Fig. 2: Persistent stabiliser-product symmetry of the X³Z³ Floquet code leads to improved performance under Z-biased noise.

a An example of such a symmetry along a single unshaded strip of the lattice, together with a Pauli-Z error, is shown throughout the measurement cycle. Arrows indicate the type of check (cA or cB for some colour c) measured at each subround. A-type plaquette operators whose product forms the symmetry at that subround are highlighted in darker colours. Plaquettes indicated by coloured dots are the locations of syndromes that would be triggered if the Z error shown were to occur at that measurement subround. b An example of a stabiliser-product symmetry just before gB checks are measured is the product of red and blue A-type plaquettes shown. Since this product is the identity along the vertical unshaded strip and commutes with Z errors on all qubits, the syndromes/anyons [coloured dots in (a)] must appear in pairs along the vertical strips.