Fig. 2: Discovering codes and encoding circuits for various numbers of physical qubits, logical qubits, and distances (see main text and Methods for d = 5).

Families of stabilizer codes tailored to symmetric depolarizing noise channels, found with our RL framework. The labels (x, y) indicate the number of non-degenerate (x) and degenerate (y) code families. The circuit size shown is the absolute minimum throughout all families. In general, different families have different circuit sizes, and even within the same family we find variations in circuit sizes. Since further training runs do not increase family populations, it is likely that there are no more stabilizer codes for the shown code parameters.