EQUS researchers have developed generalised quantum error-correcting codes that enable new codes to be generated with no additional work, and an efficient way of testing the quality of the new codes.

Quantum computers offer exciting speed-ups compared to current classical computers in solving some important problems. To ensure that quantum computers function correctly, good quantum errorcorrecting codes are vital. One way to judge the quality of an error-correcting code is to calculate its distance (the higher the distance, the better the code), but doing so is very challenging.

The EQUS team found a new way to represent and build quantum error-correcting codes, by ‘gluing together’ smaller codes. They also found an efficient way to calculate the distance of the new codes, which allows them to quickly check how good any new codes are. The preprint on local tensornetwork codes won EQUS’ Best Collaborative Paper for 2021.

The new codes, called tensornetwork codes, enable the generalised construction of all known stabiliser (or holographic) codes. The general feature of these codes is that an almost arbitrary graph can be used to generate a large family of codes, enabling the generation of new codes with no additional work. The codes also come with a standard decoder that uses tensor-network contraction to decode arbitrary new codes. It is the f irst efficient decoder for holographic codes against Pauli noise and a rare example of a decoder that is both efficient and exact. DEFINITIONS Quantum error correction is an essential aspect of a useful quantum computer, providing a way of protecting quantum information from being lost or corrupted by, for example, interactions with the environment.

To simulate these quantum error-correcting codes and understand their properties, the researchers wrote a package in the Julia programming language. The next step is to release the code publicly on GitHub, so that others can try gluing together their own error-correcting codes.

Published in the 2021 EQUS Annual Report