Case study

Nord Quantique is accelerating the path to useful quantum error correction with Boulder Opal


Quantum error correction is a key component of fault-tolerant quantum computation as it counteracts noise, but is itself susceptible to the effects of device imperfections and fluctuations.


Employing Boulder Opal’s closed-loop optimization engine, Nord Quantique successfully demonstrated a quantum error correction protocol that extends the lifetime of their logical qubit over the case without quantum error correction.


increase in logical qubit lifetime


Noise is one of the biggest challenges in quantum computing as environmental influences lead to errors that compromise the usefulness of the technology. Quantum error correction (QEC), typically implemented through an iterative cycle of error detection and application of a correction - a special form of closed-loop feedback - makes it possible to fix these errors.

In classical computing, we can simply make copies of a bit, detect errors by majority vote, and correct them. Quantum computing, however, operates under the peculiar laws of quantum mechanics, which prohibit copying information. Therefore, more sophisticated methods are required to redundantly encode a piece of quantum information into what is known as a logical qubit. One way to achieve this, analogous to the classical approach, is to use multiple two-level systems to “smear out” the information in one physical qubit over a composite logical qubit.

But this approach carries a huge penalty - in some estimates you need 100 or even 1,000 physical devices to encode a single logical qubit. This is a very painful penalty when hardware is so scarce. A more resource-efficient approach is to use a single physical system with multiple levels - potentially an infinite number - to encode the data.

Given the complexity of the physics at play, being able to perform closed-loop optimization of a few physically motivated parameters of the quantum error correction protocol with Boulder Opal is very valuable to us.
Dany Lachance-Quirion, VP Quantum Hardware at Nord Quantique

How Nord Quantique is using quantum control to achieve an overall error reduction

The researchers at Nord Quantique have implemented the latter approach with a superconducting cavity in combination with a particularly robust type of encoding, the so-called Gottesman-Kitaev-Preskill (GKP) states. To correct errors in their superconducting device, the Nord Quantique team has focused on autonomous QEC.

In contrast to typical QEC schemes, this method does not rely on measuring and correcting errors. Instead, it stabilizes the qubit by cleverly controlling its environment. While QEC aims to reduce the number of errors and thus protect the quantum information, it also introduces new sources of error due to the additional control required. Therefore, the Nord Quantique team needed to carefully fine-tune the parameters of their QEC protocol to be able to achieve an overall error reduction.

Boulder Opal offers exactly the right tools to meet this challenge. Our quantum control infrastructure software package for research professionals provides different strategies enabling you to design controls for quantum systems. Depending on the level of knowledge you have about the system, you can use model-based or model-free closed-loop optimization to find the best control parameters.

Enabling of quantum error correction protocols with closed-loop optimization

In closed-loop experimental optimization, the optimizer interacts directly with the experimental hardware. It evaluates the cost function based on measurements and iteratively modifies the candidate solutions to identify the best set of parameters. Since there is always some source of noise or imperfection in the experiment beyond what can be captured by a model of the system, it is usually a good strategy to start with model-based optimization and then refine the parameters using closed-loop optimization.

The Nord Quantique team employed Boulder Opal’s closed-loop optimization engine at two levels for their QEC experiment. First, they designed the pulses used to control the logical qubit directly on the hardware. In particular, they fine-tuned the parameters for the gates that are most sensitive to noise, called echoed conditional displacements (ECDs). With Q-CTRL’s GaussianProcess closed-loop optimizer, the Nord Quantique team determined the optimal pulses to realize ECDs in their system, laying the foundation for a reliable execution of the QEC protocol.

Adapted from arXiv:2310.11400. The use of Boulder Opal’s closed-loop optimization in Nord Quantique’s quantum error correction protocol increased the logical qubit lifetime by 14% when compared to the uncorrected case. This demonstrates that the optimized error correction scheme corrects more errors than it generates, outperforming the default protocol. In addition to the results of the experiment, simulations are shown.

When performing QEC with the optimized gates and default protocol parameters, the Nord Quantique team observed that errors were corrected at approximately the same rate as they were generated by the protocol. The full potential of the QEC approach was realized when, in addition to optimizing the pulse parameters, the team used our tools to fine-tune the parameters that define the QEC protocol itself. With Boulder Opal’s GaussianProcess closed-loop optimizer, they found optimized protocol parameters that differed significantly from the default values.

By combining the optimized gates with the optimized QEC protocol, the team was able to demonstrate an effective error reduction through their autonomous QEC routine. They measured how long the autonomously stabilized logical qubit survived before accumulating error beyond a target level. The application of the optimized protocol increased this logical qubit lifetime by 14% over the scenario without QEC and by 15% over the default protocol!

This is one of the first experiments showing a net improvement from the use of QEC. We’re thrilled to support experiments such as this, paving the way to fault-tolerant quantum computing by combining the best of error suppression and QEC.

Get started now

Make quantum technology useful