diff --git a/development/QuTiP to compare transmon and QHO.ipynb b/development/QuTiP to compare transmon and QHO.ipynb new file mode 100644 index 0000000..4a56188 --- /dev/null +++ b/development/QuTiP to compare transmon and QHO.ipynb @@ -0,0 +1,230 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9ccc7ef7", + "metadata": {}, + "source": [ + "# Comparing the transmon and the Quantum Harmonic Oscillator \n", + "\n", + "#### It is known to us from theory that the Quantum Harmonic Oscillator has evenly spaced energy levels while that is not so in the case of a transmon. Some amount of anharmonicity is required for the two-level approximation of the qubit to remain valid. The transmon qubit has a design similar to the cooper pair box (But in the latter case, the qubits encoded as charge states are particularly sensitive to charge noise).\n", + "#### In this code, I attempt to show the difference in energy levels of the QHO and the transmon by calculating them from their hamiltonian using QuTip which is basically the standard Quantum Toolbox in Python .\n", + "\n", + "Date: 22-06-2021\n", + "\n", + "In this code, we predominantly make use of the Transmon Hamiltonian\n", + "$$\n", + "\\hat{H}_{\\rm tr} = 4E_c \\hat{n}^2 - E_J \\cos \\hat{\\phi},\n", + "$$\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "5b342e53", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "# Importing standard Qiskit libraries\n", + "from qiskit import QuantumCircuit, transpile, Aer, IBMQ\n", + "from qiskit.tools.jupyter import *\n", + "from qiskit.visualization import *\n", + "from ibm_quantum_widgets import *\n", + "\n", + "# Loading your IBM Quantum account(s)\n", + "provider = IBMQ.load_account()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "e7e33e1b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Collecting qutip\n", + " Downloading qutip-4.6.2-cp38-cp38-manylinux2010_x86_64.whl (16.0 MB)\n", + "\u001b[K |████████████████████████████████| 16.0 MB 61 kB/s s eta 0:00:01 | 2.3 MB 11.0 MB/s eta 0:00:02\n", + "\u001b[?25hRequirement already satisfied: scipy>=1.0 in /opt/conda/lib/python3.8/site-packages (from qutip) (1.6.1)\n", + "Requirement already satisfied: numpy>=1.16.6 in /opt/conda/lib/python3.8/site-packages (from qutip) (1.20.1)\n", + "Requirement already satisfied: packaging in /opt/conda/lib/python3.8/site-packages (from qutip) (20.9)\n", + "Requirement already satisfied: pyparsing>=2.0.2 in /opt/conda/lib/python3.8/site-packages (from packaging->qutip) (2.4.7)\n", + "Installing collected packages: qutip\n", + "Successfully installed qutip-4.6.2\n", + "Note: you may need to restart the kernel to use updated packages.\n" + ] + } + ], + "source": [ + "pip install qutip" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "01d7b99b", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "#E_J denotes the Josephson energy, w denotes Omega which is (8*EcEj)^1/2 - Ec where -Ec refers to the anharmoncity or Delta\n", + "\n", + "E_J = 20e9\n", + "w = 5e9\n", + "Delta = -300e6\n", + "\n", + "N_phis = 101\n", + "phis = np.linspace(-np.pi,np.pi,N_phis)\n", + "mid_idx = int((N_phis+1)/2)\n", + "\n", + "# PE_QHO is denotes the potential energy of the Quantum Harmonic Oscillator \n", + "#PE_transmon denotes the Potential Energy of the transmon\n", + "#We apply the standard formulae to obtain these values\n", + "PE_QHO = 0.5*E_J*phis**2\n", + "PE_QHO = PE_QHO/w\n", + "PE_transmon = (E_J-E_J*np.cos(phis))\n", + "PE_transmon = PE_transmon/w" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "f6433478", + "metadata": {}, + "outputs": [], + "source": [ + "#We now import Qutip\n", + "import qutip\n", + "from qutip import destroy\n", + "\n", + "#Now constructing the Hamiltonian and then solving for the energies\n", + "N = 35\n", + "N_energies = 5\n", + "c = destroy(N)\n", + "H_QHO = w*c.dag()*c\n", + "E_QHO = H_QHO.eigenenergies()[0:N_energies]\n", + "H_transmon = w*c.dag()*c + (Delta/2)*(c.dag()*c)*(c.dag()*c - 1)\n", + "E_transmon = H_transmon.eigenenergies()[0:2*N_energies]" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "c2d4d2e8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.0e+00 5.0e+09 1.0e+10 1.5e+10 2.0e+10]\n", + "[0.00e+00 1.70e+09 5.00e+09 6.60e+09 9.70e+09 1.12e+10 1.41e+10 1.55e+10\n", + " 1.82e+10 1.95e+10]\n" + ] + } + ], + "source": [ + "# We now print the energy levels\n", + "print(E_QHO)\n", + "print(E_transmon)" + ] + }, + { + "cell_type": "markdown", + "id": "5b7912f6", + "metadata": {}, + "source": [ + "### As can be seen from the above generated energy level results, the values in the array E_QHO are evenly spaced, i.e they differ by 0.5e+10 units of energy , while in the case of the E_transmon, there seems to be an innate anharmonicity. \n" + ] + }, + { + "cell_type": "markdown", + "id": "40bbbcd8", + "metadata": {}, + "source": [ + "### We can now plot the graph between energy levels and phase using the inbuilt plotting tools in Qubit and Matplotlib" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "d32ad11a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(1, 1, figsize=(6,6))\n", + "\n", + "axes.plot(phis, PE_transmon, '-', color='orange', linewidth=3.0)\n", + "axes.plot(phis, PE_QHO, '--', color='blue', linewidth=3.0)\n", + "\n", + "for eidx in range(1,N_energies):\n", + " delta_E_QHO = (E_QHO[eidx]-E_QHO[0])/w\n", + " delta_E_transmon = (E_transmon[2*eidx]-E_transmon[0])/w\n", + " QHO_lim_idx = min(np.where(PE_QHO[int((N_phis+1)/2):N_phis] > delta_E_QHO)[0])\n", + " trans_lim_idx = min(np.where(PE_transmon[int((N_phis+1)/2):N_phis] > delta_E_transmon)[0])\n", + " trans_label, = axes.plot([phis[mid_idx-trans_lim_idx-1], phis[mid_idx+trans_lim_idx-1]], \\\n", + " [delta_E_transmon, delta_E_transmon], '-', color='orange', linewidth=3.0)\n", + " qho_label, = axes.plot([phis[mid_idx-QHO_lim_idx-1], phis[mid_idx+QHO_lim_idx-1]], \\\n", + " [delta_E_QHO, delta_E_QHO], '--', color='blue', linewidth=3.0)\n", + " \n", + "axes.set_xlabel('Phase $\\phi$', fontsize=24)\n", + "axes.set_ylabel('Energy Levels / $\\hbar\\omega$', fontsize=24)\n", + "axes.set_ylim(-0.2,8)\n", + "\n", + "qho_label.set_label('QHO Energies')\n", + "trans_label.set_label('Transmon Energies')\n", + "axes.legend(loc=2, fontsize=14)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/QuTiP to compare transmon and QHO.ipynb b/examples/QuTiP to compare transmon and QHO.ipynb new file mode 100644 index 0000000..4a56188 --- /dev/null +++ b/examples/QuTiP to compare transmon and QHO.ipynb @@ -0,0 +1,230 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9ccc7ef7", + "metadata": {}, + "source": [ + "# Comparing the transmon and the Quantum Harmonic Oscillator \n", + "\n", + "#### It is known to us from theory that the Quantum Harmonic Oscillator has evenly spaced energy levels while that is not so in the case of a transmon. Some amount of anharmonicity is required for the two-level approximation of the qubit to remain valid. The transmon qubit has a design similar to the cooper pair box (But in the latter case, the qubits encoded as charge states are particularly sensitive to charge noise).\n", + "#### In this code, I attempt to show the difference in energy levels of the QHO and the transmon by calculating them from their hamiltonian using QuTip which is basically the standard Quantum Toolbox in Python .\n", + "\n", + "Date: 22-06-2021\n", + "\n", + "In this code, we predominantly make use of the Transmon Hamiltonian\n", + "$$\n", + "\\hat{H}_{\\rm tr} = 4E_c \\hat{n}^2 - E_J \\cos \\hat{\\phi},\n", + "$$\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "5b342e53", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "# Importing standard Qiskit libraries\n", + "from qiskit import QuantumCircuit, transpile, Aer, IBMQ\n", + "from qiskit.tools.jupyter import *\n", + "from qiskit.visualization import *\n", + "from ibm_quantum_widgets import *\n", + "\n", + "# Loading your IBM Quantum account(s)\n", + "provider = IBMQ.load_account()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "e7e33e1b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Collecting qutip\n", + " Downloading qutip-4.6.2-cp38-cp38-manylinux2010_x86_64.whl (16.0 MB)\n", + "\u001b[K |████████████████████████████████| 16.0 MB 61 kB/s s eta 0:00:01 | 2.3 MB 11.0 MB/s eta 0:00:02\n", + "\u001b[?25hRequirement already satisfied: scipy>=1.0 in /opt/conda/lib/python3.8/site-packages (from qutip) (1.6.1)\n", + "Requirement already satisfied: numpy>=1.16.6 in /opt/conda/lib/python3.8/site-packages (from qutip) (1.20.1)\n", + "Requirement already satisfied: packaging in /opt/conda/lib/python3.8/site-packages (from qutip) (20.9)\n", + "Requirement already satisfied: pyparsing>=2.0.2 in /opt/conda/lib/python3.8/site-packages (from packaging->qutip) (2.4.7)\n", + "Installing collected packages: qutip\n", + "Successfully installed qutip-4.6.2\n", + "Note: you may need to restart the kernel to use updated packages.\n" + ] + } + ], + "source": [ + "pip install qutip" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "01d7b99b", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "#E_J denotes the Josephson energy, w denotes Omega which is (8*EcEj)^1/2 - Ec where -Ec refers to the anharmoncity or Delta\n", + "\n", + "E_J = 20e9\n", + "w = 5e9\n", + "Delta = -300e6\n", + "\n", + "N_phis = 101\n", + "phis = np.linspace(-np.pi,np.pi,N_phis)\n", + "mid_idx = int((N_phis+1)/2)\n", + "\n", + "# PE_QHO is denotes the potential energy of the Quantum Harmonic Oscillator \n", + "#PE_transmon denotes the Potential Energy of the transmon\n", + "#We apply the standard formulae to obtain these values\n", + "PE_QHO = 0.5*E_J*phis**2\n", + "PE_QHO = PE_QHO/w\n", + "PE_transmon = (E_J-E_J*np.cos(phis))\n", + "PE_transmon = PE_transmon/w" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "f6433478", + "metadata": {}, + "outputs": [], + "source": [ + "#We now import Qutip\n", + "import qutip\n", + "from qutip import destroy\n", + "\n", + "#Now constructing the Hamiltonian and then solving for the energies\n", + "N = 35\n", + "N_energies = 5\n", + "c = destroy(N)\n", + "H_QHO = w*c.dag()*c\n", + "E_QHO = H_QHO.eigenenergies()[0:N_energies]\n", + "H_transmon = w*c.dag()*c + (Delta/2)*(c.dag()*c)*(c.dag()*c - 1)\n", + "E_transmon = H_transmon.eigenenergies()[0:2*N_energies]" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "c2d4d2e8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.0e+00 5.0e+09 1.0e+10 1.5e+10 2.0e+10]\n", + "[0.00e+00 1.70e+09 5.00e+09 6.60e+09 9.70e+09 1.12e+10 1.41e+10 1.55e+10\n", + " 1.82e+10 1.95e+10]\n" + ] + } + ], + "source": [ + "# We now print the energy levels\n", + "print(E_QHO)\n", + "print(E_transmon)" + ] + }, + { + "cell_type": "markdown", + "id": "5b7912f6", + "metadata": {}, + "source": [ + "### As can be seen from the above generated energy level results, the values in the array E_QHO are evenly spaced, i.e they differ by 0.5e+10 units of energy , while in the case of the E_transmon, there seems to be an innate anharmonicity. \n" + ] + }, + { + "cell_type": "markdown", + "id": "40bbbcd8", + "metadata": {}, + "source": [ + "### We can now plot the graph between energy levels and phase using the inbuilt plotting tools in Qubit and Matplotlib" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "d32ad11a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(1, 1, figsize=(6,6))\n", + "\n", + "axes.plot(phis, PE_transmon, '-', color='orange', linewidth=3.0)\n", + "axes.plot(phis, PE_QHO, '--', color='blue', linewidth=3.0)\n", + "\n", + "for eidx in range(1,N_energies):\n", + " delta_E_QHO = (E_QHO[eidx]-E_QHO[0])/w\n", + " delta_E_transmon = (E_transmon[2*eidx]-E_transmon[0])/w\n", + " QHO_lim_idx = min(np.where(PE_QHO[int((N_phis+1)/2):N_phis] > delta_E_QHO)[0])\n", + " trans_lim_idx = min(np.where(PE_transmon[int((N_phis+1)/2):N_phis] > delta_E_transmon)[0])\n", + " trans_label, = axes.plot([phis[mid_idx-trans_lim_idx-1], phis[mid_idx+trans_lim_idx-1]], \\\n", + " [delta_E_transmon, delta_E_transmon], '-', color='orange', linewidth=3.0)\n", + " qho_label, = axes.plot([phis[mid_idx-QHO_lim_idx-1], phis[mid_idx+QHO_lim_idx-1]], \\\n", + " [delta_E_QHO, delta_E_QHO], '--', color='blue', linewidth=3.0)\n", + " \n", + "axes.set_xlabel('Phase $\\phi$', fontsize=24)\n", + "axes.set_ylabel('Energy Levels / $\\hbar\\omega$', fontsize=24)\n", + "axes.set_ylim(-0.2,8)\n", + "\n", + "qho_label.set_label('QHO Energies')\n", + "trans_label.set_label('Transmon Energies')\n", + "axes.legend(loc=2, fontsize=14)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}