{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# scqubits example: computing coherence properties\n",
"J. Koch and P. Groszkowski\n",
"\n",
"For further documentation of scqubits see https://scqubits.readthedocs.io/en/latest/.\n",
"\n",
"---"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2020-04-29T15:05:41.569377Z",
"start_time": "2020-04-29T15:05:41.535440Z"
},
"init_cell": true,
"scrolled": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"%config InlineBackend.figure_format = 'svg'\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import scqubits as scq"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Units.** To calculate coherence times, scqubits needs to know the frequency units used. The current (and default) units are:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'GHz'"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"scq.get_units()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Qubits and their noise channels\n",
"## Transmon / Cooper pair box (charge-regime parameters)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Transmon------------| [Transmon_1]\n",
" | EJ: 0.5\n",
" | EC: 12.0\n",
" | ng: 0.3\n",
" | ncut: 150\n",
" | truncated_dim: 6\n",
" |\n",
" | dim: 301\n",
"\n"
]
}
],
"source": [
"transmon = scq.Transmon(\n",
" EJ=0.5,\n",
" EC=12.0,\n",
" ng=0.3,\n",
" ncut=150\n",
")\n",
"print(transmon)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Computing and visualizing $T_1$ and $T_2$\n",
"\n",
"To list the noise channels supported by this qubit, call `supported_noise_channels()`:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"['tphi_1_over_f_cc',\n",
" 'tphi_1_over_f_ng',\n",
" 't1_capacitive',\n",
" 't1_charge_impedance']"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"transmon.supported_noise_channels()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Example: dephasing time due to 1/f charge noise.** We can calculate a given decoherence time with an appropriate method. Taking default parameters:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.770056749342735"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"transmon.tphi_1_over_f_ng()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since we are using default frequency units of GHz, the time units are 1/GHz = ns.\n",
"\n",
"Choices deviating from the default parameters are accesible via optional arguments: (eg., choose a downward transition from level 3 to 1, at T=0.100K):"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"UserWarning: By default all methods that involve calculations of the t1 coherence times/rates, return a sum of upward (i.e., excitation), and downward (i.e., relaxation) rates. To change this behavior, parameter total=False can be passed to any t1-related coherence methods. With total=False, only a one-directional transition between levels i and j is used to calculate the required t1 time or rate.\n",
"See documentation for details.\n",
"This warning can be disabled by executing:\n",
"scqubits.settings.T1_DEFAULT_WARNING=False\n",
"\n",
" /run/media/Data/Dropbox/Synced_Data/Northwestern/Research-Koch/Circuit-Hamiltonian/scqubits_branch/scqubits/scqubits/core/noise.py: 1200"
]
},
{
"data": {
"text/plain": [
"3013.2215669102766"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"transmon.t1_charge_impedance(i=3, j=1, T=0.100)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Depolarization.** scqubits can approximate the (cumulative) effective noise, calculated form the total contributions of a variety of noise channels (that can be fine-tuned by the user). In the case of depolarization noise, the effective (or combined) noise is obtained from \n",
"\n",
"\\begin{equation}\n",
"\\frac{1}{T_{1}^{\\rm eff}} = \\sum_k \\frac{1}{T_{1}^{k}},\n",
"\\end{equation}\n",
"\n",
"where the sum runs over all noise channels that the user wants included. By default, the set of noise channels correponds to the list returned by the `effective_noise_channels` method for each qubit. A different list of noise channels can be provided as an argument. \n",
"\n",
"**Dephasing.** Similarly, users can calculate effective dephasing times, which includes contributions from both pure dephasing, as well as depolarization channels. Such a $T_{2}$ time is defined as\n",
"\n",
"\\begin{equation}\n",
"\\frac{1}{T_{2}^{\\rm eff}} = \\sum_k \\frac{1}{T_{\\phi}^{k}} + \\frac{1}{2} \\sum_j \\frac{1}{T_{1}^{j}}, \n",
"\\end{equation}\n",
"\n",
"where $k$ ($j$) run over the relevant pure dephasing (depolariztion) channels that can contribute to the effective noise. \n",
"\n",
"**Example: effective $T_1$.** For the above transmon, we obtain"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2166838.6419612635"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"transmon.t1_effective()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is worth stressing that in tha case of tramson, by default, `t1_effective()` does not include all the channels that the qubit supports. This can be seen by comparing the output of "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"['tphi_1_over_f_cc',\n",
" 'tphi_1_over_f_ng',\n",
" 't1_capacitive',\n",
" 't1_charge_impedance']"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"transmon.supported_noise_channels()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"from"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"['tphi_1_over_f_cc', 'tphi_1_over_f_ng', 't1_capacitive']"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"transmon.effective_noise_channels()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"**Plotting $T_1$ vs. offset charge.** We can plot the dependence of $T_1$ on the offset charge:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "41bbea1962de4a2cb3ee294e45056e28",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Spectral data: 0%| | 0/100 [00:00, ?it/s]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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",
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"