Quantum Precoded Polar Codes

We introduce a new family of CSS codes obtained from rate-1 precoded polar codes, which harnesses the precoding benefits obtained for classical short blocklength polar codes. We optimize the rate profile and precoder of these codes with a genetic algorithm, and present codes of dimension $[\text{\hspace{0.17em}⁣}[256,2]\text{\hspace{0.17em}⁣}]$ and $[\text{\hspace{0.17em}⁣}[512,2]\text{\hspace{0.17em}⁣}]$ that have logical error rates similar to the $[\text{\hspace{0.17em}⁣}[1201,1,25]\text{\hspace{0.17em}⁣}]$ surface code over the depolarizing channel.