     "data": {
      "text/plain": [
       "array([[1.+0.j],\n",
       "       [0.+0.j]])"
      ]
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   "source": [
    "# get the dense matrix representation\n",
    "q.full()"
   ]
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    {
     "data": {
      "text/plain": [
       "(False, 'ket')"
      ]
     },
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   ],
   "source": [
    "# some additional properties\n",
    "q.isherm, q.type"
   ]
  },
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   "source": [
    "### Using `Qobj` instances for calculations\n",
    "\n",
    "With `Qobj` instances we can do arithmetic and apply a number of different operations using class methods:"
   ]
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     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & -1.0j\\\\1.0j & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
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       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[0.+0.j 0.-1.j]\n",
       " [0.+1.j 0.+0.j]]"
      ]
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   "source": [
    "sy = Qobj([[0,-1j], [1j,0]])  # the sigma-y Pauli operator\n",
    "\n",
    "sy"
   ]
  },
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     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0\\\\0.0 & -1.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 1.  0.]\n",
       " [ 0. -1.]]"
      ]
     },
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   ],
   "source": [
    "sz = Qobj([[1,0], [0,-1]]) # the sigma-z Pauli operator\n",
    "\n",
    "sz"
   ]
  },
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     "text": [
      "Two-Level Hamiltonian (qubit) = \n",
      "\n"
     ]
    },
    {
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       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & -0.100j\\\\0.100j & -1.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 1.+0.j   0.-0.1j]\n",
       " [ 0.+0.1j -1.+0.j ]]"
      ]
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   ],
   "source": [
    "# some arithmetic with quantum objects\n",
    "\n",
    "H = 1.0 * sz + 0.1 * sy\n",
    "\n",
    "print(\"Two-Level Hamiltonian (qubit) = \\n\")\n",
    "H"
   ]
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     "data": {
      "text/plain": [
       "array([[0.+0.j, 1.+0.j],\n",
       "       [1.+0.j, 0.+0.j]])"
      ]
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   "source": [
    "# The raw data of H can be extracted and put into a numpy array as follows\n",
    "H.full()"
   ]
  },
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     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & -1.0j\\\\1.0j & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[0.+0.j 0.-1.j]\n",
       " [0.+1.j 0.+0.j]]"
      ]
     },
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   ],
   "source": [
    "# The hermitian conjugate\n",
    "sy.dag()"
   ]
  },
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    {
     "data": {
      "text/plain": [
       "0.0"
      ]
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   "source": [
    "# The trace\n",
    "H.tr()"
   ]
  },
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    {
     "data": {
      "text/plain": [
       "array([-1.,  1.])"
      ]
     },
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   ],
   "source": [
    "# Eigen energies\n",
    "H.eigenenergies()"
   ]
  },
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   "source": [
    "## States and operators\n",
    "\n",
    "Normally we do not need to create `Qobj` instances from stratch, using its constructor and passing its matrix representation as argument. Instead we can use functions in QuTiP that generates common states and operators for us. Here are some examples of built-in state functions. These obtain matrix representations of states and observables in the so-called \"*Bosonic Occupation Number Representation*\", which is basically the basis given by\n",
    "\n",
    "\\begin{equation*}\n",
    "|n_1, n_2, n_3, \\dots n_N\\rangle.\n",
    "\\end{equation*}\n",
    "\n",
    "In this state, $n_i$ identical bosons populate state $i$, and there are $N$ single particle states in total.\n",
    "### State vectors"
   ]
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      "text/latex": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\1.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
       "Qobj data =\n",
       "[[0.]\n",
       " [1.]]"
      ]
     },
     "execution_count": 17,
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     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fundamental basis states (Fock states of oscillator modes)\n",
    "\n",
    "N = 2 # number of single particle states\n",
    "n = 1 # the state that will be occupied\n",
    "\n",
    "basis(N, n)    # equivalent to fock(N, n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bac4aae2-ab7d-4560-93bf-fa7c9ea52902",
   "metadata": {
    "execution": {
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    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\0.0\\\\1.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\n",
       "Qobj data =\n",
       "[[0.]\n",
       " [0.]\n",
       " [1.]\n",
       " [0.]]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fundamental basis states (Fock states of oscillator modes)\n",
    "\n",
    "N = 4 # number of states in the Hilbert space\n",
    "n = 2 # the state that will be occupied\n",
    "\n",
    "basis(N, n)    # equivalent to fock(N, n)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e220e4b6-069e-4401-bfcc-eaeebf570fa0",
   "metadata": {
    "id": "e220e4b6-069e-4401-bfcc-eaeebf570fa0"
   },
   "source": [
    "### Operators"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16a6bc91-8d8d-4ea7-a5a0-75eca2702379",
   "metadata": {
    "id": "16a6bc91-8d8d-4ea7-a5a0-75eca2702379"
   },
   "source": [
    "#### Qubit (two-level system) operators"
   ]
  },
  {
   "cell_type": "code",
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   "id": "84388fc2-6606-4332-bcd0-ce9662ce6f47",
   "metadata": {
    "execution": {
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   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 1.0\\\\1.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[0. 1.]\n",
       " [1. 0.]]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pauli sigma x\n",
    "sigmax()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "36bf7815-325e-46a0-b8fb-e21a0ffe1008",
   "metadata": {
    "execution": {
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   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & -1.0j\\\\1.0j & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[0.+0.j 0.-1.j]\n",
       " [0.+1.j 0.+0.j]]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pauli sigma y\n",
    "sigmay()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "279229ce-61bd-4ca5-82bf-91d4d554bf3c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-26T15:50:16.607715Z",
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   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0\\\\0.0 & -1.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 1.  0.]\n",
       " [ 0. -1.]]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pauli sigma z\n",
    "sigmaz()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39339f3d-7202-4c4d-87cf-147ba679ad82",
   "metadata": {
    "id": "39339f3d-7202-4c4d-87cf-147ba679ad82"
   },
   "source": [
    "#### Creation and Annihilation operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a3d86fca-e287-4775-9366-c0e659558bc9",
   "metadata": {
    "execution": {
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   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[8], [8]], shape = (8, 8), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.414 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.732 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 2.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 2.236 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 2.449 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 2.646 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[8], [8]], shape = (8, 8), type = oper, isherm = False\n",
       "Qobj data =\n",
       "[[0.         0.         0.         0.         0.         0.\n",
       "  0.         0.        ]\n",
       " [1.         0.         0.         0.         0.         0.\n",
       "  0.         0.        ]\n",
       " [0.         1.41421356 0.         0.         0.         0.\n",
       "  0.         0.        ]\n",
       " [0.         0.         1.73205081 0.         0.         0.\n",
       "  0.         0.        ]\n",
       " [0.         0.         0.         2.         0.         0.\n",
       "  0.         0.        ]\n",
       " [0.         0.         0.         0.         2.23606798 0.\n",
       "  0.         0.        ]\n",
       " [0.         0.         0.         0.         0.         2.44948974\n",
       "  0.         0.        ]\n",
       " [0.         0.         0.         0.         0.         0.\n",
       "  2.64575131 0.        ]]"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# creation operator for N=8 particles\n",
    "N=8\n",
    "create(N) # equivalent to destroy(5).dag()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64a8f24e-c8d5-4fbb-8edf-92d5e6cbfa3a",
   "metadata": {
    "id": "64a8f24e-c8d5-4fbb-8edf-92d5e6cbfa3a"
   },
   "source": [
    "#### Using `Qobj` instances we can check some well known commutation relations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f56397b1-1696-4cb1-a625-a6f4435d4882",
   "metadata": {
    "execution": {
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   "outputs": [],
   "source": [
    "def commutator(op1, op2):\n",
    "    return op1 * op2 - op2 * op1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6ce0757-5886-4373-9f5b-c5951f732706",
   "metadata": {
    "id": "a6ce0757-5886-4373-9f5b-c5951f732706"
   },
   "source": [
    "Now, let us create a creation operator and an annihilation operator and prove that they commute, *i.e*\n",
    "\n",
    "\\begin{equation*}\n",
    "\\left[a, a^\\dagger\\right] = a\\;a^\\dagger - a^\\dagger a = 1\n",
    "\\end{equation*}"
   ]
  },
  {
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    "execution": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object: dims = [[10], [10]], shape = (10, 10), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 1.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  1.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  1.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  1.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  1.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  1.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  1.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  1.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.  1.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.  0. -9.]]\n"
     ]
    }
   ],
   "source": [
    "N = 10\n",
    "\n",
    "#Annihilation operator\n",
    "a = destroy(N)\n",
    "\n",
    "print(commutator(a, a.dag()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94fe9620-f637-42f7-ace2-705ef81803ba",
   "metadata": {
    "id": "94fe9620-f637-42f7-ace2-705ef81803ba"
   },
   "source": [
    "**Oops...** The result is not exactly identity (look at the last element)! Why? Because we have truncated the Hilbert space at $10$ particles, but the exact Hilbert space has infinite particles. The last $-9$ is a **truncation error**. As long as our truncation is reasonably large, this should not pose a serious problem."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5513edb6-32f3-4814-be10-ee7dee493a58",
   "metadata": {
    "id": "5513edb6-32f3-4814-be10-ee7dee493a58"
   },
   "source": [
    "What about the algebra of spin operators? Let us prove that\n",
    "\n",
    "\\begin{align*}\n",
    "\\left[\\sigma_x, \\sigma_y\\right] &= 2i\\sigma_z,\\\\\n",
    "-i \\sigma_x \\sigma_y \\sigma_z &= \\mathbf{1}\n",
    "\\end{align*}\n"
   ]
  },
  {
   "cell_type": "code",
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[0. 0.]\n",
      " [0. 0.]]\n",
      "\n",
      "\n",
      "\n",
      "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[1. 0.]\n",
      " [0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "print(commutator(sigmax(), sigmay()) - 2j * sigmaz())\n",
    "print(\"\\n\\n\")\n",
    "print(-1j * sigmax() * sigmay() * sigmaz())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "afbb38de-450d-489d-ad4c-19c24eb8a361",
   "metadata": {
    "id": "afbb38de-450d-489d-ad4c-19c24eb8a361"
   },
   "source": [
    "## Systems of Bosons in QuTiP\n",
    "\n",
    "Let us consider a test Hamiltonian, the tight-binding model. Here, there are $N$ lattice-sites, labelled by the number $i$, in one-dimension . Each lattice site can either be empty in a vacuum state $|0\\rangle$, or 'create' a particle in a Wannier state $|i\\rangle$ localized at that site. Thus, we can define creation and annihilation operators $c_i, c^\\dagger_i$ such that\n",
    "\n",
    "\\begin{align*}\n",
    "c^\\dagger_i|0\\rangle &= |i\\rangle \\\\\n",
    "c |i\\rangle &= |0\\rangle \\\\\n",
    "c^\\dagger_i|i\\rangle &= c|0\\rangle = 0.\n",
    "\\end{align*}\n",
    "\n",
    "Now, the 'tightly-bound' Hamiltonian simply involves nearest-neighbour tunneling and nothing else. Thus\n",
    "\n",
    "\\begin{equation*}\n",
    "H = \\sum^{N-1}_{i=0} \\bigg(|i\\rangle \\langle i+1| + |i\\rangle\\langle i-1 |\\bigg)\n",
    "\\end{equation*}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35087d40-211f-4c7b-b3bf-b0eff977a41f",
   "metadata": {
    "id": "35087d40-211f-4c7b-b3bf-b0eff977a41f"
   },
   "source": [
    "In this hamiltonian, each site can now be thought of as a 'state' (the Wannier state $|i\\rangle$). Now, we have already seen how `QuTip` has a routine called `basis(N,k)` that can create a population at state $k$ for $N$ particles. If we pretend that the $k-$s are actually Wannier states at lattice sites $k$, then the Hamiltonian can be built trivially in `QuTip` as shown in the example below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b544889d-202f-4ba1-855a-c8356f9b2f16",
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    "execution": {
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   "source": [
    "#N = 100\n",
    "N = 30\n",
    "\n",
    "H = sum([basis(N,i) * basis(N, i + 1).dag() for i in range(N - 1)]) +\\\n",
    "    sum([basis(N,i) * basis(N, i - 1).dag() for i in range(1, N)])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d9722f8-3000-4c4c-91fb-8067196b0078",
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    "id": "1d9722f8-3000-4c4c-91fb-8067196b0078",
    "tags": []
   },
   "source": [
    "Here, the `sum()` routine is also from `QuTip`. Now, let us diagonalize this Hamiltonian and plot the eigenvalues"
   ]
  },
  {
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   "source": [
    "evals = H.eigenenergies()\n",
    "# satisfy periodic boundary conditions we need E(-k) = E(k)\n",
    "numerical = np.concatenate((np.flip(evals, 0), evals), axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf0cf85c-5b50-4f05-99f0-94b73b114f48",
   "metadata": {
    "id": "cf0cf85c-5b50-4f05-99f0-94b73b114f48"
   },
   "source": [
    "Now, consider the analytical solution of the eigenvalue problem $H|\\psi_k\\rangle = \\epsilon_k |\\psi_k\\rangle$, which are the Bloch states given by $|\\psi_k\\rangle = \\sum_n e^{-ink}|k\\rangle$ with eigenvalues $\\epsilon_k = -2\\cos{k}$, where $k$ is a lattice momentum lying in the First Brillouin Zone, *i.e* $k_n = 2\\pi/n\\in [-\\pi,\\pi]$. Let us compare the analytical and numerical solutions.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1bc5cb5a-d3c1-41d3-a24c-42fade8a29a5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-26T18:55:35.619269Z",
     "iopub.status.busy": "2022-02-26T18:55:35.618609Z",
     "iopub.status.idle": "2022-02-26T18:55:35.792858Z",
     "shell.execute_reply": "2022-02-26T18:55:35.792394Z",
     "shell.execute_reply.started": "2022-02-26T18:55:35.619245Z"
    },
    "id": "1bc5cb5a-d3c1-41d3-a24c-42fade8a29a5",
    "outputId": "62866d4a-c0a2-4c55-8c66-621e5a05a30f",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rcParams['figure.figsize'] = (12,8)\n",
    "plt.rcParams['font.size'] = 20\n",
    "k = np.linspace(-np.pi, np.pi, 2*N)\n",
    "\n",
    "#plt.scatter(k[::3],numerical[::3].real, label='Eigenvalues of H')\n",
    "plt.scatter(k,numerical.real, label='Eigenvalues of H')\n",
    "\n",
    "analytical = -2 * np.cos(k)\n",
    "plt.title(f\"Tightly bound electrons in a lattice, size {N}\")\n",
    "plt.plot(k,analytical, label='Analytical energies')\n",
    "plt.xlabel(\"k\")\n",
    "plt.ylabel(\"eps\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03cf343b-6d23-4bb2-ae5d-00fb20ffd17b",
   "metadata": {
    "id": "03cf343b-6d23-4bb2-ae5d-00fb20ffd17b"
   },
   "source": [
    "## Systems of Fermions in QuTiP\n",
    "\n",
    "Fermions are a little harder to simulate in `QutiP`, but they can be done. Consider a system of $N$ coupled spin-$1/2$ particles. The Hamiltonian is given by\n",
    "\n",
    "\\begin{equation*}\n",
    "H = \\sum^{N-1}_{i=0}\\omega_i \\sigma^z_i +  g\\sum^{N-1}_{i=0}\\sigma^x_i\\sigma^x_{i+1}\n",
    "\\end{equation*}\n",
    "\n",
    "We have to be a little careful with our choice of $N$, since the dimensions of the Hamiltonian scale as $2^N\\times 2^N$, so if our $N$ is too large, we'll swiftly run out of computer memory *and* disk space. This happens because each spin-$1/2$ has a Hilbert space dimension of $2$, and the terms in the sum above are actually shorthand for the full exact operators, which involve tensor products with unity at the empty sites, thus, a term like $\\sigma^x_i\\sigma^x_{i+1}$ will actually become a full tensor product of $N-2$ unit matrices and two $\\sigma_x$s. For example, in a system \n",
    "of $5$ such fermions\n",
    "\n",
    "\\begin{align*}\n",
    "\\sigma^x_0\\sigma^x_1 & \\rightarrow \\sigma^x \\otimes\\sigma^x \\otimes \\mathbf{1}\\otimes \\mathbf{1}\\otimes \\mathbf{1}\\\\\n",
    "\\sigma^x_1\\sigma^x_2 & \\rightarrow \\mathbf{1}\\otimes \\sigma^x \\otimes\\sigma^x \\otimes \\mathbf{1}\\otimes \\mathbf{1}\\\\\n",
    "\\dots & \\dots \\\\\n",
    "\\sigma^x_3\\sigma^x_4 &\\rightarrow \\mathbf{1}\\otimes \\mathbf{1}\\otimes \\mathbf{1}\\otimes \\sigma^x \\otimes\\sigma^x \\\\\n",
    "\\dots & \\dots \\\\\n",
    "\\sigma^z_0&\\rightarrow \\sigma^z \\otimes \\mathbf{1}\\otimes \\mathbf{1}\\otimes \\mathbf{1} \\otimes\\mathbf{1}\\\\\n",
    "\\sigma^z_1&\\rightarrow \\mathbf{1}\\otimes\\sigma^z \\otimes \\mathbf{1}\\otimes \\mathbf{1}\\otimes \\mathbf{1} \\\\\n",
    "\\sigma^z_2&\\rightarrow \\mathbf{1}\\otimes \\mathbf{1}\\otimes \\sigma^z\\otimes \\mathbf{1} \\otimes\\mathbf{1}\\\\\n",
    "\\dots & \\dots\n",
    "\\end{align*}\n",
    "\n",
    "Let us keep $N<11$. Suppose $N=3$. Let us vary $\\omega_1$ and keep everything else fixed, and plot the energy eigenvalues as functions of $\\omega_1$ using `QuTiP`. The $\\otimes$ operation can be done using the `tensor()` function, and the identity $\\mathbf{1}$ can be obtained from the `qeye()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8ca62721-904d-4fa5-8530-5b56dff03c6e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-26T18:55:48.148948Z",
     "iopub.status.busy": "2022-02-26T18:55:48.148791Z",
     "iopub.status.idle": "2022-02-26T18:55:48.154364Z",
     "shell.execute_reply": "2022-02-26T18:55:48.153765Z",
     "shell.execute_reply.started": "2022-02-26T18:55:48.148931Z"
    },
    "id": "8ca62721-904d-4fa5-8530-5b56dff03c6e",
    "tags": []
   },
   "outputs": [],
   "source": [
    "def evals_multw(w1list, w2, w3, g12, g13):\n",
    "\n",
    "    # Pre-compute operators for the hamiltonian\n",
    "    sz1 = tensor(sigmaz(), qeye(2), qeye(2))\n",
    "    sx1 = tensor(sigmax(), qeye(2), qeye(2))\n",
    "\n",
    "    sz2 = tensor(qeye(2), sigmaz(), qeye(2))\n",
    "    sx2 = tensor(qeye(2), sigmax(), qeye(2))\n",
    "\n",
    "    sz3 = tensor(qeye(2), qeye(2), sigmaz())\n",
    "    sx3 = tensor(qeye(2), qeye(2), sigmax())\n",
    "  \n",
    "    evals_mat = np.zeros((len(w1list),2**3))\n",
    "    for idx, w1 in enumerate(w1list):\n",
    "        # evaluate the Hamiltonian\n",
    "        H = w1 * sz1 + w2 * sz2 + w3 * sz3 +\\\n",
    "            g12 * sx1 * sx2 + g13 * sx1 * sx3\n",
    "        # find the energy eigenvalues of the composite system\n",
    "        evals = H.eigenenergies()\n",
    "        evals_mat[idx,:] = np.real(evals)\n",
    "\n",
    "    return evals_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c063cd9e-1b85-4113-8290-4e56200dfbe9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-26T18:55:50.359394Z",
     "iopub.status.busy": "2022-02-26T18:55:50.359224Z",
     "iopub.status.idle": "2022-02-26T18:55:50.423605Z",
     "shell.execute_reply": "2022-02-26T18:55:50.423095Z",
     "shell.execute_reply.started": "2022-02-26T18:55:50.359378Z"
    },
    "id": "c063cd9e-1b85-4113-8290-4e56200dfbe9",
    "tags": []
   },
   "outputs": [],
   "source": [
    "w1  = 1.0 * 2 * np.pi   # atom 1 frequency: sweep this one\n",
    "w2  = 0.9 * 2 * np.pi   # atom 2 frequency\n",
    "w3  = 1.1 * 2 * np.pi   # atom 3 frequency\n",
    "g12 = 0.05 * 2 * np.pi   # atom1-atom2 coupling strength\n",
    "g13 = 0.05 * 2 * np.pi   # atom1-atom3 coupling strength\n",
    "\n",
    "w1list = np.linspace(0.75, 1.25, 50) * 2 * np.pi # atom 1 frequency range\n",
    "evals_mat = evals_multw(w1list, w2, w3, g12, g13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a2a569ee-be1f-48f0-9da9-74e5030acae0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-26T18:55:52.587167Z",
     "iopub.status.busy": "2022-02-26T18:55:52.587018Z",
     "iopub.status.idle": "2022-02-26T18:55:52.713881Z",
     "shell.execute_reply": "2022-02-26T18:55:52.713435Z",
     "shell.execute_reply.started": "2022-02-26T18:55:52.587151Z"
    },
    "id": "a2a569ee-be1f-48f0-9da9-74e5030acae0",
    "outputId": "a72deab2-035a-44ed-9e1b-5323dd5cb5bf",
    "tags": []
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['font.size'] = 20\n",
    "fig, ax = plt.subplots(figsize=(12,6))\n",
    "\n",
    "for n in [1,2,3]:\n",
    "    ax.plot(w1list / (2*np.pi), (evals_mat[:,n]-evals_mat[:,0]) / (2*np.pi), 'b')\n",
    "\n",
    "ax.set_xlabel('Energy splitting of electron 1')\n",
    "ax.set_ylabel('Eigenenergies')\n",
    "ax.set_title('Energy spectrum of three coupled electrons')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64e7c3f8-b5ac-4cfd-aa97-a179b3fc2afb",
   "metadata": {
    "id": "64e7c3f8-b5ac-4cfd-aa97-a179b3fc2afb"
   },
   "source": [
    "## Unitary dynamics\n",
    "\n",
    "Unitary evolution of a quantum system in `QuTiP` can be calculated with the `mesolve` function. This solves the Schrodinger equation\n",
    "\n",
    "\\begin{equation*}\n",
    "H|\\psi\\rangle = i \\frac{d}{dt}|\\psi\\rangle,\n",
    "\\end{equation*}\n",
    "\n",
    "using prebuilt numerical methods. The name `mesolve` is short for Master-eqaution solve (for dissipative dynamics), but if no collapse operators (which describe the dissipation) are given to the solve it falls back on the unitary evolution of the Schr\\\"odinger equation.\n",
    "\n",
    "The evolution solvers in QuTiP returns a class of type `Odedata`, which contains the solution to the problem posed to the evolution solver. \n",
    "\n",
    "For example, considor a single spin-$1/2$ particle with Hamiltonian $H = \\sigma_x$ and initial state $\\left|1\\right>$ (in the $\\sigma_z-$basis): Its evolution can be calculated as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "27692205-39a3-4f10-bbaf-d737303a4211",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-26T18:31:24.362511Z",
     "iopub.status.busy": "2022-02-26T18:31:24.362314Z",
     "iopub.status.idle": "2022-02-26T18:31:24.376049Z",
     "shell.execute_reply": "2022-02-26T18:31:24.375470Z",
     "shell.execute_reply.started": "2022-02-26T18:31:24.362492Z"
    },
    "id": "27692205-39a3-4f10-bbaf-d737303a4211",
    "outputId": "1a9fbc22-c78e-48d8-aae7-3feeec31f3c1",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result object with sesolve data.\n",
      "--------------------------------\n",
      "states = True\n",
      "num_collapse = 0\n"
     ]
    }
   ],
   "source": [
    "# Hamiltonian\n",
    "H = sigmax()\n",
    "\n",
    "# initial state\n",
    "psi0 = basis(2, 0)\n",
    "\n",
    "# list of times for which the solver should store the state vector\n",
    "tlist = np.linspace(0, 10, 100)\n",
    "\n",
    "result = mesolve(H, psi0, tlist, [], [])\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "607e2487-7bda-408a-8197-1ce4551c9d18",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-26T18:27:54.088039Z",
     "iopub.status.busy": "2022-02-26T18:27:54.087888Z",
     "iopub.status.idle": "2022-02-26T18:27:54.092433Z",
     "shell.execute_reply": "2022-02-26T18:27:54.092030Z",
     "shell.execute_reply.started": "2022-02-26T18:27:54.088023Z"
    },
    "id": "607e2487-7bda-408a-8197-1ce4551c9d18",
    "outputId": "6f3d916b-d7ec-47e1-dd28-da367d083ce8"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}-0.839\\\\0.544j\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
       "Qobj data =\n",
       "[[-0.8390774+0.j        ]\n",
       " [ 0.       +0.54401206j]]"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.states[-1] # the finial state"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b20b06b-abe2-46ce-a81d-1b7cab5a31f8",
   "metadata": {
    "id": "0b20b06b-abe2-46ce-a81d-1b7cab5a31f8"
   },
   "source": [
    "### Expectation values\n",
    "\n",
    "The expectation values of an operator given a state vector or density matrix (or list thereof) can be calculated using the `expect` function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "34a47389-1eb3-4556-a0df-7f0b50869b6f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-26T18:29:13.356939Z",
     "iopub.status.busy": "2022-02-26T18:29:13.356720Z",
     "iopub.status.idle": "2022-02-26T18:29:13.385125Z",
     "shell.execute_reply": "2022-02-26T18:29:13.384794Z",
     "shell.execute_reply.started": "2022-02-26T18:29:13.356922Z"
    },
    "id": "34a47389-1eb3-4556-a0df-7f0b50869b6f",
    "outputId": "37e30d36-48cc-4e39-c4ed-5b38b701742d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  0.97966324,  0.91948013,  0.82189857,  0.69088756,\n",
       "        0.53177579,  0.3510349 ,  0.15601625, -0.04534808, -0.24486795,\n",
       "       -0.43442821, -0.60631884, -0.75354841, -0.87012859, -0.95131766,\n",
       "       -0.99381332, -0.99588712, -0.95745468, -0.88007921, -0.76690787,\n",
       "       -0.62254375, -0.45285867, -0.26475429, -0.06588149,  0.13567091,\n",
       "        0.33170513,  0.51424779,  0.67587427,  0.81001063,  0.91120109,\n",
       "        0.97532984,  0.99978853,  0.9835823 ,  0.92737033,  0.83343897,\n",
       "        0.70560878,  0.54907906,  0.37021643,  0.17629587, -0.02479521,\n",
       "       -0.22487778, -0.41581382, -0.58983733, -0.73987014, -0.85980992,\n",
       "       -0.94477826, -0.9913192 , -0.99753971, -0.96318677, -0.88965766,\n",
       "       -0.77994308, -0.63850553, -0.4710978 , -0.28452892, -0.08638732,\n",
       "        0.11526793,  0.31223484,  0.49650212,  0.660575  ,  0.79778003,\n",
       "        0.90253662,  0.97058393,  0.99915421,  0.98708537,  0.9348683 ,\n",
       "        0.84462688,  0.72003156,  0.56615011,  0.38924141,  0.19650096,\n",
       "       -0.00423183, -0.20479249, -0.39702355, -0.57310633, -0.72587894,\n",
       "       -0.84912758, -0.93783928, -0.9884058 , -0.99877041, -0.9685115 ,\n",
       "       -0.89885984, -0.79264843, -0.65419728, -0.4891377 , -0.30418323,\n",
       "       -0.10685663,  0.09481617,  0.29263248,  0.47854644,  0.64499632,\n",
       "        0.785212  ,  0.89349043,  0.96542751,  0.9980973 ,  0.99017096,\n",
       "        0.94197089,  0.85545757,  0.73414984,  0.58298172,  0.40810176])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expect(sigmaz(), result.states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a43842de-0381-403b-93c6-2171d8c1daa9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-26T18:29:22.098102Z",
     "iopub.status.busy": "2022-02-26T18:29:22.097935Z",
     "iopub.status.idle": "2022-02-26T18:29:22.606603Z",
     "shell.execute_reply": "2022-02-26T18:29:22.606077Z",
     "shell.execute_reply.started": "2022-02-26T18:29:22.098087Z"
    },
    "id": "a43842de-0381-403b-93c6-2171d8c1daa9",
    "outputId": "a48d8a12-894d-4b2f-800a-c229f339e3f1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1,1)\n",
    "\n",
    "axes.plot(tlist, expect(sigmaz(), result.states))\n",
    "\n",
    "axes.set_xlabel(r'$t$', fontsize=20)\n",
    "axes.set_ylabel(r'$\\left<\\sigma_z\\right>$', fontsize=20);"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "include_colab_link": true,
   "name": "Special_Topics_Pt2.ipynb",
   "provenance": []
  },
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