{ "cells": [ { "cell_type": "markdown", "id": "580116e2", "metadata": {}, "source": [ "## Fluxonium qubit coupled to a resonator\n", "\n", "In many superconducting quantum circuits, external magnetic fluxes play a crucial role in determining the system dynamics. In particular, flux-tunable devices such as the fluxonium qubit explicitly rely on an externally applied magnetic flux to control their Hamiltonian and energy spectrum.\n", "\n", "Classical electromagnetic simulators, such as Ansys HFSS, are extremely powerful tools for extracting circuit parameters (e.g., capacitances and inductances) from a given layout. However, they are not designed to incorporate external flux degrees of freedom directly into the quantum Hamiltonian. As a result, they cannot capture flux-dependent phenomena, which are essential for the accurate modeling of many superconducting circuits.\n", "\n", "One of the key features of QuLTRA is the ability to include external magnetic fluxes directly in the circuit description and propagate their effect through the quantization procedure. This allows for the simulation of flux-dependent Hamiltonians and observables.\n", "\n", "In this tutorial, we demonstrate how to include external flux in a simulation by considering a fluxonium qubit capacitively coupled to a $\\lambda/4$ resonator. This system represents a standard building block in circuit QED and provides a clear example of how external flux modifies the spectrum of the device.\n", "\n", "In this tutorial, we compute the linear modes of the circuit, which do not depend on the external flux. We then study how the dispersive shift $\\chi$ varies as a function of the external flux.\n", "\n", "To do this, we compute the eigenvalues and eigenvectors of the Hamiltonian and identify the eigenstates corresponding to $|g0\\rangle$, $|g1\\rangle$, $|e0\\rangle$, and $|e1\\rangle$, where $g$ and $e$ denote the qubit states (approximated as a two-level system), and $0,1,\\dots$ denote the excitation level of the resonator.\n", "\n", "This identification is performed constructively. Starting from the ground state, we apply the resonator creation operator in order to generate states of the form $|gn\\rangle$.\n", "\n", "Similarly, starting from the state $|e0\\rangle$, which, under the assumption that the qubit frequency is lower than the resonator frequency, corresponds to the first excited state above the ground state, we apply the resonator creation operator to generate states of the form $|en\\rangle$." ] }, { "cell_type": "code", "execution_count": 4, "id": "6b42732a", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import qultra as qu\n", "import qutip as qp\n", "\n", "c=299792458 #m/s\n", "e = 1.60217657e-19 # electron charge\n", "h = 6.62606957e-34 # Plank's\n", "hbar=h/2/np.pi\n", "Phi0=h/(2*e)" ] }, { "cell_type": "code", "execution_count": 2, "id": "73c62c13", "metadata": {}, "outputs": [], "source": [ "#fluxoium parameters\n", "Ec=0.943 #GHz\n", "Ej=4.028 #GHz\n", "El=0.775 #GHz\n", "\n", "C=e**2/2/(Ec*1e9)/h\n", "L=(Phi0/(2*np.pi))**2/(El*1e9)/h\n", "J=(Phi0/(2*np.pi))**2/(Ej*1e9)/h\n", "\n", "\n", "l=4.5e-3 #resonator length in m\n", "\n", "Cg=3e-15 #capacitance between resonator and qubit in F\n", "\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "5b36e262", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[5.614417429783949, 6.544733180860585]\n" ] } ], "source": [ "#construct the circuit with qultra\n", "\n", "net=[qu.C(0,1,C),qu.L(0,1,L),qu.J(0,1,J),qu.C(1,2,Cg),qu.CPW(2,0,l)]\n", "\n", "flux_res=qu.QCircuit(net,5,7)\n", "print(flux_res.mode_frequencies())\n" ] }, { "cell_type": "markdown", "id": "83218746", "metadata": {}, "source": [ "To include external fluxes in the circuit description, one simply assigns the desired external flux value to Josephson junctions and inductors via the phi_ext attribute." ] }, { "cell_type": "code", "execution_count": null, "id": "e19a79a0", "metadata": {}, "outputs": [], "source": [ "\n", "phi_ext = np.linspace(0, 2*np.pi, 100)\n", "chi_vec=[]\n", "\n", "for phi in phi_ext:\n", " net[2].phi_ext=phi #apply external flux to the junction\n", " H=flux_res.hamiltonian(excitations=[25,25],taylor=False)\n", " eval,vec=H.eigenstates()\n", "\n", "\n", " eigenval=(eval-eval[0])/1e9\n", "\n", " ground=vec[0] #|g0>\n", " qubit=vec[1] #|e0>\n", " a_res=qp.tensor(qp.qeye(25),qp.destroy(25))\n", "\n", " ext=a_res.dag()*ground\n", " ext_q=a_res.dag()*qubit\n", "\n", " overlaps = [abs(ext.overlap(ev))**2 for ev in vec]\n", " overlaps_q=[abs(ext_q.overlap(ev))**2 for ev in vec]\n", " idx_01 = np.argmax(overlaps) #|g1>\n", " idx_11 = np.argmax(overlaps_q) #|e1>\n", " idx_00=0 #|g0>\n", " idx_10=1 #|e0>\n", "\n", " chi_1=eigenval[idx_11]-eigenval[idx_10] #|e1>-|e0>\n", " chi_0=eigenval[idx_01]-eigenval[idx_00] #|g1>-|g0>\n", "\n", " chi=chi_1-chi_0 #dispersive shift\n", " chi_vec.append(chi*1e3) #convert to MHz" ] }, { "cell_type": "code", "execution_count": 6, "id": "5e242c6e", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\simyz\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.11_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python311\\site-packages\\matplotlib\\cbook.py:1719: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return math.isfinite(val)\n", "C:\\Users\\simyz\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.11_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python311\\site-packages\\matplotlib\\cbook.py:1355: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return np.asarray(x, float)\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "plt.plot(phi_ext, chi_vec)\n", "plt.xlabel('External Flux (rad)', fontsize='16')\n", "plt.ylabel('Dispersive Shift (MHz)',fontsize='16')\n", "plt.title('Dispersive Shift vs External Flux for Fluxonium Qubit')\n", "plt.xticks(fontsize=14)\n", "plt.yticks(fontsize=14)\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "571eb808", "metadata": {}, "outputs": [], "source": [] } ], "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": "3.11.9" } }, "nbformat": 4, "nbformat_minor": 5 }