Deploying high performance noise-robust quantum controls requires information about the noise in your hardware.  In the filter function framework this is captured through the noise power spectral density, a frequency-domain representation of different noise processes.  Having access to this information is a key requirement for both the evaluation of control performance and control optimization.

In general this information is not easily determined - here we provide you with tools to directly measure the noise affecting your qubits.  In short, you can use your qubit as a measurement device to directly probe the noisy environment, if you apply the right controls during the measurement procedure.  

We provide you all of the controls you need and perform all of the processing on your behalf with just a few simple inputs.  There's no need to be an expert in the underlying methodologies - we implement the right constraints to ensure you get the best outcome.

The general workflow follows the following outline:

  1. Create controls.  Tell us the kind of noise you'd like to characterize and some information about what information you'd like - measurement resolution, the frequency range you care about, etc.
  2. Output controls determined specifically based on your input constraints.  These will be saved in a library for future use.
  3. Perform measurements using the prescribed controls.
  4. Upload measurement results and our computational engine will perform all data fusion to reconstruct a noise spectrum.

This information will then be accessible across different workspaces where noise power spectral densities are used in performance evaluation or optimization.  

We provide approaches to characterize both multiplicative control noise and dephasing, and offer options for different characterization routines depending on the level of control available in your system.

Our tools are developed with the objective of minimizing the required amount of background knowledge about the underlying control and reconstruction techniques.  With a small amount of input about the performance limits of your hardware, we can set appropriate bounds and select the most appropriate controls for your application.  

For instance, the "MAX ACHIEVABLE EXPERIMENT DURATION" may be defined by a heating process as in trapped ions or a stochastic T1 time.  With this knowledge we'll ensure that controls don't exceed your system's capabilities.

Pulsed vs Continuously Shaped Control

The level of control available in an experimental system can vary significantly.  We provide control options which cater to the constraints faced by all of our customers.

In cases where experimental simplicity is prioritized, noise information can be obtained using timed sequences of simple driven rotations, often referred to as pulsed dynamical decoupling sequences.  Here simple quantum bit flips (pi rotations) are sequenced in order to produce a filter function with a dominant peak at the frequency defined by the inverse interpulse delay.   These controls have the benefit of relative experimental simplicity, but suffer from spectral leakage and require more complicated data fusion procedures in order to appropriately account for the many harmonics appearing in the filter function.

Shaped controls based on so-called Slepian waveforms are highly effective for the characterization of both control noise and dephasing.  These controls are provably optimal in terms of spectral concentration, i.e. how much spectral weight resides within a target band.   Accordingly they mitigate issues of spectral leakage which cause unwanted out-of-band signals to contribute to the measurement as a form of "interference."  They can be thought of as mathematically optimal "window" functions applied directly to the qubit itself, restricting the qubit's sensitivity to noise.  Shaping the control appropriately can change the control's spectral response, as captured through the filter function.  These approaches are powerful in their ability to suppress out of band interference and require very simple post-measurement processing, but require arbitrary pulse shaping.

Exploring Controls

Once a control is created you can explore it using a set of interactive visualizations.  Here we show the filter functions for a specific pulsed decoupling protocol used for noise characterization.  

Clicking on any filter function in the top graph will activate the relevant control and visualization.

Note: In the case of pulsed controls, using long sequences with many pulses can result in very narrowly peaked filter functions in frequency (this is a benefit in the case of the actual measurement process).  In such cases we only display the peak location, rather than a continuously sampled filter function in order to simplify the visualization.  Rest assured the correct filter function values are employed in the reconstruction process!

Downloading Controls & Uploading Measurements

Once you have created a set of controls which is appropriately tailored to your system, you can download controls for implementation in your experiment.  At this stage we provide both the controls to be output along with a template file required for uploading the measurement results.  Details on data and file formats can be found here.

Once measurements for each required control are performed in your hardware, you can directly upload the results for use in spectrum reconstruction. 

Data Fusion and Spectrum Reconstruction

Once measurements are uploaded, we check the file format and automatically perform the relevant spectrum reconstruction (based on header information within the JSON file in which you upload data). Depending on the form of control you implement for the noise characterization routine, we will employ different options for the mathematical procedure used in data fusion to produce a spectrum reconstruction.

In the case of pulsed control for dephasing noise we rely on a matrix inversion procedure.  This is relatively computationally intense.  For shaped controls based on Slepians we perform you will have the choice to either employ a single-taper estimate directly derived from the measurement results.   

Following data fusion, the returned spectrum is added to your library and displayed in the main page of the workspace.  You can explore and compare spectrum reconstructions, and use them across the various workspaces in Black Opal.

Information on the relevant technical background can be found in the following manuscripts:

Optimally band-limited spectroscopy of control noise using a qubit sensor,” L. M. Norris, D. Lucarelli, V. M. Frey, S. Mavadia, M. J. Biercuk, L. Viola, Physical Review A 98, 032315 (2018).

Application of optimal band-limited control protocols to quantum noise sensing,” V. M. Frey, S. Mavadia, L. M. Norris, W. de Ferranti, D. Lucarelli, L. Viola, and M. J. Biercuk, Nature Communications 8, 2189 (2017).

Dynamical decoupling sequence construction as a filter design problem,” M.J. Biercuk, A.C. Doherty, and H. Uys, Journal of Physics B: Atomic, molecular, optical physics 44, 154002 (2011).


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