Defining noise power spectra

We provide you a variety of tools to input noise power spectra of interest to your experiment. This is a simple frequency-domain representation of different kinds of noise (e.g. multiplicative control noise or ambient dephasing noise) exhibiting time-dependence. The noise power spectrum enters into a calculation of the average operational measures and worst-case error for a control solution which is displayed in BLACK OPAL’s performance metrics

In this short tutorial we provide an overview of the two key approaches to this action in BLACK OPAL.

Determining an analytic power spectrum

For convenience, our interface allows you to establish a noise power spectrum using analytic functions defined over fixed frequency intervals. Start by selecting the “EDIT NOISE” button in the Filter Functions and Noise Power Spectra section of the workspace:


The default view will show a “1/f” spectrum over a specific frequency range relevant to your input Rabi rate.

An important parameter needed for calculations of operational infidelity is the strength of the noise. The units of this are generally complex and difficult to parse. However the BLACK OPAL package simplifies this problem by calculating noise strength directly from experimental measurables: the Rabi oscillation decay envelope for control noise and the free evolution decay for ambient dephasing. Just set the appropriate parameter using the drop down and the noise is automatically scaled. In the example below, we select a Rabi decay envelope of approximately 1 ms and scale the noise automatically.


The BLACK OPAL package allows you to analytically define the power spectrum’s frequency dependence over a variety of ranges. The default is “1” but you can simply select this and input the relevant frequency regions. Use input fields to change the bounds on these frequency ranges as well as the analytic frequency dependence. Complex forms can be input by choosing ohmic scaling (noise increasing with frequency) to mimic regions with strong noise spurs.


Once you’ve completed defining the power spectrum simply click “SAVE NOISE” and all calculations and graphs on the main BLACK OPAL page will be updated.


Uploading a measured spectrum

If you have already measured noise in your system and want to upload it for use in calculations and control comparisons, simply drag and drop a CSV formatted noise file into the interface and it will be automatically uploaded (example dephasing spectrum data available here).


The required format is a three-column CSV:

Frequency (Hz),Power,Uncertainty

If you don’t know the uncertainty in your measured noise power, simply fill in zeroes in that column.


If you’d like to change the uploaded noise spectrum, simply drag-and-drop a new file and the interface will automatically update.


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