Calculating loss rates¶

Qcircuit.
loss_rates
(**kwargs)[source]¶ Returns the loss rates of the circuit normal modes.
The array is ordered ordered with increasing normal mode frequencies such that the first element of the array corresponds to the loss rate of the lowest frequency mode. Losses are provided in units of Hertz, not in angular frequency.
 Parameters
kwargs – Values for unspecified circuit components, ex:
L=1e9
. Returns
Normal mode losses of the circuit
 Return type
numpy.array
Notes
These loss rates \(\kappa_m\) correspond to twice the imaginary parts of the complex frequencies which make the conductance matrix singular, or equivalently twice the imaginary parts of the poles of the impedance calculated between the nodes of an inductor or josephon junction.
For further details on the underlying theory, see https://arxiv.org/pdf/1908.10342.pdf.
The dynamics of the circuit can be studied in QuTiP by considering collapse operators for the mth mode \(\sqrt{2\pi\kappa_m(n_{th,m}+1)}\hat{a}_m\) and \(\sqrt{2\pi\kappa_m(n_{th,m})}\hat{a}_m^\dagger\) where \(n_{th,m}\) is the average thermal occupation of mode \(m\) and \(\hat{a}_m\) is the annihilation operator of the mth normal mode of the circuit. Note that dissipation rates that are obtained from this function have to be converted to angular frequencies through the factor \(2\pi\). If you are also using a hamiltonian generated from qucat, then it too should be converted to angular frequencies by multiplying the entire Hamiltonian by \(2\pi\) when performing timedependant simulations.