TunableTransmon#
The flux-tunable transmon qubit [Koch2007] is a simple modification of the fixed-frequency transmon obtained. It is obtained by replacing the Josephson junction by a SQUID loop of two Josephson junctions. A flux threaded through this loop can then be used to change the effective Josephson energy of the circuit and thus make the transmon tunable.
expressed in the charge basis. Here, the parameters are those of the fixed-frequency transmon except for the effective Josephson energy \(E_\text{J,eff}(\Phi_\text{ext}) = E_{\text{J,max}} \sqrt{\cos^2(\pi\Phi_\text{ext}/\Phi_0)+ d^2 \sin^2 (\pi\Phi_\text{ext}/\Phi_0)}\), where \(E_\text{J,max} = E_\text{J1} + E_\text{J2}\) is the maximum Josephson energy, and \(d=(E_\text{J1}-E_\text{J2})/(E_\text{J1}+E_\text{J2})\) is the relative junction asymmetry.
An instance of a tunable transmon qubit is created like this:
tune_tmon = scqubits.TunableTransmon(
EJmax=50.0,
EC=0.5,
d=0.01,
flux=0.0,
ng=0.0,
ncut=30
)
From within Jupyter notebook, a GUI-based creation is supported via:
tune_tmon = scqubits.TunableTransmon.create()
This functionality is enabled if the ipywidgets
package is installed, and displays GUI forms prompting for
the entry of the required parameters.
Wavefunctions and visualization of eigenstates#
Return the transmon wave function in number basis. |
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Return the transmon wave function in phase basis. |
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Plots transmon wave function in charge basis |
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Alias for plot_wavefunction |
Implemented operators#
The following operators are implemented for use in matrix element calculations.
Returns charge operator n in the charge or eigenenergy basis. |
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Returns operator \(e^{i\varphi}\) in the charge or eigenenergy basis. |
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Returns operator \(\cos \varphi\) in the charge or eigenenergy basis. |
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Returns operator \(\sin \varphi\) in the charge or eigenenergy basis. |
Computation and visualization of matrix elements#
Returns table of matrix elements for operator with respect to the eigenstates of the qubit. |
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Plots matrix elements for operator, given as a string referring to a class method that returns an operator matrix. |
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Calculates matrix elements for a varying system parameter, given an array of parameter values. |
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Generates a simple plot of a set of eigenvalues as a function of one parameter. |
Estimation of coherence times#
Show plots of coherence for various channels supported by the qubit as they vary as a function of a changing parameter. |
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Plot effective \(T_1\) coherence time (rate) as a function of changing parameter. |
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Plot effective \(T_2\) coherence time (rate) as a function of changing parameter. |
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Calculate the transition time (or rate) using Fermi's Golden Rule due to a noise channel with a spectral density spectral_density and system noise operator noise_op. |
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\(T_1\) due to dielectric dissipation in the Josephson junction capacitances. |
Noise due to charge coupling to an impedance (such as a transmission line). |
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Calculate the effective \(T_1\) time (or rate). |
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Noise due to a bias flux line. |
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Calculate the effective \(T_2\) time (or rate). |
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Calculate the 1/f dephasing time (or rate) due to arbitrary noise source. |
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Calculate the 1/f dephasing time (or rate) due to critical current noise. |
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Calculate the 1/f dephasing time (or rate) due to flux noise. |