Hubbard-Time-Evolution.ipynb

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    "$$\\newcommand{\\ket}[1]{\\left|{#1}\\right\\rangle}$$\n",
    "$$\\newcommand{\\bra}[1]{\\left\\langle{#1}\\right|}$$\n",
    "# 1-D, 3-Site Hubbard Model\n",
    "\n",
    "The Hubbard Hamiltonian for a 1-D chain of sites is:\n",
    "\n",
    "\\begin{equation} H = -t\\sum_{<ij>,\\sigma}(\\hat{c}_{i_\\sigma}\\hat{c}_{j_\\sigma} + \\hat{c}_{j_\\sigma}^\\dagger\\hat{c}_{i_\\sigma} ) + U\\sum_i\\hat{c}_{i_\\uparrow}^{\\dagger}\\hat{c}_{i_\\uparrow}\\hat{c}_{i_\\downarrow}^{\\dagger}\\hat{c}_{i_\\downarrow}\n",
    "\\end{equation}\n",
    "and under the Jordan-Wigner mapping, this Hamiltonian becomes:\n",
    "\n",
    "\\begin{equation}\n",
    "H = -\\frac{t}{2}\\sum_{<ij>}Z_{i+1:j-1}(X_{i}X_{j} + Y_{i}Y_{j}) + \\frac{U}{4}\\sum_{ij}(I-Z_{i})(I-Z_{j})\n",
    "\\end{equation}\n",
    "where $Z_{i}$, $X_{i}$, and $Y_{i}$ are the corresponding Pauli matrices acting on the $i^{th}$ fermionic mode and for a chain with only 3-sites, there are no Pauli $Z$ strings in the hopping term of the Hamiltonian for a one-dimensional chain.\n",
    "\n",
    "## 3-Site Hamiltonian and Qubit Mapping\n",
    "\n",
    "Writing out the sum over the three sites, the Hamiltonian becomes:\n",
    "\n",
    "\\begin{align}\n",
    "     H = &-\\frac{t}{2}(X_0X_1 + Y_0Y_1) - \\frac{t}{2}(X_1X_2 + Y_1Y_2) \\nonumber \\\\ \n",
    "&-\\frac{t}{2}(X_3X_4 + Y_3Y_4) - \\frac{t}{2}(X_4X_5 + Y_4Y_5) \\nonumber\\\\\n",
    "&+ \\frac{U}{4}(I-Z_0)(I-Z_3)+ \\frac{U}{4}(I-Z_1)(I-Z_4) + \\frac{U}{4}(I-Z_2)(I-Z_5) \\nonumber\\\\\n",
    "= &H_{01} + H_{12} + H_{23} + H_{34} + H_{03} + H_{14} + H_{25}\n",
    "\\end{align}\n",
    "\n",
    "### Qubit Mapping\n",
    "\n",
    "Each site in the 3-site chain is represented by two qubits, one for each spin, and the wavefunction is represented as\n",
    "\n",
    "$$ \\ket{\\psi} = \\ket{q_0}\\ket{q_1}\\ket{q_2}\\ket{q_3}\\ket{q_4}\\ket{q_5} $$\n",
    "\n",
    "where $\\ket{q_i} = \\{ \\ket{0}, \\ket{1} \\} $ represent unoccupied or occupied sites, $i=0,1,2$ are the spin up electron occupations and $i=3,4,5$ are the spin down electron occupations.\n",
    "\n",
    "\n",
    "## Time Evolution\n",
    "\n",
    "We want to simulate the time evolution of $\\ket{\\psi}$ via \n",
    "\n",
    "$$ \\ket{\\psi(t+\\Delta t)} = e^{-iH\\Delta t}\\ket{\\psi(t)} $$\n",
    "\n",
    "\n",
    "We can do this via the Suzuki-Trotter formula which states that, to first order in $\\Delta t$\n",
    "\n",
    "$$e^{iH\\Delta t} \\approx e^{iH_{10}^{\\uparrow}\\Delta t}e^{iH_{12}^{\\uparrow}\\Delta t}e^{iH_{10}^{\\downarrow}\\Delta t}e^{iH_{12}^{\\downarrow}\\Delta t}e^{iH_0\\Delta t}e^{iH_1\\Delta t}e^{iH_2\\Delta t} $$.\n",
    "\n",
    "\n",
    "So what do the gates look like for each of these terms?\n",
    "\n",
    "#### Hopping Terms\n",
    "\n",
    "For each pair of hopping terms we have\n",
    "\\begin{equation}e^{-i\\Delta t(\\frac{-t}{2})(X_iX_j + Y_iY_j)} \\approx e^{\\frac{it\\Delta t}{2}X_iX_j} e^{\\frac{it\\Delta t}{2}Y_iY_j}.\n",
    "\\label{eq:op-expansion}\n",
    "\\end{equation}\n",
    "\n",
    "Expanding the first term on the right hand side\n",
    "\n",
    "\\begin{align}\n",
    "e^{\\frac{it\\Delta t}{2}X_iX_j} = & \\sum_{k=0}^{\\infty} \\frac{1}{k!}\\left(\\frac{it\\Delta t}{2}X_iX_j\\right)^k \\nonumber \\\\\n",
    " =& \\sum_{k, even}\\frac{i^k}{k!}\\left( \\frac{t\\Delta t}{2} \\right)^k I + \\sum_{k, odd}\\frac{i^k}{k!}\\left( \\frac{t\\Delta t}{2} \\right)X_i X_j \\nonumber \\\\ \n",
    " = &\\cos\\left(\\frac{t\\Delta t}{2}\\right)I + i\\sin\\left( \\frac{t\\Delta t}{2}\\right)X_i X_j \\nonumber \\\\\n",
    " = &\\begin{pmatrix}\\cos\\theta & 0 & 0 & i\\sin\\theta \\\\ 0 & \\cos\\theta & i\\sin\\theta & 0 \\\\ 0 & i\\sin\\theta & \\cos\\theta & 0 \\\\ i\\sin\\theta & 0 & 0 & \\cos\\theta\\end{pmatrix},\n",
    "\\end{align}\n",
    "with $\\theta=\\frac{t\\Delta t}{2}$, and written in the $\\ket{q_{i}q_{j}}$ basis.\n",
    "\n",
    "Similarly for the $Y_i Y_j$ terms\n",
    "\n",
    "\\begin{align}\n",
    "    e^{i\\frac{t\\Delta t}{2}Y_i Y_j} =& \\cos\\left(\\frac{t\\Delta t}{2}\\right)I + i\\sin\\left(\\frac{t\\Delta t}{2}\\right)Y_i Y_j \\nonumber \\\\\n",
    "= & \\begin{pmatrix}\\cos\\theta & 0 & 0 & -i\\sin\\theta \\\\ 0 & \\cos\\theta & i\\sin\\theta & 0 \\\\ 0 & i\\sin\\theta & \\cos\\theta & 0 \\\\ -i\\sin\\theta & 0 & 0 & \\cos\\theta\\end{pmatrix}.\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "Note also that these matrices are diagonal save for the 4x4 block corresponding to a gate acting on qubits $i$ and $j$.\n",
    "\n",
    "### On-Site Terms\n",
    "\n",
    "\n",
    "Now we'll expand the on-site term, $e^{i\\frac{U\\Delta t}{4}(I-Z_i)(I-Z_j)}$.  First we examine the powers of $(I-Z_i)(I-Z_j)$:\n",
    "\n",
    "\\begin{align} (I-Z_i)^2(I-Z_j)^2 &= (I + I - 2Z_i)(I+I-2Z_j) = 4(I-Z_i)(I-Z_j) \\\\\n",
    "(I-Z_i)^3(I-Z_j)^3& = (I-Z_i)(I-Z_j)(I-Z_i)^2(I-Z_j)^2 \\nonumber \\\\\n",
    "&= 4(I-Z_i)^2(I-Z_j)^2 = 16(I-Z_i)(I-Z_j)\\\\\n",
    "(I-Z_i)^4(I-Z_j)^4& = 16(I-Z_i)^2(I-Z_j)^2 = 4^3(I-Z_i)(I-Z_j)\\\\\n",
    "\\implies (I-Z_i)^k(I-Z_j)^k& = 4^{k-1}(I-Z_i)(I-Z_j), \\end{align}\n",
    "\n",
    "then writing out the expansion of $e^{i\\frac{U\\Delta t}{4}(I-Z_i)(I-Z_j)}$ we get\n",
    "\n",
    "\\begin{align} e^{i\\frac{U\\Delta t}{4}(I-Z_i)(I-Z_j)} &= \\sum_k \\frac{1}{k!}\\left(\\frac{i\\Delta tU}{4}\\right)^k(I-Z_i)^k(I-Z_j)^k \\\\\n",
    "&= I+(I-Z_i)(I-Z_j)\\sum_k \\frac{\\left(i\\Delta tU\\right)^k}{k!}\\frac{4^{k-1}}{4^k} - \\frac{1}{4}(I-Z_i)(I-Z_j) \\\\\n",
    "& = I-\\frac{1}{4}(I-Z_i)(I-Z_j) + \\frac{1}{4}e^{iU\\Delta t}(I-Z_i)(I-Z_j)  \\\\\n",
    "& \\boxed{= I-(I-Z_i)(I-Z_j)\\left(1-e^{iU\\Delta t} \\right) } \\\\\n",
    "&= \\begin{pmatrix}1 & 0 & 0 & 0\\\\ 0 & 1& 0 & 0 \\\\ 0 & 0 & 1 & 0 \\\\ 0 & 0 & 0 & e^{iU\\Delta t} \\end{pmatrix} .\n",
    "\\end{align}\n",
    "\n",
    "## Measurement\n",
    "\n",
    "The onsite terms of the Hamiltonian map to a matrix of the form\n",
    "\n",
    "$$ (I-Z_i^\\uparrow)(I-Z_i^\\downarrow) = \\ket{11}\\bra{11}_{\\uparrow\\downarrow} $$,\n",
    "\n",
    "the on-site energy for each site is the probability that the two qubits $\\ket{q_j}_\\uparrow$,$\\ket{q_j}_\\downarrow$ corresponding to site $j$ are *both* measured in the $\\ket{1}$ state.\n",
    "\n",
    "The hopping terms of the Hamiltonian require a bit more preparation.  To efficiently measure the hopping terms, first transform the hopping operator using the circuit found in Fig. 5 of the *Cade, Mineh, Montanaro, Stanisic* arXiv paper, *Strategies for solving the Fermi-Hubbard Model on Near-Term Quantum Computers.*  This diagonalizes the operator to\n",
    "\n",
    "$$ D = \\ket{01}\\bra{01} - \\ket{10}\\bra{10} $$\n",
    "\n",
    "which is equivalent to the probability of getting the outcome '01' minus the probability of getting '10' for any pair of qubits in the chain.  It also should be noted that the qubit pairs $(i-1, i)$ and $(i,i+1)$ cannot be measured simultaneously under this transformation and so if we have more than 2 sites, we need at least 2 circuit runs to measure *all* hopping terms.\n",
    "\n",
    "### Tunneling w/ Different Hopping Terms\n",
    "\n",
    "To simulate tunneling between sites, we apply the time evolution operator several times and measure the probabilities of each site.  To simulate hopping between different materials, the angle $\\theta = \\frac{t\\Delta t}{2}$ is changed to $\\theta' = \\frac{t' \\Delta t}{2}$ on the appropriate term in the evolution operator.\n",
    "\n",
    "\n",
    "$^1$https://web.cs.ucdavis.edu/~bai/publications/varneyleebai09.pdf"
   ]
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   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/kaelyn/anaconda3/envs/qiskit/lib/python3.7/site-packages/qiskit/providers/ibmq/ibmqfactory.py:192: UserWarning: Timestamps in IBMQ backend properties, jobs, and job results are all now in local time instead of UTC.\n",
      "  warnings.warn('Timestamps in IBMQ backend properties, jobs, and job results '\n",
      "ibmqfactory.load_account:WARNING:2021-03-28 13:42:32,979: Credentials are already in use. The existing account in the session will be replaced.\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "# Importing standard Qiskit libraries and configuring account\n",
    "from qiskit import QuantumCircuit, execute, Aer, IBMQ, BasicAer, QuantumRegister, ClassicalRegister\n",
    "from qiskit.compiler import transpile, assemble\n",
    "from qiskit.quantum_info import Operator\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "from qiskit.tools.jupyter import *\n",
    "from qiskit.visualization import *\n",
    "import random as rand\n",
    "import scipy.linalg as la\n",
    "\n",
    "provider = IBMQ.load_account()\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.colors as mcolors\n",
    "import numpy as np\n",
    "from matplotlib import rcParams\n",
    "rcParams['text.usetex'] = True\n",
    "\n",
    "def reverse_list(s):\n",
    "    temp_list = list(s)\n",
    "    temp_list.reverse()\n",
    "    return ''.join(temp_list)\n",
    "\n",
    "\n",
    "#Useful tool for converting an integer to a binary bit string\n",
    "def get_bin(x, n=0):\n",
    "    \"\"\"\n",
    "    Get the binary representation of x.\n",
    "    Parameters: x (int), n (int, number of digits)\"\"\"\n",
    "    binry = format(x, 'b').zfill(n)\n",
    "    sup = list( reversed( binry[0:int(len(binry)/2)] ) )\n",
    "    sdn = list( reversed( binry[int(len(binry)/2):len(binry)] ) )\n",
    "    \n",
    "    return format(x, 'b').zfill(n)\n",
    "    #return ''.join(sup)+''.join(sdn)\n",
    "\n",
    "\n"
   ]
  },
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   "cell_type": "code",
   "execution_count": 15,
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   "source": [
    "'''The task here is now to define a function which will either update a given circuit with a time-step\n",
    "or return a single gate which contains all the necessary components of a time-step'''\n",
    "\n",
    "\n",
    "#==========Set Parameters of the System=============#\n",
    "\n",
    "dt = 0.2 #Delta t\n",
    "t = 1.0  #Hopping parameter\n",
    "U = 2.  #On-Site repulsion\n",
    "time_steps = 30\n",
    "nsite = 3\n",
    "trotter_slices = 5\n",
    "\n",
    "\n",
    "#==========Needed Functions=============#\n",
    "#Function to apply a full set of time evolution gates to a given circuit\n",
    "def qc_evolve(qc, numsite, dt, t, U, num_steps):\n",
    "    #Compute angles for the onsite and hopping gates\n",
    "    # based on the model parameters t, U, and dt\n",
    "    theta = t*dt/(2*trotter_slices) \n",
    "    phi = U*dt/(trotter_slices)\n",
    "    numq = 2*numsite\n",
    "    y_hop = Operator([[np.cos(theta), 0, 0, -1j*np.sin(theta)],\n",
    "                [0, np.cos(theta), 1j*np.sin(theta), 0],\n",
    "                [0, 1j*np.sin(theta), np.cos(theta), 0],\n",
    "                [-1j*np.sin(theta), 0, 0, np.cos(theta)]])\n",
    "    x_hop = Operator([[np.cos(theta), 0, 0, 1j*np.sin(theta)],\n",
    "                [0, np.cos(theta), 1j*np.sin(theta), 0],\n",
    "                [0, 1j*np.sin(theta), np.cos(theta), 0],\n",
    "                [1j*np.sin(theta), 0, 0, np.cos(theta)]])\n",
    "    z_onsite = Operator([[1, 0, 0, 0],\n",
    "               [0, 1, 0, 0],\n",
    "               [0, 0, 1, 0],\n",
    "               [0, 0, 0, np.exp(1j*phi)]])\n",
    "    \n",
    "    #Loop over each time step needed and apply onsite and hopping gates\n",
    "    for step in range(num_steps):\n",
    "        \n",
    "        for trot in range(trotter_slices):\n",
    "        #Onsite Terms\n",
    "            for i in range(0, numsite):\n",
    "                qc.unitary(z_onsite, [i,i+numsite], label=\"Z_Onsite\")\n",
    "        \n",
    "            #Add barrier to separate onsite from hopping terms    \n",
    "            qc.barrier()\n",
    "\n",
    "            #Hopping terms\n",
    "            for i in range(0,numsite-1):\n",
    "                #Spin-up chain\n",
    "                qc.unitary(y_hop, [i,i+1], label=\"YHop\")\n",
    "                qc.unitary(x_hop, [i,i+1], label=\"Xhop\")\n",
    "                #Spin-down chain\n",
    "                qc.unitary(y_hop, [i+numsite, i+1+numsite], label=\"Xhop\")\n",
    "                qc.unitary(x_hop, [i+numsite, i+1+numsite], label=\"Xhop\")\n",
    "\n",
    "            #Add barrier after finishing the time step\n",
    "            qc.barrier()\n",
    "    #Measure the circuit\n",
    "    for i in range(numq):\n",
    "        qc.measure(i, i)\n",
    "        \n",
    "\n",
    "\n",
    "#Function to run the circuit and store the counts for an evolution with\n",
    "# num_steps number of time steps.\n",
    "def sys_evolve(nsites, dt, t, U, num_steps):\n",
    "    numq = 2*nsites\n",
    "    data = np.zeros((2**numq, num_steps))\n",
    "    for t_step in range(0, num_steps):\n",
    "        #Create circuit with t_step number of steps\n",
    "        q = QuantumRegister(numq)\n",
    "        c = ClassicalRegister(numq)\n",
    "        qcirc = QuantumCircuit(q,c)\n",
    "\n",
    "    #Initialize circuit by setting the occupation to \n",
    "    # a spin up and down electron in the middle site\n",
    "    \n",
    "    #=========I TURNED THIS OFF FOR A SPECIFIC CASE==============\n",
    "        #qcirc.x(int(nsites/2))\n",
    "        #qcirc.x(nsites+int(nsites/2))\n",
    "    \n",
    "       # if nsites==3:\n",
    "            #Half-filling\n",
    "        #    qcirc.x(1)\n",
    "          #  qcirc.x(4)\n",
    "         #   qcirc.x(0)\n",
    "            #1 electron\n",
    "        qcirc.x(1)\n",
    "        \n",
    "            \n",
    "    #=======USE THE REGION ABOVE TO SET YOUR INITIAL STATE=======\n",
    "        qcirc.barrier()\n",
    "        #Append circuit with Trotter steps needed\n",
    "        qc_evolve(qcirc, nsites, dt, t, U, t_step)\n",
    "        \n",
    "    \n",
    "    #Choose provider and backend\n",
    "        provider = IBMQ.get_provider()\n",
    "        #backend = Aer.get_backend('statevector_simulator')\n",
    "        backend = Aer.get_backend('qasm_simulator')\n",
    "        #backend = provider.get_backend('ibmq_qasm_simulator')\n",
    "        #backend = provider.get_backend('ibmqx4')\n",
    "        #backend = provider.get_backend('ibmqx2')\n",
    "        #backend = provider.get_backend('ibmq_16_melbourne')\n",
    "\n",
    "        shots = 8192\n",
    "        max_credits = 10 #Max number of credits to spend on execution\n",
    "        job_exp = execute(qcirc, backend=backend, shots=shots, max_credits=max_credits)\n",
    "        job_monitor(job_exp)\n",
    "        result = job_exp.result()\n",
    "        counts = result.get_counts(qcirc)\n",
    "        print(result.get_counts(qcirc))\n",
    "        print(\"Job: \",t_step+1, \" of \", time_steps,\" complete.\")\n",
    "    \n",
    "    #Store results in data array and normalize them\n",
    "        for i in range(2**numq):\n",
    "            if counts.get(get_bin(i,numq)) is None:\n",
    "                dat = 0\n",
    "            else:\n",
    "                dat = counts.get(get_bin(i,numq))\n",
    "            data[i,t_step] = dat/shots\n",
    "    return data\n",
    "\n"
   ]
  },
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   "source": [
    "### Run Time Evolution of System"
   ]
  },
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   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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   ],
   "source": [
    "\n",
    "\n",
    "#Run simulation\n",
    "run_results = sys_evolve(nsite, dt, t, U, time_steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f49d2392cd0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "#Process and plot data\n",
    "'''The procedure here is, for each fermionic mode, add the probability of every state containing\n",
    "that mode (at a given time step), and renormalize the data based on the total occupation of each mode.\n",
    "Afterwards, plot the data as a function of time step for each mode.'''\n",
    "proc_data = np.zeros((2*nsite, time_steps))\n",
    "timesq = np.arange(0.,time_steps*dt, dt)\n",
    "\n",
    "#Sum over time steps\n",
    "for t in range(time_steps):\n",
    "    #Sum over all possible states of computer\n",
    "    for i in range(2**(2*nsite)):\n",
    "        #num = get_bin(i, 2*nsite)\n",
    "        num = ''.join( list( reversed(get_bin(i,2*nsite)) ) )\n",
    "        #For each state, check which mode(s) it contains and add them\n",
    "        for mode in range(len(num)):\n",
    "            if num[mode]=='1':\n",
    "                proc_data[mode,t] += run_results[i,t]\n",
    "    \n",
    "    #Renormalize these sums so that the total occupation of the modes is 1\n",
    "    norm = 0.0\n",
    "    for mode in range(len(num)):\n",
    "        norm += proc_data[mode,t]\n",
    "    proc_data[:,t] = proc_data[:,t] / norm\n",
    "    \n",
    "'''\n",
    "At this point, proc_data is a 2d array containing the occupation \n",
    "of each mode, for every time step\n",
    "'''\n",
    "    \n",
    "#Create plots of the processed data\n",
    "fig2, ax2 = plt.subplots(figsize=(20,10))\n",
    "colors = list(mcolors.TABLEAU_COLORS.keys())\n",
    "\n",
    "for i in range(nsite):\n",
    "    #Create string label\n",
    "    strup = \"Site \"+str(i+1)+r'$\\uparrow$'\n",
    "    strdwn = \"Site \"+str(i+1)+r'$\\downarrow$'\n",
    "    ax2.plot(timesq, proc_data[i,:], marker=\"^\", color=str(colors[i]), label=strup)\n",
    "    ax2.plot(timesq, proc_data[i+nsite,:], marker=\"v\", color=str(colors[i]), label=strdwn)\n",
    "\n",
    "\n",
    "#ax2.set_ylim(0, 0.55)\n",
    "ax2.set_xlim(0, time_steps*dt+dt/2.)\n",
    "#ax2.set_xticks(np.arange(0,time_steps*dt+dt, 0.2))\n",
    "#ax2.set_yticks(np.arange(0,0.55, 0.05))\n",
    "ax2.tick_params(labelsize=16)\n",
    "ax2.set_title('Time Evolution of 3 Site One Dimensional Chain', fontsize=22)\n",
    "ax2.set_xlabel('Time', fontsize=24)\n",
    "ax2.set_ylabel('Probability', fontsize=24)\n",
    "ax2.legend(fontsize=20)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time Steps:  10  Step Size:  0.5\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x1440 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot the raw data as a colormap\n",
    "xticks = np.arange(2**(nsite*2))\n",
    "xlabels=[]\n",
    "print(\"Time Steps: \",time_steps, \" Step Size: \",dt)\n",
    "for i in range(2**(nsite*2)):\n",
    "    xlabels.append(get_bin(i,6))\n",
    "    \n",
    "fig, ax = plt.subplots(figsize=(10,20))\n",
    "c = ax.pcolor(run_results, cmap='binary')\n",
    "ax.set_title('Time Evolution of 3 Site One Dimensional Chain', fontsize=22)\n",
    "plt.yticks(xticks, xlabels, size=18)\n",
    "ax.set_xlabel('Time Step', fontsize=22)\n",
    "ax.set_ylabel('State', fontsize=26)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below is the circuit diagram of the initalization to the state $\\ket{\\psi_0}=\\ket{010}_\\uparrow\\ket{010}_\\downarrow$ an a single time step.  As the system is evolved, all gates past the first barrier are repeated.\n",
    "![title](img/circuit-diagram.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exact Diagonalization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most straightforward way to find the ground state energy of a Fermi-Hubbard system is by diagonalizing its Hamiltonian.  For even modest system sizes in more than one-dimension this becomes very difficult because the Hamiltonian matrix is too large either to store in memory or diagonalize.  However, for one-dimensional chains and small system sizes, this is fairly trivial.\n",
    "\n",
    "We can also further simplify the matrix to be diagonalized by selecting the occupation and spin sector we wish to examine because, unless the Hamiltonian includes either a spin-orbit term or an electron bath, there are no far off-diagonal terms and thus the matrix to be simplified can be reduced.\n",
    "\n",
    "The code below will create a Hamiltonian matrix of a single electron in the three site chain.  We will then compute eigenvalues as well as the time evolution operator to compare with our results above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2. -1.  0. -1.  0.  0.  0.  0.  0.]\n",
      " [-1.  0. -1.  0. -1.  0.  0.  0.  0.]\n",
      " [ 0. -1.  0.  0.  0. -1.  0.  0.  0.]\n",
      " [-1.  0.  0.  0. -1.  0. -1.  0.  0.]\n",
      " [ 0. -1.  0. -1.  2. -1.  0. -1.  0.]\n",
      " [ 0.  0. -1.  0. -1.  0.  0.  0. -1.]\n",
      " [ 0.  0.  0. -1.  0.  0.  0. -1.  0.]\n",
      " [ 0.  0.  0.  0. -1.  0. -1.  0. -1.]\n",
      " [ 0.  0.  0.  0.  0. -1.  0. -1.  2.]]\n",
      "\n",
      "Eigenvalue:  (3.8200893743747892+0j)\n",
      "Eigenvector: \n",
      " [-3.19981759e-01  1.78562883e-01  6.27963030e-01  5.77350269e-01\n",
      "  3.25057584e-01 -1.79982325e-01  8.90599924e-17 -6.74297708e-17\n",
      "  9.83409616e-17]\n",
      "\n",
      "Eigenvalue:  (-2.279452315768611+0j)\n",
      "Eigenvector: \n",
      " [ 2.91197700e-01  3.82075671e-01 -2.29850422e-01 -7.50814067e-17\n",
      "  4.44036917e-01 -1.38643720e-01 -3.53553391e-01 -5.00000000e-01\n",
      "  3.53553391e-01]\n",
      "\n",
      "Eigenvalue:  (2.7320508075688763+0j)\n",
      "Eigenvector: \n",
      " [-1.52455962e-01  3.35234625e-01 -2.42305496e-16 -1.87756706e-17\n",
      " -2.97555918e-16  6.03634762e-01 -5.00000000e-01  6.27935562e-17\n",
      " -5.00000000e-01]\n",
      "\n",
      "Eigenvalue:  (2+0j)\n",
      "Eigenvector: \n",
      " [ 2.91197700e-01  3.82075671e-01 -2.29850422e-01  6.34931835e-17\n",
      "  4.44036917e-01 -1.38643720e-01  3.53553391e-01  5.00000000e-01\n",
      " -3.53553391e-01]\n",
      "\n",
      "Eigenvalue:  (-0.7320508075688779+0j)\n",
      "Eigenvector: \n",
      " [-6.39963518e-01  3.57125766e-01 -3.79476553e-16 -5.77350269e-01\n",
      "  5.78511731e-17 -3.59964650e-01 -1.61576200e-16  5.48586119e-17\n",
      "  4.21429799e-18]\n",
      "\n",
      "Eigenvalue:  (0.45936294139381934+0j)\n",
      "Eigenvector: \n",
      " [ 2.91197700e-01  3.82075671e-01  2.29850422e-01  3.31262738e-17\n",
      " -4.44036917e-01 -1.38643720e-01 -3.53553391e-01  5.00000000e-01\n",
      "  3.53553391e-01]\n",
      "\n",
      "Eigenvalue:  (-1.414213562373094+0j)\n",
      "Eigenvector: \n",
      " [-1.52455962e-01  3.35234625e-01 -1.33219972e-17  3.04242038e-16\n",
      " -4.22971005e-16  6.03634762e-01  5.00000000e-01  8.96562373e-17\n",
      "  5.00000000e-01]\n",
      "\n",
      "Eigenvalue:  (5.252746927828867e-17+0j)\n",
      "Eigenvector: \n",
      " [ 2.91197700e-01  3.82075671e-01  2.29850422e-01 -7.76114256e-17\n",
      " -4.44036917e-01 -1.38643720e-01  3.53553391e-01 -5.00000000e-01\n",
      " -3.53553391e-01]\n",
      "\n",
      "Eigenvalue:  (1.4142135623730951+0j)\n",
      "Eigenvector: \n",
      " [-3.19981759e-01  1.78562883e-01 -6.27963030e-01  5.77350269e-01\n",
      " -3.25057584e-01 -1.79982325e-01 -1.03102426e-16 -3.85420277e-17\n",
      "  2.60556006e-16]\n",
      "\n",
      "[array([[ 1.02388326e-01, -5.71368654e-02,  2.00936715e-01,\n",
      "        -1.84741555e-01,  1.04012497e-01,  5.75910610e-02,\n",
      "         3.29908956e-17,  1.23327458e-17, -8.33731690e-17],\n",
      "       [-5.71368654e-02,  3.18847031e-02, -1.12130889e-01,\n",
      "         1.03093328e-01, -5.80432192e-02, -3.21381628e-02,\n",
      "        -1.84102664e-17, -6.88217557e-18,  4.65256315e-17],\n",
      "       [ 2.00936715e-01, -1.12130889e-01,  3.94337567e-01,\n",
      "        -3.62554625e-01,  2.04124145e-01,  1.13022246e-01,\n",
      "         6.47445118e-17,  2.42029685e-17, -1.63619539e-16],\n",
      "       [-1.84741555e-01,  1.03093328e-01, -3.62554625e-01,\n",
      "         3.33333333e-01, -1.87672083e-01, -1.03912844e-01,\n",
      "        -5.95262133e-17, -2.22522500e-17,  1.50432080e-16],\n",
      "       [ 1.04012497e-01, -5.80432192e-02,  2.04124145e-01,\n",
      "        -1.87672083e-01,  1.05662433e-01,  5.85046197e-02,\n",
      "         3.35142254e-17,  1.25283784e-17, -8.46957056e-17],\n",
      "       [ 5.75910610e-02, -3.21381628e-02,  1.13022246e-01,\n",
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      "       [-1.84741555e-01,  1.03093328e-01, -3.62554625e-01,\n",
      "         3.33333333e-01, -1.87672083e-01, -1.03912844e-01,\n",
      "        -5.95262133e-17, -2.22522500e-17,  1.50432080e-16],\n",
      "       [ 1.04012497e-01, -5.80432192e-02,  2.04124145e-01,\n",
      "        -1.87672083e-01,  1.05662433e-01,  5.85046197e-02,\n",
      "         3.35142254e-17,  1.25283784e-17, -8.46957056e-17],\n",
      "       [ 5.75910610e-02, -3.21381628e-02,  1.13022246e-01,\n",
      "        -1.03912844e-01,  5.85046197e-02,  3.23936373e-02,\n",
      "         1.85566143e-17,  6.93688375e-18, -4.68954757e-17],\n",
      "       [ 3.29908956e-17, -1.84102664e-17,  6.47445118e-17,\n",
      "        -5.95262133e-17,  3.35142254e-17,  1.85566143e-17,\n",
      "         1.06301102e-32,  3.97377655e-33, -2.68639562e-32],\n",
      "       [ 1.23327458e-17, -6.88217557e-18,  2.42029685e-17,\n",
      "        -2.22522500e-17,  1.25283784e-17,  6.93688375e-18,\n",
      "         3.97377655e-33,  1.48548790e-33, -1.00423568e-32],\n",
      "       [-8.33731690e-17,  4.65256315e-17, -1.63619539e-16,\n",
      "         1.50432080e-16, -8.46957056e-17, -4.68954757e-17,\n",
      "        -2.68639562e-32, -1.00423568e-32,  6.78894320e-32]]), array([[ 1.02388326e-01, -5.71368654e-02,  2.00936715e-01,\n",
      "        -1.84741555e-01,  1.04012497e-01,  5.75910610e-02,\n",
      "         3.29908956e-17,  1.23327458e-17, -8.33731690e-17],\n",
      "       [-5.71368654e-02,  3.18847031e-02, -1.12130889e-01,\n",
      "         1.03093328e-01, -5.80432192e-02, -3.21381628e-02,\n",
      "        -1.84102664e-17, -6.88217557e-18,  4.65256315e-17],\n",
      "       [ 2.00936715e-01, -1.12130889e-01,  3.94337567e-01,\n",
      "        -3.62554625e-01,  2.04124145e-01,  1.13022246e-01,\n",
      "         6.47445118e-17,  2.42029685e-17, -1.63619539e-16],\n",
      "       [-1.84741555e-01,  1.03093328e-01, -3.62554625e-01,\n",
      "         3.33333333e-01, -1.87672083e-01, -1.03912844e-01,\n",
      "        -5.95262133e-17, -2.22522500e-17,  1.50432080e-16],\n",
      "       [ 1.04012497e-01, -5.80432192e-02,  2.04124145e-01,\n",
      "        -1.87672083e-01,  1.05662433e-01,  5.85046197e-02,\n",
      "         3.35142254e-17,  1.25283784e-17, -8.46957056e-17],\n",
      "       [ 5.75910610e-02, -3.21381628e-02,  1.13022246e-01,\n",
      "        -1.03912844e-01,  5.85046197e-02,  3.23936373e-02,\n",
      "         1.85566143e-17,  6.93688375e-18, -4.68954757e-17],\n",
      "       [ 3.29908956e-17, -1.84102664e-17,  6.47445118e-17,\n",
      "        -5.95262133e-17,  3.35142254e-17,  1.85566143e-17,\n",
      "         1.06301102e-32,  3.97377655e-33, -2.68639562e-32],\n",
      "       [ 1.23327458e-17, -6.88217557e-18,  2.42029685e-17,\n",
      "        -2.22522500e-17,  1.25283784e-17,  6.93688375e-18,\n",
      "         3.97377655e-33,  1.48548790e-33, -1.00423568e-32],\n",
      "       [-8.33731690e-17,  4.65256315e-17, -1.63619539e-16,\n",
      "         1.50432080e-16, -8.46957056e-17, -4.68954757e-17,\n",
      "        -2.68639562e-32, -1.00423568e-32,  6.78894320e-32]]), array([[ 1.02388326e-01, -5.71368654e-02,  2.00936715e-01,\n",
      "        -1.84741555e-01,  1.04012497e-01,  5.75910610e-02,\n",
      "         3.29908956e-17,  1.23327458e-17, -8.33731690e-17],\n",
      "       [-5.71368654e-02,  3.18847031e-02, -1.12130889e-01,\n",
      "         1.03093328e-01, -5.80432192e-02, -3.21381628e-02,\n",
      "        -1.84102664e-17, -6.88217557e-18,  4.65256315e-17],\n",
      "       [ 2.00936715e-01, -1.12130889e-01,  3.94337567e-01,\n",
      "        -3.62554625e-01,  2.04124145e-01,  1.13022246e-01,\n",
      "         6.47445118e-17,  2.42029685e-17, -1.63619539e-16],\n",
      "       [-1.84741555e-01,  1.03093328e-01, -3.62554625e-01,\n",
      "         3.33333333e-01, -1.87672083e-01, -1.03912844e-01,\n",
      "        -5.95262133e-17, -2.22522500e-17,  1.50432080e-16],\n",
      "       [ 1.04012497e-01, -5.80432192e-02,  2.04124145e-01,\n",
      "        -1.87672083e-01,  1.05662433e-01,  5.85046197e-02,\n",
      "         3.35142254e-17,  1.25283784e-17, -8.46957056e-17],\n",
      "       [ 5.75910610e-02, -3.21381628e-02,  1.13022246e-01,\n",
      "        -1.03912844e-01,  5.85046197e-02,  3.23936373e-02,\n",
      "         1.85566143e-17,  6.93688375e-18, -4.68954757e-17],\n",
      "       [ 3.29908956e-17, -1.84102664e-17,  6.47445118e-17,\n",
      "        -5.95262133e-17,  3.35142254e-17,  1.85566143e-17,\n",
      "         1.06301102e-32,  3.97377655e-33, -2.68639562e-32],\n",
      "       [ 1.23327458e-17, -6.88217557e-18,  2.42029685e-17,\n",
      "        -2.22522500e-17,  1.25283784e-17,  6.93688375e-18,\n",
      "         3.97377655e-33,  1.48548790e-33, -1.00423568e-32],\n",
      "       [-8.33731690e-17,  4.65256315e-17, -1.63619539e-16,\n",
      "         1.50432080e-16, -8.46957056e-17, -4.68954757e-17,\n",
      "        -2.68639562e-32, -1.00423568e-32,  6.78894320e-32]]), array([[ 1.02388326e-01, -5.71368654e-02,  2.00936715e-01,\n",
      "        -1.84741555e-01,  1.04012497e-01,  5.75910610e-02,\n",
      "         3.29908956e-17,  1.23327458e-17, -8.33731690e-17],\n",
      "       [-5.71368654e-02,  3.18847031e-02, -1.12130889e-01,\n",
      "         1.03093328e-01, -5.80432192e-02, -3.21381628e-02,\n",
      "        -1.84102664e-17, -6.88217557e-18,  4.65256315e-17],\n",
      "       [ 2.00936715e-01, -1.12130889e-01,  3.94337567e-01,\n",
      "        -3.62554625e-01,  2.04124145e-01,  1.13022246e-01,\n",
      "         6.47445118e-17,  2.42029685e-17, -1.63619539e-16],\n",
      "       [-1.84741555e-01,  1.03093328e-01, -3.62554625e-01,\n",
      "         3.33333333e-01, -1.87672083e-01, -1.03912844e-01,\n",
      "        -5.95262133e-17, -2.22522500e-17,  1.50432080e-16],\n",
      "       [ 1.04012497e-01, -5.80432192e-02,  2.04124145e-01,\n",
      "        -1.87672083e-01,  1.05662433e-01,  5.85046197e-02,\n",
      "         3.35142254e-17,  1.25283784e-17, -8.46957056e-17],\n",
      "       [ 5.75910610e-02, -3.21381628e-02,  1.13022246e-01,\n",
      "        -1.03912844e-01,  5.85046197e-02,  3.23936373e-02,\n",
      "         1.85566143e-17,  6.93688375e-18, -4.68954757e-17],\n",
      "       [ 3.29908956e-17, -1.84102664e-17,  6.47445118e-17,\n",
      "        -5.95262133e-17,  3.35142254e-17,  1.85566143e-17,\n",
      "         1.06301102e-32,  3.97377655e-33, -2.68639562e-32],\n",
      "       [ 1.23327458e-17, -6.88217557e-18,  2.42029685e-17,\n",
      "        -2.22522500e-17,  1.25283784e-17,  6.93688375e-18,\n",
      "         3.97377655e-33,  1.48548790e-33, -1.00423568e-32],\n",
      "       [-8.33731690e-17,  4.65256315e-17, -1.63619539e-16,\n",
      "         1.50432080e-16, -8.46957056e-17, -4.68954757e-17,\n",
      "        -2.68639562e-32, -1.00423568e-32,  6.78894320e-32]]), array([[ 1.02388326e-01, -5.71368654e-02,  2.00936715e-01,\n",
      "        -1.84741555e-01,  1.04012497e-01,  5.75910610e-02,\n",
      "         3.29908956e-17,  1.23327458e-17, -8.33731690e-17],\n",
      "       [-5.71368654e-02,  3.18847031e-02, -1.12130889e-01,\n",
      "         1.03093328e-01, -5.80432192e-02, -3.21381628e-02,\n",
      "        -1.84102664e-17, -6.88217557e-18,  4.65256315e-17],\n",
      "       [ 2.00936715e-01, -1.12130889e-01,  3.94337567e-01,\n",
      "        -3.62554625e-01,  2.04124145e-01,  1.13022246e-01,\n",
      "         6.47445118e-17,  2.42029685e-17, -1.63619539e-16],\n",
      "       [-1.84741555e-01,  1.03093328e-01, -3.62554625e-01,\n",
      "         3.33333333e-01, -1.87672083e-01, -1.03912844e-01,\n",
      "        -5.95262133e-17, -2.22522500e-17,  1.50432080e-16],\n",
      "       [ 1.04012497e-01, -5.80432192e-02,  2.04124145e-01,\n",
      "        -1.87672083e-01,  1.05662433e-01,  5.85046197e-02,\n",
      "         3.35142254e-17,  1.25283784e-17, -8.46957056e-17],\n",
      "       [ 5.75910610e-02, -3.21381628e-02,  1.13022246e-01,\n",
      "        -1.03912844e-01,  5.85046197e-02,  3.23936373e-02,\n",
      "         1.85566143e-17,  6.93688375e-18, -4.68954757e-17],\n",
      "       [ 3.29908956e-17, -1.84102664e-17,  6.47445118e-17,\n",
      "        -5.95262133e-17,  3.35142254e-17,  1.85566143e-17,\n",
      "         1.06301102e-32,  3.97377655e-33, -2.68639562e-32],\n",
      "       [ 1.23327458e-17, -6.88217557e-18,  2.42029685e-17,\n",
      "        -2.22522500e-17,  1.25283784e-17,  6.93688375e-18,\n",
      "         3.97377655e-33,  1.48548790e-33, -1.00423568e-32],\n",
      "       [-8.33731690e-17,  4.65256315e-17, -1.63619539e-16,\n",
      "         1.50432080e-16, -8.46957056e-17, -4.68954757e-17,\n",
      "        -2.68639562e-32, -1.00423568e-32,  6.78894320e-32]])]\n"
     ]
    }
   ],
   "source": [
    "#Try by constructing the matrix and finding the eigenvalues\n",
    "N = 3\n",
    "Nup = 2\n",
    "Ndwn = N - Nup\n",
    "\n",
    "t = 1.0\n",
    "U = 2.\n",
    "\n",
    "#Check if two states are different by a single hop\n",
    "def hop(psii, psij):\n",
    "    #Check spin down\n",
    "    hopp = 0\n",
    "    if psii[0]==psij[0]:\n",
    "        #Create array of indices with nonzero values\n",
    "        indi = np.nonzero(psii[1])[0]\n",
    "        indj = np.nonzero(psij[1])[0]\n",
    "        for i in range(len(indi)):\n",
    "            if abs(indi[i]-indj[i])==1:\n",
    "                hopp = -t\n",
    "                return hopp\n",
    "    #Check spin up\n",
    "    if psii[1]==psij[1]:\n",
    "        indi = np.nonzero(psii[0])[0]\n",
    "        indj = np.nonzero(psij[0])[0]\n",
    "        for i in range(len(indi)):\n",
    "            if abs(indi[i]-indj[i])==1:\n",
    "                hopp = -t\n",
    "                return hopp\n",
    "    return hopp\n",
    "            \n",
    "\n",
    "#On-site terms\n",
    "def repel(l,state):\n",
    "    if state[0][l]==1 and state[1][l]==1:\n",
    "        return state\n",
    "    else:\n",
    "        return []\n",
    "        \n",
    "#States for 3 electrons with net spin up\n",
    "'''\n",
    "states = [ [[1,1,0],[1,0,0]], [[1,1,0],[0,1,0]], [[1,1,0], [0,0,1]],\n",
    "           [[1,0,1],[1,0,0]], [[1,0,1],[0,1,0]], [[1,0,1], [0,0,1]],\n",
    "           [[0,1,1],[1,0,0]], [[0,1,1],[0,1,0]], [[0,1,1], [0,0,1]] ]\n",
    "\n",
    "#States for 2 electrons in singlet state\n",
    "'''\n",
    "states = [ [[1,0,0],[1,0,0]], [[1,0,0],[0,1,0]], [[1,0,0],[0,0,1]],\n",
    "           [[0,1,0],[1,0,0]], [[0,1,0],[0,1,0]], [[0,1,0],[0,0,1]],\n",
    "           [[0,0,1],[1,0,0]], [[0,0,1],[0,1,0]], [[0,0,1],[0,0,1]] ]\n",
    "#'''\n",
    "#States for a single electron\n",
    "#states = [ [[1,0,0],[0,0,0]], [[0,1,0],[0,0,0]], [[0,0,1],[0,0,0]] ]\n",
    "#'''\n",
    "H = np.zeros((len(states),len(states)) )\n",
    "#Construct Hamiltonian matrix\n",
    "for i in range(len(states)):\n",
    "    psi_i = states[i]\n",
    "    for j in range(len(states)):\n",
    "        psi_j = states[j]\n",
    "        \n",
    "        if j==i:\n",
    "            for l in range(0,N):\n",
    "                if psi_i == repel(l,psi_j):\n",
    "                    H[i,j] = U\n",
    "                    break\n",
    "        else:\n",
    "            H[i,j] = hop(psi_i, psi_j)\n",
    "\n",
    "print(H)\n",
    "results = la.eig(H)\n",
    "print()\n",
    "for i in range(len(results[0])):\n",
    "    print('Eigenvalue: ',results[0][i])\n",
    "    print('Eigenvector: \\n',results[1][i])\n",
    "    print()\n",
    "\n",
    "dens_ops = []\n",
    "eigs = []\n",
    "for vec in results[1]:\n",
    "    dens_ops.append(np.outer(results[1][i],results[1][i]))\n",
    "    eigs.append(results[0][i])\n",
    "    print(dens_ops)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Time Evolution\n",
    "\n",
    "Next we will create the time evolution operator explicitly via matrix exponentiation and apply it to an initial state of a single $\\uparrow$ electron in the middle site.  Then plot its time evolution, we do this by applying each step as\n",
    "\n",
    "\\begin{equation}\n",
    "    \\ket{\\Psi(t+\\Delta t)} = e^{-iH\\Delta t}\\ket{\\Psi(t)}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.5 0.  0.  0.  0.5 0. ]\n",
      "[4.95037292e-01 4.95027680e-03 1.24307427e-05 4.95023817e-03\n",
      " 4.90083017e-01 4.96674457e-03]\n",
      "[4.80586866e-01 1.92175304e-02 1.95603181e-04 1.92151070e-02\n",
      " 4.61313217e-01 1.94716762e-02]\n",
      "[0.45789068 0.04114624 0.00096308 0.04111954 0.41652299 0.04235747]\n",
      "[0.42879619 0.06827634 0.00292747 0.06813303 0.36007455 0.07179241]\n",
      "[0.39547059 0.09773215 0.00679726 0.09721653 0.2973628  0.10542067]\n",
      "[0.36008486 0.12666092 0.01325422 0.12522605 0.23419835 0.1405756 ]\n",
      "[0.32452812 0.15264289 0.02282899 0.14930934 0.17614382 0.17454684]\n",
      "[0.29020282 0.17400464 0.03579254 0.16723517 0.1278867  0.20487813]\n",
      "[0.2579312  0.18998924 0.05207956 0.17760961 0.09273195 0.22965844]\n",
      "[0.22797843 0.20076558 0.07125599 0.1799553  0.07228536 0.24775934]\n",
      "[0.20017418 0.20728786 0.09253796 0.17465571 0.06637302 0.25897127]\n",
      "[0.17409672 0.21103939 0.11486389 0.16278952 0.07320769 0.26400279]\n",
      "[0.14927571 0.21370939 0.1370149  0.14589762 0.08977311 0.26432927]\n",
      "[0.12537243 0.21685607 0.15777149 0.12573221 0.11236126 0.26190654]\n",
      "[0.10230583 0.22160642 0.17608775 0.10403389 0.13717175 0.25879436]\n",
      "[0.08030797 0.22843386 0.19125817 0.08236939 0.16087385 0.25675676]\n",
      "[0.05990728 0.23704356 0.20304916 0.06204408 0.18104058 0.25691534]\n",
      "[0.04185053 0.24638172 0.21176775 0.04408375 0.19639142 0.25952484]\n",
      "[0.02698222 0.25477122 0.21824655 0.02926539 0.20681709 0.26391751]\n",
      "[0.01610304 0.26016142 0.22373554 0.01816928 0.21320082 0.2686299 ]\n",
      "[0.00982853 0.26046418 0.22970729 0.0112263  0.21708494 0.27168876]\n",
      "[0.00846624 0.25393369 0.23760007 0.0087443  0.2202551  0.2710006 ]\n",
      "[0.01192634 0.23953512 0.24853854 0.01090994 0.22432107 0.264769  ]\n",
      "[0.01967716 0.21724164 0.2630812  0.01777545 0.23036586 0.25185869]\n",
      "[0.03075376 0.18820238 0.28104386 0.02924665 0.23871537 0.23203798]\n",
      "[0.04382327 0.15473859 0.30143814 0.04508857 0.24885576 0.20605567]\n",
      "[0.05730513 0.12015017 0.3225447  0.06495696 0.25950037 0.17554266]\n",
      "[0.06953711 0.08834677 0.34211612 0.08845205 0.26878643 0.14276152]\n",
      "[0.07897026 0.06335041 0.35767932 0.11517794 0.2745668  0.11025526]\n",
      "[0.08436852 0.04874355 0.36688792 0.14478404 0.27475334 0.08046263]\n",
      "[0.08498457 0.0471502  0.36786522 0.17696545 0.26766503 0.05536951]\n",
      "[0.08068332 0.05983565 0.35948103 0.21140956 0.25233511 0.03625533]\n",
      "[0.07198983 0.08649113 0.34151904 0.24769312 0.22873516 0.02357172]\n",
      "[0.06004885 0.12523795 0.3147132  0.28515358 0.19788209 0.01696433]\n",
      "[0.04649658 0.17284799 0.28065543 0.32277317 0.16180514 0.01542169]\n",
      "[0.03325989 0.22514133 0.24159878 0.35911994 0.12336673 0.01751334]\n",
      "[0.02231055 0.27749551 0.20019394 0.39238245 0.08595078 0.02166677]\n",
      "[0.0154099  0.32538784 0.15920226 0.42051529 0.05305433 0.02643038]\n",
      "[0.0138811  0.36489432 0.12122458 0.44148506 0.02783723 0.03067771]\n",
      "[0.01844202 0.39308292 0.08847505 0.45357792 0.01269763 0.03372445]\n",
      "[0.02912176 0.40826135 0.06261689 0.45570844 0.00894149 0.03535007]\n",
      "[0.04527085 0.41006336 0.04466578 0.44766104 0.01660334 0.03573562]\n",
      "[0.06566101 0.39938009 0.0349589  0.43020402 0.03445075 0.03534522]\n",
      "[0.08865709 0.37815921 0.0331837  0.40504    0.06017379 0.03478621]\n",
      "[0.11243405 0.34910595 0.03846    0.3745907  0.09072739 0.03468191]\n",
      "[0.13520601 0.31532588 0.04946811 0.34165045 0.12276756 0.03558199]\n",
      "[0.15543394 0.27995175 0.06461431 0.3089722  0.15310716 0.03792064]\n",
      "[0.17198287 0.2457966  0.08222053 0.27886568 0.17911702 0.0420173 ]\n",
      "[0.18420805 0.21507315 0.10071879 0.25288513 0.19901253 0.04810233]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/kaelyn/anaconda3/envs/qiskit/lib/python3.7/site-packages/ipykernel_launcher.py:40: ComplexWarning: Casting complex values to real discards the imaginary part\n"
     ]
    }
   ],
   "source": [
    "dt = 0.1\n",
    "tsteps = 50\n",
    "times = np.arange(0., tsteps*dt, dt)\n",
    "\n",
    "t_op = la.expm(-1j*H*dt)\n",
    "#print(np.subtract(np.identity(len(H)), dt*H*1j))\n",
    "#print(t_op)\n",
    "wfk = [0., 1., 0., 0., .0, 0., 0., 0., 0.] #Half-filling initial state\n",
    "#wfk = [0., 0., 0., 0., 1.0, 0., 0., 0., 0.] #2 electron initial state\n",
    "#wfk = [0., 1., 0.] #1 electron initial state\n",
    "\n",
    "\n",
    "evolve = np.zeros([tsteps, len(wfk)])\n",
    "mode_evolve = np.zeros([tsteps, 6])\n",
    "evolve[0] = wfk\n",
    "\n",
    "#Figure out how to generalize this later\n",
    "#'''\n",
    "mode_evolve[0][0] = (evolve[0][0]+evolve[0][1]+evolve[0][2]) /2.\n",
    "mode_evolve[0][1] = (evolve[0][3]+evolve[0][4]+evolve[0][5]) /2.\n",
    "mode_evolve[0][2] = (evolve[0][6]+evolve[0][7]+evolve[0][8]) /2.\n",
    "mode_evolve[0][3] = (evolve[0][0]+evolve[0][3]+evolve[0][6]) /2.\n",
    "mode_evolve[0][4] = (evolve[0][1]+evolve[0][4]+evolve[0][7]) /2.\n",
    "mode_evolve[0][5] = (evolve[0][2]+evolve[0][5]+evolve[0][8])  /2.\n",
    "'''\n",
    "mode_evolve[0][0] = (evolve[0][0]+evolve[0][1]+evolve[0][2]+evolve[0][3]+evolve[0][4]+evolve[0][5]) /3.\n",
    "mode_evolve[0][1] = (evolve[0][0]+evolve[0][1]+evolve[0][2]+evolve[0][6]+evolve[0][7]+evolve[0][8]) /3.\n",
    "mode_evolve[0][2] = (evolve[0][3]+evolve[0][4]+evolve[0][5]+evolve[0][6]+evolve[0][7]+evolve[0][8]) /3.\n",
    "mode_evolve[0][3] = (evolve[0][0]+evolve[0][3]+evolve[0][6]) /3.\n",
    "mode_evolve[0][4] = (evolve[0][1]+evolve[0][4]+evolve[0][7]) /3.\n",
    "mode_evolve[0][5] = (evolve[0][2]+evolve[0][5]+evolve[0][8]) /3.\n",
    "'''\n",
    "print(mode_evolve[0])\n",
    "#Define density matrices\n",
    "\n",
    "\n",
    "for t in range(1, tsteps):\n",
    "    #t_op = la.expm(-1j*H*t)\n",
    "    wfk = np.dot(t_op, wfk)\n",
    "    evolve[t] = np.multiply(np.conj(wfk), wfk)\n",
    "    norm = np.sum(evolve[t])\n",
    "    #print(evolve[t])\n",
    "    #Store data in modes rather than basis defined in 'states' variable\n",
    "    #''' #Procedure for two electrons\n",
    "    mode_evolve[t][0] = (evolve[t][0]+evolve[t][1]+evolve[t][2]) / (2)\n",
    "    mode_evolve[t][1] = (evolve[t][3]+evolve[t][4]+evolve[t][5]) / (2)\n",
    "    mode_evolve[t][2] = (evolve[t][6]+evolve[t][7]+evolve[t][8]) / (2)\n",
    "    mode_evolve[t][3] = (evolve[t][0]+evolve[t][3]+evolve[t][6]) / (2)\n",
    "    mode_evolve[t][4] = (evolve[t][1]+evolve[t][4]+evolve[t][7]) / (2)\n",
    "    mode_evolve[t][5] = (evolve[t][2]+evolve[t][5]+evolve[t][8]) / (2)\n",
    "    ''' #Procedure for half-filling\n",
    "    mode_evolve[t][0] = (evolve[t][0]+evolve[t][1]+evolve[t][2]+evolve[t][3]+evolve[t][4]+evolve[t][5]) /3.\n",
    "    mode_evolve[t][1] = (evolve[t][0]+evolve[t][1]+evolve[t][2]+evolve[t][6]+evolve[t][7]+evolve[t][8]) /3.\n",
    "    mode_evolve[t][2] = (evolve[t][3]+evolve[t][4]+evolve[t][5]+evolve[t][6]+evolve[t][7]+evolve[t][8]) /3.\n",
    "    mode_evolve[t][3] = (evolve[t][0]+evolve[t][3]+evolve[t][6]) /3.\n",
    "    mode_evolve[t][4] = (evolve[t][1]+evolve[t][4]+evolve[t][7]) /3.\n",
    "    mode_evolve[t][5] = (evolve[t][2]+evolve[t][5]+evolve[t][8]) /3.\n",
    "    #'''\n",
    "    print(mode_evolve[t])\n",
    "    #print(np.linalg.norm(evolve[t]))\n",
    "    \n",
    "\n",
    "#print(len(evolve[:,0]) )\n",
    "#print(len(times))\n",
    "#print(evolve[:,0])\n",
    "#print(min(evolve[:,0]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results\n",
    "\n",
    "We will then compare the results from the classical numerical simulation with the quantum one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f49d1619f50>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Create plots of the processed data\n",
    "fig2, ax2 = plt.subplots(figsize=(20,10))\n",
    "colors = list(mcolors.TABLEAU_COLORS.keys())\n",
    "\n",
    "\n",
    "sit1 = \"Exact Site \"+str(1)+r'$\\uparrow$'\n",
    "sit2 = \"Exact Site \"+str(2)+r'$\\uparrow$'\n",
    "sit3 = \"Exact Site \"+str(3)+r'$\\uparrow$'\n",
    "#ax2.plot(times, evolve[:,0], linestyle='--', color=colors[0], linewidth=2.5, label=sit1)\n",
    "#ax2.plot(times, evolve[:,1], linestyle='--', color=str(colors[1]), linewidth=2.5, label=sit2)\n",
    "#ax2.plot(times, evolve[:,2], linestyle='--', color=str(colors[2]), linewidth=2., label=sit3)\n",
    "#ax2.plot(times, np.zeros(len(times)))\n",
    "\n",
    "\n",
    "for i in range(nsite):\n",
    "    #Create string label\n",
    "    strupq = \"Quantum Site \"+str(i+1)+r'$\\uparrow$'\n",
    "    strdwnq = \"Quantum Site \"+str(i+1)+r'$\\downarrow$'\n",
    "    strup = \"Numerical Site \"+str(i+1)+r'$\\uparrow$'\n",
    "    strdwn = \"Numerical Site \"+str(i+1)+r'$\\downarrow$'\n",
    "    #ax2.plot(timesq, proc_data[i,:], marker=\"*\", color=str(colors[i]), markersize=5, label=strupq)\n",
    "    #ax2.plot(timesq, proc_data[i+nsite,:], marker=\"v\", color=str(colors[i]), markersize=5, label=strdwnq)\n",
    "    ax2.plot(times, mode_evolve[:,i], linestyle='-', color=str(colors[i]), linewidth=2, label=strup)\n",
    "    ax2.plot(times, mode_evolve[:,i+3], linestyle='--', color=str(colors[i]), linewidth=2, label=strdwn)\n",
    "    #ax2.plot(times, evolve[:,i], linestyle='-', color=str(colors[i]), linewidth=2, label=strup)\n",
    "    #ax2.plot(times, evolve[:,i+3], linestyle='--', color=str(colors[i]), linewidth=2, label=strdwn)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "ax2.set_ylim(0, .5)\n",
    "ax2.set_xlim(0, tsteps*dt+dt/2.)\n",
    "ax2.set_xticks(np.arange(0,tsteps*dt+dt, 2*dt))\n",
    "ax2.set_yticks(np.arange(0,0.5, 0.05))\n",
    "ax2.tick_params(labelsize=16)\n",
    "ax2.set_title('Time Evolution of 2 Electrons in 3 Site Chain', fontsize=22)\n",
    "ax2.set_xlabel('Time', fontsize=24)\n",
    "ax2.set_ylabel('Probability', fontsize=24)\n",
    "ax2.legend(fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparing Quantum & Classical Approaches"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1 Electron"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Placing one electron into the middle site, we evolve the system in ime.  For a hopping term of $t=1$, on-site energy $U=2$ a time step of $\\delta t= 0.1$ (with units of inverse energy and $\\hbar=1$) and $5$ Trotter steps the following plot compares the classical numerical approach to time evolution with the quantum approach.\n",
    "~![title](img/t-1-U-2.0-dt-0.1-1electron.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 Electrons"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Placing one electron into the middle site, we evolve the system in ime.  For a hopping term of $t=1$, on-site energy $U=2$ and a time step of $\\delta t= 0.1$ (with units of inverse energy and $\\hbar=1$) the following plot compares the classical numerical approach to time evolution with the quantum approach.\n",
    "~![title](img/t-1-U-2.0-dt-0.1-2electrons.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Placing two electrons of opposite spin into the middle site as the input state ($\\ket{\\psi_0}=\\ket{010}_\\uparrow\\ket{010}_\\downarrow$), we evolve the system in time.  For a hopping term of $t=1$ and on-site energy of $U=2$ and a time step of $\\delta t=0.1$ (with units of inverse energy and $\\hbar=1$) the following plot demonstrates the occupation oscillating between the middle and outer sites in the chain.  As the system evolves, this oscillation decays and begins to settle into an equilibrium occupation.\n",
    "~![title](img/t-1-U-2-dt-0.1-tsteps-30.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This decays can be seen better if we double the time the system is evolved further\n",
    "![title](img/3-site-evolution-dt-0.1-tsteps-60.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interesting evolutions can be seen for the 4 and 5 site chains\n",
    "![title](img/4site_t-1-U-2-dt-0.1.png)\n",
    "![title](img/5site_t-1-U-2-dt-0.1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Changing U\n",
    "\n",
    "All plots below have paramaters of $\\Delta t = 0.1$, $t = 1.0$, and a run for $30$ time steps.\n",
    "\n",
    "### U=0.5\n",
    "![title](img/t-1-U-0.5-dt-0.1-tsteps-30.png)\n",
    "\n",
    "### U=1.0\n",
    "![title](img/t-1-U-1.0-dt-0.1-tsteps-30.png)\n",
    "\n",
    "### U=1.5\n",
    "![title](img/t-1-U-1.5-dt-0.1-tsteps-30.png)\n",
    "\n",
    "### U=2.0\n",
    "![title](img/t-1-U-2.0-dt-0.1-tsteps-30.png)\n",
    "\n",
    "### U=2.5\n",
    "![title](img/t-1-U-2.5-dt-0.1-tsteps-30.png)"
   ]
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   "outputs": [],
   "source": []
  }
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