Visualizing normal-modes

Qcircuit.show_normal_mode(mode, quantity='current', plot=True, return_fig_ax=False, add_title=True, add_legend=True, **kwargs)[source]

Plots a visual representation of a normal mode.

Only works if the circuit was created using the GUI. Plots a schematic of the circuit overlayed with arrows representing the complex amplitude of a certain quantity \(X\) which can be flux, current, charge or voltage.

More specifically, the complex amplitude of \(X\) if a single-photon amplitude coherent state were populating a given mode mode.

Current is shown in units of Ampere, voltage in Volts, charge in electron charge, and flux in units of the reduced flux quantum (defined as \(\hbar/2e\))

The direction of the arrows show what we are defining as positive current for that component.

Parameters

  • mode (integer) – Determine what mode to plot, where 0 designates the lowest frequency mode, and the others are arranged in order of increasing frequency

  • quantity (string) – One of ‘current’ (default), ‘flux’,’charge’,’voltage’ Determines what quantity the arrows should represent.

  • plot (Boolean, optional) – If set to True (default), the function will call plt.show() to display the circuit

  • return_fig_ax (Boolean, optional) – If set to True (default is False), the function will return figure and axis for further processing using matplotlib.

  • add_title (Boolean, optional) – If set to True (default), the function will add a title detailing the modes frequency, anharmonicity and dissipation rate

  • add_legend (Boolean, optional) – If set to True (default), the function will add a legend detailing the definition of arrow size and arrow direction

Notes

This annotated quantity, called a phasor, is calculated by multiplying the voltage transfer function \(T_{rc}\) (between a reference component \(r\) and the annotated component \(c\) ), with \(X_{zpf,m,r}\), the zero-point fluctuations of \(\hat{X}\) at the reference component.

Note that resistors make the transfer function \(T_{rc}\), and hence the phasors complex.

Since this is plotted for a single-photon amplitude coherent state, the absolute value of the annotation is equal to the contribution of a mode to the zero-point fluctuations accross this component.

For more detail on the underlying theory, see https://arxiv.org/pdf/1908.10342.pdf.