In [ ]:
!pip install ipyvuetify
Collecting ipyvuetify
Downloading ipyvuetify-1.8.10-py2.py3-none-any.whl (11.7 MB)
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Collecting ipyvue<2,>=1.7 (from ipyvuetify)
Downloading ipyvue-1.10.1-py2.py3-none-any.whl (2.7 MB)
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Requirement already satisfied: ipywidgets>=7.0.0 in /usr/local/lib/python3.10/dist-packages (from ipyvue<2,>=1.7->ipyvuetify) (7.7.1)
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Requirement already satisfied: ipython-genutils~=0.2.0 in /usr/local/lib/python3.10/dist-packages (from ipywidgets>=7.0.0->ipyvue<2,>=1.7->ipyvuetify) (0.2.0)
Requirement already satisfied: traitlets>=4.3.1 in /usr/local/lib/python3.10/dist-packages (from ipywidgets>=7.0.0->ipyvue<2,>=1.7->ipyvuetify) (5.7.1)
Requirement already satisfied: widgetsnbextension~=3.6.0 in /usr/local/lib/python3.10/dist-packages (from ipywidgets>=7.0.0->ipyvue<2,>=1.7->ipyvuetify) (3.6.6)
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Requirement already satisfied: tornado>=4.2 in /usr/local/lib/python3.10/dist-packages (from ipykernel>=4.5.1->ipywidgets>=7.0.0->ipyvue<2,>=1.7->ipyvuetify) (6.3.2)
Requirement already satisfied: setuptools>=18.5 in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets>=7.0.0->ipyvue<2,>=1.7->ipyvuetify) (67.7.2)
Collecting jedi>=0.16 (from ipython>=4.0.0->ipywidgets>=7.0.0->ipyvue<2,>=1.7->ipyvuetify)
Downloading jedi-0.19.1-py2.py3-none-any.whl (1.6 MB)
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Requirement already satisfied: decorator in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets>=7.0.0->ipyvue<2,>=1.7->ipyvuetify) (4.4.2)
Requirement already satisfied: pickleshare in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets>=7.0.0->ipyvue<2,>=1.7->ipyvuetify) (0.7.5)
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Installing collected packages: jedi, ipyvue, ipyvuetify
Successfully installed ipyvue-1.10.1 ipyvuetify-1.8.10 jedi-0.19.1
In [ ]:
!pip install ipywidgets
Requirement already satisfied: ipywidgets in /usr/local/lib/python3.10/dist-packages (7.7.1) Requirement already satisfied: ipykernel>=4.5.1 in /usr/local/lib/python3.10/dist-packages (from ipywidgets) (5.5.6) Requirement already satisfied: ipython-genutils~=0.2.0 in /usr/local/lib/python3.10/dist-packages (from ipywidgets) (0.2.0) Requirement already satisfied: traitlets>=4.3.1 in /usr/local/lib/python3.10/dist-packages (from ipywidgets) (5.7.1) Requirement already satisfied: widgetsnbextension~=3.6.0 in /usr/local/lib/python3.10/dist-packages (from ipywidgets) (3.6.6) Requirement already satisfied: ipython>=4.0.0 in /usr/local/lib/python3.10/dist-packages (from ipywidgets) (7.34.0) Requirement already satisfied: jupyterlab-widgets>=1.0.0 in /usr/local/lib/python3.10/dist-packages (from ipywidgets) (3.0.9) Requirement already satisfied: jupyter-client in /usr/local/lib/python3.10/dist-packages (from ipykernel>=4.5.1->ipywidgets) (6.1.12) Requirement already satisfied: tornado>=4.2 in /usr/local/lib/python3.10/dist-packages (from ipykernel>=4.5.1->ipywidgets) (6.3.2) Requirement already satisfied: setuptools>=18.5 in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets) (67.7.2) Requirement already satisfied: jedi>=0.16 in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets) (0.19.1) Requirement already satisfied: decorator in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets) (4.4.2) Requirement already satisfied: pickleshare in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets) (0.7.5) Requirement already satisfied: prompt-toolkit!=3.0.0,!=3.0.1,<3.1.0,>=2.0.0 in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets) (3.0.43) Requirement already satisfied: pygments in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets) (2.16.1) Requirement already satisfied: backcall in /usr/local/lib/python3.10/dist-packages (from 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In [ ]:
!pip install scqubits
Collecting scqubits
Downloading scqubits-3.3.0-py3-none-any.whl (6.5 MB)
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Installing collected packages: cython, qutip, scqubits
Attempting uninstall: cython
Found existing installation: Cython 3.0.7
Uninstalling Cython-3.0.7:
Successfully uninstalled Cython-3.0.7
Successfully installed cython-0.29.37 qutip-4.7.3 scqubits-3.3.0
scqubits example: the fluxonium qubit¶
J. Koch and P. Groszkowski
For further documentation of scqubits see https://scqubits.readthedocs.io/en/latest/.
In [ ]:
import numpy as np
import scqubits as scq
Fluxonium qubit¶
$H_\text{fl}=-4E_\text{C}\partial_\phi^2-E_\text{J}\cos(\phi-\varphi_\text{ext}) +\frac{1}{2}E_L\phi^2$
Creation via GUI (ipywidgets needs to be installed for this to work.)
In [ ]:
fluxonium = scq.Fluxonium.create()
Warning: Starting with v3.2, scqubits uses the optional package 'ipyuetify' for graphical user interfaces. To use this functionality, add the package via `conda install -c conda-forge ipyvuetify` or `pip install ipyvuetify`. For use with jupyter lab, additionally execute `jupyter labextension install jupyter-vuetify`. /usr/local/lib/python3.10/dist-packages/scqubits/utils/misc.py: 145
In [ ]:
print(fluxonium)
Fluxonium-----------| [Fluxonium_4]
| EJ: 8.9
| EC: 2.5
| EL: 0.5
| flux: 0.0
| cutoff: 110
| truncated_dim: 10
|
| dim: 110
Programmatic creation
In [ ]:
fluxonium2 = scq.Fluxonium(
EJ=8.9,
EC=2.5,
EL=0.5,
cutoff = 110,
flux = 0.5
)
Computing and visualizing spectra¶
In [ ]:
fluxonium.eigenvals()
Out[ ]:
array([-2.7022458 , 6.05619946, 6.27730681, 8.29978855, 14.23074422,
16.86961382])
In [ ]:
flux_list = np.linspace(-0.5, 0.5, 151)
fluxonium.plot_evals_vs_paramvals('flux', flux_list, evals_count=8);
In [ ]:
fluxonium.cos_phi_operator()
Out[ ]:
array([[ 2.05740661e-01, 0.00000000e+00, -4.60050104e-01, ...,
0.00000000e+00, 1.78616165e-61, 0.00000000e+00],
[ 0.00000000e+00, -4.44868435e-01, 0.00000000e+00, ...,
-6.10025949e-59, 0.00000000e+00, 1.86480751e-60],
[-4.60050104e-01, 0.00000000e+00, -6.67742262e-02, ...,
0.00000000e+00, -4.34635215e-58, 0.00000000e+00],
...,
[ 0.00000000e+00, -6.10025949e-59, 0.00000000e+00, ...,
-9.18367880e-02, 0.00000000e+00, -3.20968756e-02],
[ 1.78616165e-61, 0.00000000e+00, -4.34635215e-58, ...,
0.00000000e+00, -4.30134088e-02, 0.00000000e+00],
[ 0.00000000e+00, 1.86480751e-60, 0.00000000e+00, ...,
-3.20968756e-02, 0.00000000e+00, -1.10641059e-02]])
In [ ]:
fluxonium.plot_evals_vs_paramvals('flux', flux_list, evals_count=9, subtract_ground=True);
In [ ]:
fluxonium.flux = 0.5
fluxonium.plot_wavefunction(esys=None, which=range(5), mode='real');
In [ ]:
fluxonium = scq.Fluxonium(
EJ=5.7,
EC=1.2,
EL=1.0,
cutoff = 150,
flux = 0.5
)
fig, axes=fluxonium.plot_wavefunction(esys=None, which=[0,1,2,3,4,5], mode='real');
Matrix elements¶
In [ ]:
phimat = fluxonium.matrixelement_table('phi_operator', evals_count=10)
print(phimat)
[[-2.34134190e-14 -2.42020774e+00 6.45548989e-15 5.96669304e-01 1.92424514e-15 -1.26034410e-02 7.31749126e-16 1.05152531e-02 -4.45241993e-16 -2.08796925e-03] [-2.42020774e+00 2.39071672e-14 1.16100233e+00 -2.78726136e-15 1.98939356e-01 -1.31717780e-15 1.96392027e-02 -6.44908705e-16 -1.88229452e-03 -1.79144226e-15] [ 6.45548989e-15 1.16100233e+00 -4.64160953e-16 -2.02810531e+00 -1.38397953e-15 2.87499531e-01 -6.94237581e-18 -3.19256763e-02 -2.51655509e-16 1.96457721e-04] [ 5.96669304e-01 -2.78726136e-15 -2.02810531e+00 2.98985200e-15 -2.11221368e+00 -1.09868917e-15 1.78076985e-01 -2.70727653e-15 4.52028150e-02 -7.46241842e-15] [ 1.92424514e-15 1.98939356e-01 -1.38397953e-15 -2.11221368e+00 -1.59508169e-15 2.41344721e+00 1.39647373e-15 1.41490331e-01 8.98123343e-17 -5.74957935e-02] [-1.26034410e-02 -1.31717780e-15 2.87499531e-01 -1.09868917e-15 2.41344721e+00 2.94739514e-15 -2.65902027e+00 1.68514874e-15 7.06894388e-02 -5.43778276e-15] [ 7.31749126e-16 1.96392027e-02 -6.94237581e-18 1.78076985e-01 1.39647373e-15 -2.65902027e+00 -4.35788601e-15 -2.95543793e+00 -2.55361461e-15 2.89606649e-02] [ 1.05152531e-02 -6.44908705e-16 -3.19256763e-02 -2.70727653e-15 1.41490331e-01 1.68514874e-15 -2.95543793e+00 -3.50883754e-15 3.32236039e+00 -1.95241273e-14] [-4.45241993e-16 -1.88229452e-03 -2.51655509e-16 4.52028150e-02 8.98123343e-17 7.06894388e-02 -2.55361461e-15 3.32236039e+00 4.31002167e-14 3.82811850e+00] [-2.08796925e-03 -1.79144226e-15 1.96457721e-04 -7.46241842e-15 -5.74957935e-02 -5.43778276e-15 2.89606649e-02 -1.95241273e-14 3.82811850e+00 1.29539701e-14]]
In [ ]:
fluxonium.plot_matrixelements('n_operator', evals_count=16);
In [ ]:
fluxonium.plot_matelem_vs_paramvals('n_operator', 'flux', flux_list, select_elems=5);
