Things are getting real in the quantum technology space. And as quantum computing matures, the need for solutions helping to achieve high-performance control operations is growing.

But how do you know you can trust an approach appearing in the market to deliver when the rubber hits the road?

The team at Q-CTRL completely understands how important this question is. And we embrace it so much that it forms the basis of one of our core values: Be Trusted.

So when it comes to the products we offer - including complex control solutions built on advanced mathematical techniques - we work hard to ensure you can trust what we’ve built by testing in real quantum computers.

Q-CTRL founder and CEO, Professor Michael Biercuk, said: “My background is as an experimentalist and I know how easily sensible-sounding approximations can deviate from real life.”

“We need to be sure the core technology behind both BLACK OPAL and BOULDER OPAL functions as expected when deployed in real quantum computing hardware. So we do the tests ourselves in collaboration with the Quantum Control Laboratory at the University of Sydney.”

By probing the underlying science - and even exploring when it fails - we can be sure Q-CTRL is building products that provide the most value to our customers.

Here we introduce the experimental validations behind three of our core capabilities in order to give you the confidence you need in our products.

1. Filter Functions for Single-qubit Gates… EXPERIMENTALLY VALIDATED

Our team has specialized in an approach to describing the interaction of a control and laboratory noise based on mathematical objects called filter functions . With filter functions in hand it’s possible to create controls that reduce the likelihood of error (AKA “Infidelity”) in a quantum computer.

These filter functions were a solid starting point for our product suite because the science that underpins it appeared on the front cover of Nature Physics in October 2014.

The data (markers) matched the predictions of our theory (lines) nearly perfectly
The data (markers) matched the predictions of our theory (lines) nearly perfectly

Q-CTRL has built on this research from the University of Sydney’s Quantum Control Laboratory to give our clients an intuitive visual heuristic for explaining how a particular control will perform in realistic lab settings. Where the filter function is small in the space of the frequency of noise present in a system, that noise will be suppressed or “filtered out .” Experiments induced a small disturbance that allowed us to actually measure the filter function of the controls applied. The data (markers) matched the predictions of our theory (lines) nearly perfectly, down to the limits on our measurement process, with no free “fitting” parameters used to improve agreement.

At the time of publication, a News & Views editorial comment - ‘Engineering a Revolution ‘ - on the significance of that science was published in Nature Physics by Professor William Oliver from the Lincoln Laboratory at the Massachusetts Institute of Technology. Professor Oliver said: “[The experiments have] validated an alternative design framework that enables the engineering of high-performance quantum control operations in systems that face realistic, time-varying noise environments.

So when it comes to the way we create and analyze single-qubit operations in BLACK OPAL , you know that the science is sound.

But if that’s not enough, the mathematical filter functions were used by a team at Tsinghua University to extend the lifetime of a qubit to 10 minutes !

2. Machine Learning-derived Controls… EXPERIMENTALLY VALIDATED

In the Q-CTRL core numerical package behind BLACK OPAL and BOULDER OPAL , we have built a powerful machine learning toolkit for the optimization of novel quantum control operations. This way, we can help you find error-robust controls tailored to your needs that operate faster than analytically defined solutions appearing in the literature. That promise sounds fantastic, but does it hold up? Absolutely.

We put Q-CTRL-derived control solutions - techniques that we have never seen appearing anywhere else - to the test against standard approaches. And despite their apparent complexity (they involve changing the phase or amplitude of a control many times throughout a short operation), they worked very much as expected.

We performed a test in which we applied two different small imperfections that would normally cause an error in a control operation. The resulting qubit error is shown on the vertical axis - higher corresponds to more error. In our experiments with standard controls the error gets larger and larger as the imperfection becomes more significant.

Q-CTRL solutions perform in a nearly constant manner, staying low in the graphs.
Q-CTRL solutions perform in a nearly constant manner, staying low in the graphs.

But not so with Q-CTRL solutions! Even as the imperfections grow to very large values (moving away from the center of the x-axes), Q-CTRL solutions perform in a nearly constant manner, staying low in the graphs. This means that if unexpected problems arise in your hardware, Q-CTRL solutions will keep performing well, exactly the way you’d hope.

These tests were performed in the University of Sydney’s Quantum Control Laboratory with control solutions created and output directly from BLACK OPAL and run on a trapped-ion quantum computer. And you can do the same on your own hardware with confidence that the solutions work!

3. Filter Functions for Two-qubit Gates… EXPERIMENTALLY VALIDATED

One of the toughest problems in quantum computing is improving the performance of multi-qubit gates - the operations that produce entanglement between qubits.

A major development driven by Q-CTRL was an extension of the mathematics of filter functions to include multi-qubit gates . And as before, we’ve worked hard to ensure that the techniques used to build Q-CTRL products are experimentally validated.

filter functions accurately predict the response of a two-qubit gate (Mølmer–Sørensen)
filter functions accurately predict the response of a two-qubit gate (Mølmer–Sørensen)

As before, we put these new tools to the test in the lab at the University of Sydney. The results, appearing in a collaborative arXiv paper again show that the filter functions accurately predict the response of a two-qubit gate (Mølmer–Sørensen) to an applied imperfection.

And it is this predictive power that has allowed us to create a whole suite of new error-suppressing 2-qubit control solutions for Mølmer–Sørensen gates (also validated in this paper), along with new solutions for parametrically driven and cross-resonance gates in superconducting circuits.

Everything we build has the solid foundation you need to feel confident that our products will work for you. That’s what we mean when we make it a core value to Be Trusted.