Calculating loss rates

Qcircuit.loss_rates(**kwargs)

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 un-specified circuit components, ex: L=1e-9.

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 m-th 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 m-th 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 time-dependant simulations.