In the quest for robust quantum computing, topologically ordered phases of matter have emerged as a promising avenue for encoding and processing quantum information.

A 2024 EQUS study revealed a promising path toward more robust memory for future quantum computers.

Quantum systems are very susceptible to noise, and so errors occur in quantum memories very quickly.

EQUS researchers have thus invested significant effort in correcting errors in quantum memories – a process called quantum error correction.

One way to protect quantum memories is to encode information in the ‘topology’ of an object.

A great example for understanding topology is a knot. There are many types of knots, and they are highly protected from noise. You can bend, stretch, twist a knot and it will basically stay the ‘same’ knot, To actually change a knot, you need to do something more drastic – untie it and re-tie it a different way, which really requires some care.

Similarly, topologically ordered systems can serve as robust quantum memories, protected from any noise that acts locally on the system.

In the 2024 EQUS paper, the team considered a quantum system that is a bit like a knot, and encoded quantum information into the type of knot.

This makes for a great quantum memory.

The paper looks at a particularly simple but powerful set of knots (i.e. topologies) that are denoted by different colours, and so we call this error-correcting code a ‘colour code’. Much of the paper concerns understanding the different knots (topologies) and how they are related.

This topological approach to quantum error correction, which has been a hot topic for the past 20 years, has seen significant advances recently. Breakthrough experiments at Google in 2024 demonstrated how the simplest quantum error-correcting code of this type could perform in practice.

“The EQUS colour code work is a more sophisticated and potentially more powerful ‘big brother’ of the simple code that Google used”, says EQUS Chief Investigator Prof Stephen Bartlett (University of Sydney).

The result was a significant accomplishment for EQUS’ 1kQubit flagship, and will feed into ongoing work in this area. “We are seeking to understand theoretically what will be possible with real quantum devices that are expected in the next few years,” says Stephen.

“Already, Google’s most recent experiment has been able to demonstrate the simplest version of what we are proposing, and we expect that the next generation of devices will make use of our theoretical results to demonstrate even better codes, and with better performance.”

Future quantum computers will be able to leverage such ideas to squeeze increased performance out of their hardware, bringing the benefits of quantum computing even sooner.

This paper was a collaboration between EQUS and the group of Prof Jens Eisert at Freie Universität Berlin.

This story was first published in the 2024 EQUS annual report.