Preparing for a computational search for new error correction codes

Quantum computing promises to revolutionise areas ranging from cryptography to materials design, but a significant error correction challenge remains before quantum computing can operate at scale.

A 2024 paper by EQUS Chief Investigator Prof Tom Stace and colleagues at the University of Queensland explores the application of reinforcement learning to the challenge of searching for the error correction needed for future scaling of quantum computing1.

Error correction crucial for quantum computing at scale

Unlike existing digital computers, which operate with exceptionally low error rates, quantum components are far more sensitive to noise, and thus error-prone.

As Tom explains, “Quantum hardware is ‘noisy’—many orders of magnitude noisier than digital components—so any functionally useful quantum computers will need error correction embedded directly into the system.”

Error correction in quantum computing would operate similarly to many engineering systems, with redundancy built in to handle hardware imperfections and maintain functionality even when individual parts fail.

This built-in redundancy would allow logical processing and information to remain accurate despite relatively frequent errors in the underlying physical qubits.

Improving on genius, what replaces the 1997 Surface Code?

For the last two decades, quantum error correction has been dominated by a mathematically elegant solution developed by Alexei Kitaev in 1997, which was itself based on ideas from the 1970s on toy models of fundamental physics.

While acknowledging the impact of this inspirational piece of work, which has shaped quantum error correction for over two decades, Tom explains that this code is just one point in a vast landscape of potential solutions.

“The hypothesis is that there might be much better codes out there—ones that are optimised for specific quantum hardware.” Tom says. “But finding them manually among a vast ‘solution space’, or variety of possible solutions, is nearly impossible.”

However, we can look to computational optimisation tools, like machine learning and other techniques to ’fast-track’ the search.

As lead author Caroline Mauron puts it, “Rather than relying on a flash of genius to invent the next breakthrough code, we wanted to use automated tools to systematically search for and evaluate solutions.”

“The first challenge is to ‘phrase’ the problem ‘properly’ for computers to solve,” says Caroline, an EQUS alumni now managing a crypto derivatives trading firm. “This includes not only phrasing the definition of ‘good’ error correction code, but also phrasing methods for seeking improvements, how to define quality, and how to know whether the program was on the right track.”

The team adopted a mathematical framework known as tensor networks, which are generalisations of vectors and matrices, to represent and explore these possibilities.

Tensor networks provide a powerful tool for modelling the relationships between qubits and the redundancy in error-correcting codes, a useful metric for the efficiency of the proposed code.

Tensor networks are particularly useful for challenges to be solved ‘in parallel’—i.e. by many computer processors at once—including with machine learning techniques.

Modern GPUs (graphics processing units) are well-suited for handling tensor-based computations, making the tensor approach both efficient and scalable.

A gaming solution: applying reinforcement learning

“In this paper, we treat the search for good codes as a ‘game’, in which the starting pieces of the game are an initial set of code fragments, represented as small tensors,” says collaborating author Dr Terry Farrelly from whose research the original idea for the project came.

In their study, the team used reinforcement learning, a type of machine learning originally developed to teach computers how to play games like chess and Go.

Just as these algorithms learn strategies for winning, Tom’s team applied them to the problem of assembling better quantum error-correcting codes from smaller building blocks.

To illustrate the benefits of their approach, the researchers began with simple, well-understood codes and showed how they could combine these into larger, more complex codes with higher performance than the initial constituents.

This process is analogous to connecting together smaller Lego models to build something bigger, while ensuring that the final structure remains efficient and functional.

“If we can automate the search for better error-correcting codes, it could help close the gap between current hardware capabilities and the requirements for scalable quantum computing,” says Terry.

Looking ahead

EQUS’ 1kQubit Flagship program aims to develop fault-tolerant quantum computing architectures by integrating robust error correction into scalable systems. By advancing tools for designing tailored error-correcting codes, the tensor network work contributes directly to the program’s mission of building the next generation of quantum devices.

While this study represents a first step, it has already set the stage for more ambitious efforts. With funding gained from the Australian government’s Advanced Strategic Capabilities Accelerator (ASCA), Tom and his collaborators are working to scale up this approach. The goal is to create a platform where researchers can input hardware parameters—for example, specifying whether qubits were superconducting qubits, neutral atoms or trapped ions—and receive optimised error-correcting codes tailored to their specific needs.

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