Quantum error correction research reveals fundamental insights on quantum systems

Newswise — As scientists and researchers increasingly look to quantum computing to aid in complex problem-solving and advance our understanding of the universe – quantum error correction has become a critical area of scientific inquiry. Increasing the accuracy and reliability of quantum computers is essential as scientists explore their practical applications – both for fundamental science and future technological applications.

Today, the Perimeter Institute for Theoretical Physics (Perimeter) is proud to celebrate our researchers whose published work in Nature Physics on September 3, 2024 documents their discovery of a new way to separate nontrivial quantum error correction codes from trivial ones. The research shows that this new boundary line isn’t arbitrary, and therefore represents fundamental progress on how quantum systems work in the real world. It paves the way for future applications not just in quantum computing – but also in condensed matter (with regards to topological order) and quantum gravity (with regards to conformal field theories).

In their article, researchers Jinmin Yi, Weicheng Ye, Daniel Gottesman and Zi-Wen Liu – who have each been supported in their work by Perimeter – detail their discovery of a mathematically rigorous connection between Approximate Quantum Error Correction (AQEC) code properties and the complexity of quantum circuits. Using this connection, scientists can now evaluate the precision level of the quantum code.

Additionally, the researchers’ discovery that AQEC codes emerge naturally could help answer some of physics’ biggest, most challenging questions.

“This new dividing line that we’re proposing between acceptable and unacceptable codes corresponds to something physically meaningful,” said Dr. Daniel Gottesman, a longtime Perimeter faculty member and current Co-Director of the Joint Center for Quantum Information and Computer Science at the University of Maryland. “It shows that this was not just some random thing that we came up with, but that it’s connected to something fundamental.”

The discovery has applications in several fields of study. For example, researchers studying topological order – which explores the intricate properties of quantum materials like fractional quantum Hall states and certain superconductors – have long wrestled with the gap between entanglement conditions and code properties. These scientists now have the tools to better understand the relationship between these conditions, and advance our understanding of unique materials. 

Jinmin Yi, a Perimeter PHD student and co-author of the paper, says that their research has provided “a quantitative understanding of why these two notions are actually different,” unlocking potential for future research.

The study of AQECs has also uncovered intriguing insights for scientists who are looking to integrate quantum mechanics with Einstein’s theory of general relativity – one of physics’ most persistent challenges. Specifically, evaluating AQECs using subsystem variance has indicated that certain Conformal Field Theory systems are more likely to integrate with gravitational descriptions.

While each of these areas deserves further study, the initial results are encouraging, and invite future exploration into the scope and utility of AQEC, along with its physical and practical applications.

Additional Resources:

Complexity and order in approximate quantum error-correcting codes

A new link between generalized quantum error correcting codes, complexity, and physics

The Perimeter Institute for Theoretical Physics

Perimeter Institute is the world’s largest research hub devoted to theoretical physics, fostering breakthroughs in the fundamental understanding of our universe, from the smallest particles to the entire cosmos. For 25 years, Perimeter’s innovative approach has empowered scientists worldwide to explore emerging scientific fields, giving researchers the freedom they need to question assumptions and blaze new trails. Research at Perimeter is motivated by the understanding that fundamental science advances human knowledge and catalyzes innovation, and that today’s theoretical physics is tomorrow’s technology. Founded by visionary Mike Lazaridis in 1999 and located in the Region of Waterloo, the not-for-profit Institute is a unique public-private endeavour, including the Governments of Ontario and Canada, that enables cutting-edge research, trains the next generation of scientific pioneers, and shares the power of physics through award-winning educational outreach and public engagement.