**Black Opal** is a hardware-agnostic platform that helps you leverage the power of control engineering to reduce decoherence and errors at the physical layer in your quantum hardware.

You can create drop-in replacements for your single and multi-qubit operations with improved error performance and gain actionable information about the dominant noise sources in your hardware.

Our approach to helping you perform like an expert in quantum control combines an intuitive interface with a back-end cloud-compute engine to streamline complex computations.

Control solutions are output to permit direct integration with experimental hardware, quantum compilers, and other higher-level quantum programming languages.

If you're ever lost, help is within easy reach. You can ask questions, read through our detailed help guides, or deep-dive with our technical documentation. Just look out for the prompts should you need a little guidance.

## Design an error-suppressing single-qubit control

Here we'll step you through a simple workflow to understand some of the key features and functionalities of Black Opal.

- Choose a Workspace
- Input Hardware Constraints
- Select Controls for Analysis
- Calculate and Compare Filter Functions
- Add a Noise Power Spectral Density
- Calculate an Error Budget
- Run a Machine Learning Optimizer
- Output Data

Already familiar? Jump to Next Steps

## 1. Choose a Workspace

You're able to develop, test, and analyze controls for different control settings, spanning from single qubits undergoing driven rotations to more complex multiqubit operations and N-dimensional manifolds. All analyses are performed in the same computational framework and use common interface structures, but each workspace includes features tailored to the specific target operations. You can toggle between workspaces by clicking on the relevant tabs without impacting any of the calculations you've performed.

The default workspace is 1-qubit, where you can study driven operations on a single qubit in the presence of time-varying noise. A graphical legend on the left appears the first time you enter this workspace to help guide you; click on it to get information about the assumed control Hamiltonian at a glance. The legend will be hidden after first use but can be selected again later by clicking on the vertical banner.

## 2. Input Hardware Constraints

You can choose between standard hardware configurations - superconducting and trapped ion - or you can fully customize your setup using our graphical interface. Key information such as the maximum Rabi rate in your system and the relevant pulse shape you employ can be input at the top of the interface to connect the calculations performed in Black Opal to real units of relevance to your experiments. We've simplified this process to request the minimum amount of information possible from you.

## 3. Select Controls for Analysis

A list of controls available to you is presented on the left side of the workspace. You can choose to add any to your performance evaluation or click "Details" to learn more about how this control functions; these will reflect the hardware constraints you've already input.

All of the technical details associated with each control are just one click away. Depending on what's most natural for your physical hardware, you can represent the control solution in either Cartesian or Cylindrical coordinates. Segments of the control can be visualized simultaneously on the Bloch sphere and line graphs using a mouse-over. We present these charts in easy-to-interpret units, but real lab-frame units are available in the table below.

## 4. Calculate and Compare Filter Functions

Once you've selected controls for analysis filter functions for the controls are calculated.

The filter functions are a simple visual heuristic allowing you to understand the susceptibility of different controls to realistic laboratory noise sources. Low values of the filter function indicate noise suppression - so look for filters that trend downwards to the bottom left of the graph. If the filter is flat, that means it is broadband susceptible to noise all the way to DC. The graphs presented are fully interactive and data can be downloaded if desired.

For the 1-qubit workspace we automatically provide information about multiplicative noise in the control field and additive ambient dephasing. Noise Hamiltonian details are provided in the legend.

## 5. Add a Noise Power Spectral Density

For either type of noise in the 1-qubit workspace, you can amend the form of the noise power spectral density used in analyses. This is a critical function which describes the time-varying noise in your system, using a compact frequency-domain representation.

Clicking on Edit Noise allows you to either using our graphical interface to edit the strength and shape of the noise power spectral density or upload a power spectrum from your experiment.

Because the noise strength comes in unfriendly units, all you need to provide is an estimate of either the 1/e Rabi decay time or free-evolution decay time and we will produce the right scaling for the noise power spectral density.

A few example noise power spectral densities are included as a default. If you're comfortable with these features you can even run a prescribed characterization routine on your hardware and Black Opal will estimate the noise power spectrum for you.

## 6. Calculate an Error Budget

The net error (infidelity) expected in an operation is given by the overlap in frequency of the noise power spectral density and the control filter function. These are shown on the same graph for simplicity once the noise is uploaded. If the noise has significant strength at frequencies higher than the "knee" in the filter function, performance will be significantly degraded. This can generally be overcome by choosing a filter with improved noise suppression or increasing the Rabi rate to extend the so-called "decoupling limit".

Black Opal automatically calculates the expected average infidelity and worst-case error for each of the selected controls allowing easy comparison of the performance of your controls in the presence of the selected noise power spectral densities. This error budget is broken down to show the individual contributions and all values are automatically recalculated any time you change the selected controls or noise power spectral densities.

## 7. Run a Machine Learning Optimizer

With an input noise power spectral density you can use our machine learning package to create a control optimized for filtering the dominant noise spectral components by selecting Optimize Controls at the top right.

Numerically optimized control solutions can in principle dramatically outperform "generic" control solutions in cases where the noise has distinct features - especially at high frequencies. For instance, the optimizer can produce band-stop filters to target specific noise frequencies at the general cost of low-frequency noise suppression.

Begin by telling us what your optimized solution should be called and the type of optimization to be used: a high-speed, fixed-noise-frequency optimizer, or a highly customized, broadband optimizer (For more details see our guide to optimization for driven controls).

You can select whether one or both noise processes should be considered, how complex you'd like your control waveform to be, and how much longer than the benchmark primitive the control can be. We automatically set limits to ensure you'll end up with a solution better than the primitive.

Because these calculations can be complex we will notify you when your control solution is ready for use and visualization. The control is then added to your library and can be compared alongside others at any time.

## 8. Output Data

Throughout the Black Opal interface you are given the option to download the control solutions which best meet your needs. The controls are defined in either a CSV or JSON file, and either a compact analytic format or a sampled format appropriate for programming control hardware. These solutions can then be directly integrated into experimental systems or quantum compilers.

**Tip**: *When programming hardware signal generators, our output data formats match typical system needs. The Cartesian format maps directly to IQ modulation while the Cylindrical format is appropriate for AM or PhiM.*

## Next Steps

Once you're comfortable with basic workflows for control analysis and optimization you can explore our advanced features to extract maximum performance from your quantum hardware. Full details on the available features in the Premium Edition of Black Opal are available through our comprehensive documentation but we highlight a few opportunities here.

#### Import measured waveforms and analyze the impact of distortion

The filter function framework efficiently captures the effects of bandwidth limits and control distortions. If you have measured how waveforms are distorted by transmission lines and other components, upload the waveform as a Custom Control and analyze the impacts of these distortions on noise susceptibility and performance metrics.

#### Experimentally reconstruct your noise power spectral density

We provide tools allowing you to perform a simple set of measurements on your hardware in order to characterize various forms of noise, giving you actionable information to improve your hardware and deploy optimized controls. Techniques are based on either pulsed dynamic decoupling or bandwidth-optimized Slepian functions. Simply choose the control which is most suitable for your system, upload experimental measurement results, and Black Opal will perform the relevant data fusion in order to produce an estimate of the noise power spectral density experienced by your devices. This information can be used in other parts of the Black Opal package for performance analysis and control evaluation

#### Explore and optimize controls beyond single qubits

The filter function formalism is extensible to two-qubit logic, multiqubit operations with spectator levels, multiqubit circuits, and even qudits. Use our tools to analyze multidimensional systems and create optimized multiqubit control sequences. Bosonic modes can be included where appropriate.