Correcting spanning errors with a fractal code

Understand

The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors.

• Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$ such as the cubic code $-$ to be robust to highly correlated, one-dimensional errors that span their lattice.
• The challenge remains to design decoding algorithms that utilise the high distance of these codes.
• Here, we begin the development of such algorithms by proposing an efficient decoder for the `Fibonacci code'; a two-dimensional classical code that mimics the fractal nature of the cubic code.