Romanesco codes: Bias-tailored qLDPC codes from fractal codes

Abstract: We introduce and analyze a family of Clifford-deformed bivariate bicycle codes that are tailored for biased noise. Our qLDPC codes are defined on a bipartite hexagonal lattice with limited-range gates and low-weight stabilizers. The code is non-CSS, featuring stabilizer generators that are each half X and half Z. We find small examples with high encoding rate that perform well for a large range of bias. In the limit of large noise bias, the code reduces to two independent classical cellular automaton codes, giving a distance scaling better than is possible with 2D topological quantum codes. Our construction combines two classical cellular automaton codes, LDPC codes that were recently proposed for use with noise-biased cat qubits, related to each other by a reflection. Each stabilizer in the quantum code is obtained by multiplying an all-X stabilizer from the first code with an all-Z stabilizer from the second code, or the other way around. The result is a self-dual quantum code with a number of qubits equal to the sum of the input codes and stabilizer weight and locality determined by the input codes. Under strong noise bias, the effective distance of the quantum code approaches the distance of the input codes. We simulate the logical performance of our qLDPC codes under code-capacity noise and find strong suppression of the logical error rate.