Smarter quantum computers with dual-code error correction

Various methods are used to correct errors in quantum computers. Not all operations can be implemented equally well with different correction codes. Therefore, a research team from the University of Innsbruck, together with a team from RWTH Aachen and Forschungszentrum Jülich, has developed a method and implemented it experimentally, with which a quantum computer can switch back and forth between two correction codes and thus perform all computing operations protected against errors.

Computers also make mistakes. These are usually suppressed by technical measures or detected and corrected during the calculation. In quantum computers, this involves some effort, as no copy can be made of an unknown quantum state. This means that the state cannot be saved multiple times during the calculation and an error cannot be detected by comparing these copies.

Inspired by classical computer science, quantum physics has developed a different method in which the quantum information is distributed across several entangled quantum bits and stored redundantly in this way. How this is done is defined in so-called correction codes. In 2022, a team led by Thomas Monz from the Department of Experimental Physics at the University of Innsbruck and Markus Müller from the Department of Quantum Information at RWTH Aachen and the Peter Grünberg Institute at Forschungszentrum Jülich in Germany implemented a universal set of operations on fault-tolerant quantum bits, demonstrating how an algorithm can be programmed on a quantum computer so that errors can be corrected efficiently.

However, different quantum error correction codes also come with different difficulties. A theorem states that no correction code can implement all the gate operations required for freely programmable computations with the logical quantum bits easily and protected against errors.

Quantum gates are realised with different correction codes

To circumvent this difficulty, Müller’s research group has established a method that allows the quantum computer to switch back and forth between two correction codes in an error-tolerant manner. “In this way, the quantum computer can switch to the second code whenever a logic gate that is difficult to realise appears in the first code. This makes it easier to implement all the gates required for computing,” said Friederike Butt, a doctoral student in Müller’s research group.

She developed the quantum circuits on which the experiment is based and implemented them in close collaboration with Monz’s research group in Innsbruck. “Together, we have succeeded in realising a universal set of quantum gates on an ion trap quantum computer using two combined quantum error correction codes,” said PhD student Ivan Pogorelov from the Innsbruck research group.

“This result is based on our many years of good collaboration with Markus Müller’s team,” said Monz, who knows the theoretical physicist from his doctoral studies at the University of Innsbruck.

The findings of the study were published in the journal Nature Physics.

Image caption: The Innsbruck quantum computer calculates with algorithms that switch back and forth between two different quantum error correction codes to realise error-corrected computing operations. Image credit: Helene Hainzer, University of Innsbruck.