Quantum_chip_design_presim.ipynb

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  {
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   "source": [
    "# Quantum Hardware design ref.\n",
    "This file always stays the same and will be used in all designs for \"presim\" all we do is just change variables to suit our specific circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba1d8e70",
   "metadata": {},
   "source": [
    "## Quantum Harmonic Oscillator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "111c4a86",
   "metadata": {},
   "outputs": [],
   "source": [
    "import qiskit_metal as metal\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "b1a36bc1",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_metal.analyses.hamiltonian.HO_wavefunctions import wavefunction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "78b8ecc1",
   "metadata": {},
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
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     },
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   ],
   "source": [
    "# Let's define the range of x-axis values (representating charge) to be from (-5,5)\n",
    "x = np.linspace(-5,5,100)\n",
    "\n",
    "# Let's plot the first five energy levels (N=0 through N=4) of the harmonic oscillator\n",
    "# We'll just take L=C=1.0 for simplicity\n",
    "plt.plot(x, wavefunction(1, 1, 0, x), 'k') # N=0; ground state (black)\n",
    "plt.plot(x, wavefunction(1, 1, 1, x), 'b') # N=1; first excited state (blue)\n",
    "plt.plot(x, wavefunction(1, 1, 2, x), 'r') # N=2; second excited state (red)\n",
    "plt.plot(x, wavefunction(1, 1, 3, x), 'g') # N=3; third excited state (green)\n",
    "plt.plot(x, wavefunction(1, 1, 4, x), 'y') # N=4; fourth excited state (yellow)\n",
    "plt.xlabel(\"Charge [Q]\")\n",
    "plt.ylabel(\"Wavefunction [Psi]\")\n",
    "\n",
    "# show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de835eeb",
   "metadata": {},
   "source": [
    "## Plotting Eigenvalues as a Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "f34733ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_metal.analyses.hamiltonian.transmon_charge_basis import Hcpb\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "52aeaf5b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We'll use the variable x to represent the offset charge (ng), which will vary from -2.0 to 2.0\n",
    "x = np.linspace(-2.0,2.0,101)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "843d35a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a value of the Josephson Energy (E_J) as well as the ratio between the E_J and the Charging Energy (E_C):\n",
    "E_J = 1000.0\n",
    "ratio = 1.0\n",
    "E_C = E_J/ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "712ec8b3",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(38.902777777777786, 0.5, 'Em/E01')"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we'll normalize the calculated energies by the 0->1 transition state energy evaluated at the degenercy point (ng=0.5)\n",
    "H_norm = Hcpb(nlevels=2, Ej=E_J, Ec=E_C, ng=0.5)\n",
    "norm = H_norm.fij(0,1)\n",
    "\n",
    "# Next we'll empty lists to the first three eigenvalues (m=0, m=1, m=2):\n",
    "E0 = []\n",
    "E1 = []\n",
    "E2 = []\n",
    "\n",
    "# For a given value of offset charge (ng, represented by x) we will calculate the CPB Hamiltonian using the previously assigned values of E_J and E_C. Then we calculate the eigenvalue for a given value of m.\n",
    "for i in x:\n",
    "    H = Hcpb(nlevels=3, Ej=E_J, Ec=E_C, ng=i)\n",
    "    E0.append(H.evalue_k(0)/norm)\n",
    "    E1.append(H.evalue_k(1)/norm)\n",
    "    E2.append(H.evalue_k(2)/norm)\n",
    "\n",
    "# define the minimum of E0 and set this to E=0\n",
    "floor = min(E0)\n",
    "\n",
    "plt.plot(x, E0 - floor, 'k')\n",
    "plt.plot(x, E1 - floor, 'r')\n",
    "plt.plot(x, E2 - floor, 'b')\n",
    "plt.xlabel(\"ng\")\n",
    "plt.ylabel(\"Em/E01\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4761475",
   "metadata": {},
   "source": [
    "## Energy levels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "eb9ebad8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%config IPCompleter.greedy = True\n",
    "%matplotlib inline\n",
    "%config Completer.use_jedi = False\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "from qiskit_metal.analyses.hamiltonian.transmon_charge_basis import Hcpb\n",
    "from qiskit_metal.analyses.hamiltonian.transmon_CPB_analytic import Hcpb_analytic\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "3e30ab87",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-2.0,2.0,101) # this represents the charging energy (ng)\n",
    "H_norm = Hcpb(nlevels=2, Ej=1000.0, Ec=1000.0, ng=0.5) # Hamiltonian definition\n",
    "norm = H_norm.fij(0,1) # normalization constant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "a8ac12d8",
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      "text/plain": [
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    "E0, E1, E2 = [], [], []\n",
    "\n",
    "# For a given value of offset charge (ng, represented by x) we will calculate the CPB Hamiltonian using the previously assigned values of E_J and E_C. Then we calculate the eigenvalue for a given value of m.\n",
    "for i in x:\n",
    "    H = Hcpb(nlevels=3, Ej=1000.0, Ec=1000.0, ng=i)\n",
    "    E0.append(H.evalue_k(0)/norm)\n",
    "    E1.append(H.evalue_k(1)/norm)\n",
    "    E2.append(H.evalue_k(2)/norm)\n",
    "\n",
    "# define the minimum of E0 and set this to E=0\n",
    "floor = min(E0)\n",
    "\n",
    "plt.plot(x, E0 - floor, 'k', label=\"m=0\")\n",
    "plt.plot(x, E1 - floor, 'r', label=\"m=1\")\n",
    "plt.plot(x, E2 - floor, 'b', label=\"m=2\")\n",
    "plt.xlabel(\"ng\")\n",
    "plt.ylabel(\"Em/E01\")\n",
    "plt.legend(title=\"Energy Level:\", loc='upper right')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e81822d",
   "metadata": {},
   "source": [
    "## Wavefunction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "c4da0509",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Transmon frequencies\n",
      "\n",
      " ω01/2π =   5604 MHz\n",
      "   α/2π =     11 MHz\n",
      "\n"
     ]
    }
   ],
   "source": [
    "H = Hcpb(nlevels=3, Ej=13971.3, Ec=295.2, ng=0.001)\n",
    "print(f\"\"\"\n",
    "Transmon frequencies\n",
    "\n",
    " ω01/2π = {H.fij(0,1): 6.0f} MHz\n",
    "   α/2π = {H.anharm(): 6.0f} MHz\n",
    "\"\"\")"
   ]
  },
  {
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   "id": "6118e48e",
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   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "for k in range (3):\n",
    "    ψ, θ = H.psi_k(k,101)\n",
    "    plt.plot(θ, ψ.real+ψ.imag, label=f\"|{k}>\") # it's in either quadrature, but not both\n",
    "plt.xlabel(\"Junction phase θ (wrapped in the interval [-π, π])\")\n",
    "plt.ylabel(\"Re(ψ(θ))\")\n",
    "plt.legend(title=\"Level\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "81614b58",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-2.2354805729522635e-09+1.7634461200402775e-17j)\n"
     ]
    }
   ],
   "source": [
    "Psi0, theta0 = H.psi_k(0)\n",
    "Psi1, theta1 = H.psi_k(1)\n",
    "print(np.dot(Psi0,Psi1.conj()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "d86a4eaa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.9999999999999998+0j)\n",
      "(1+0j)\n"
     ]
    }
   ],
   "source": [
    "print(np.dot(Psi0, Psi0.conj()))\n",
    "print(np.dot(Psi1, Psi1.conj()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcb2e12a",
   "metadata": {},
   "source": [
    "## Decoherence time T2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "ecbf1e34",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(0,80,101)     # ratio of Ej/Ec, varying from 0 to 80\n",
    "T2 = []                       # empty list for T2"
   ]
  },
  {
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   "execution_count": 63,
   "id": "75bbbd5f",
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     "data": {
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       "Text(0, 0.5, 'T2 (sec)')"
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   "source": [
    "E_c = 1000.0\n",
    "for i in x:\n",
    "    H_half = Hcpb(nlevels=15, Ej=i*E_c, Ec=E_c, ng=0.5)\n",
    "    H_zero = Hcpb(nlevels=15, Ej=i*E_c, Ec=E_c, ng=0.0)\n",
    "    eps = abs(H_half.evalue_k(1) - H_zero.evalue_k(1))\n",
    "    T2.append(1.0/(2.0*(1E-4)*(1E6)*eps) )\n",
    "\n",
    "plt.plot(x, T2)\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"Ej/Ec\")\n",
    "plt.ylabel(\"T2 (sec)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3233d91e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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