{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Fluxonium"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Introduction"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this notebook, we calculate Fluxonium qubit properties such as energy spectrum, eigenfunctions, and decoherence rates for different loss channels."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Circuit Description"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The following Fluxonium qubit consists of an inductor with $E_L=0.46~\\text{GHz}$ and Josephson Junction with $E_J=10.2~\\text{GHz}$. The capacitor with $E_{C_J}=3.6~\\text{GHz}$ is assigned to Josephson Junction rather than the inductor. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Firstly, we import the SQcircuit and the relavant libraries"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import SQcircuit as sq\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We define the single inductive loop of the circuit via `Loop` class"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"loop1 = sq.Loop()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The elements of the circuit can be defined via `Capacitor`, `Inductor`, and `Junction` classes in SQcircuit, and to define the circuit, we use the `Circuit` class. "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# define the circuit elements\n",
"C = sq.Capacitor(3.6, 'GHz',Q=1e6 ,error=10)\n",
"L = sq.Inductor(0.46,'GHz',Q=500e6 ,loops=[loop1])\n",
"JJ = sq.Junction(10.2,'GHz',cap =C , A=1e-7, x=3e-06, loops=[loop1])\n",
"\n",
"# define the circuit\n",
"elements = {\n",
" (0, 1): [L, JJ]\n",
"}\n",
"\n",
"cr = sq.Circuit(elements, flux_dist='all')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"By creating an object of `Circuit` class, SQcircuit systematically finds the correct set of transformations and basis to make the circuit ready to be diagonalized.\n",
"\n",
"Before setting the truncation numbers for each mode and diagonalizing the Hamiltonian, we can gain more insight into our circuit by calling the `description()` method. This prints out the Hamiltonian and a listing of the modes, whether they are harmonic or charge modes, and the frequency for each harmonic in GHz (the default unit)."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\hat{H} =~\\omega_1\\hat a^\\dagger_1\\hat a_1~~+~E_{L_{1}}(\\hat{\\varphi}_1)(\\varphi_{\\text{ext}_{1}})~-~E_{J_{1}}\\cos(\\hat{\\varphi}_1)$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$------------------------------------------------------------$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\text{mode}~1:~~~~~~~~~~~\\text{harmonic}~~~~~~~~~~~\\hat{\\varphi}_1~=~\\varphi_{zp_{1}}(\\hat a_1+\\hat a^\\dagger_1)~~~~~~~~~~~\\omega_1/2\\pi~=~3.63978~~~~~~~~~~~\\varphi_{zp_{1}}~=~1.99e+00$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$------------------------------------------------------------$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\text{parameters}:~~~~~~~~~~~E_{L_{1}}~=~0.46~~~~~~~~~~~E_{J_{1}}~=~10.2~~~~~~~~~~~$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\text{loops}:~~~~~~~~~~~~~~~~~~~~\\varphi_{\\text{ext}_{1}}/2\\pi~=~0.0~~~~~~~~~~~$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cr.description()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We determinte the size of the Hilbert space and truncation number for the only mode of the circuit."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"cr.set_trunc_nums([60])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To generate the spectrum and decoherence rates of the circuit, firstly, we need to change and sweep the external flux of `loop1` by the `set_flux()` method. Then, we need to find the eigenfrequencies and decherence rates of the circuit that correspond to that external flux via `diag()` and `dec_rate()` method. In the following lines of code the `spec` is a 2D NumPy array that each column of it contains the eigenfrequencies with respect to its external flux. The `decays` is a Python dictionary that contains the decoherence rates for each type of loss channel."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"n_eig = 5\n",
"\n",
"phiExt = np.linspace(0, 1, 500)\n",
"\n",
"decays = {'capacitive':np.zeros_like(phiExt),\n",
" 'inductive':np.zeros_like(phiExt),\n",
" 'cc':np.zeros_like(phiExt),\n",
" 'quasiparticle':np.zeros_like(phiExt)}\n",
"\n",
"spec = np.zeros((n_eig, len(phiExt)))\n",
"\n",
"for i, phi in enumerate(phiExt):\n",
" loop1.set_flux(phi)\n",
" spec[:, i], _ = cr.diag(n_eig)\n",
" for dec_type in decays:\n",
" decays[dec_type][i]=cr.dec_rate(dec_type=dec_type, states=(1,0))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Circuit Spectrum"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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