Tailoring three-dimensional surface codes for biased noise

Tailored surface codes in two dimensions have recently been shown to exhibit high error correction thresholds and subthreshold performance in presence of biased noise.

Tailoring has involved deforming the surface code stabilizers via Clifford Pauli permutations as well as considering different dimensions and boundary conditions.

In this work, we apply these tailoring ideas to the three dimensional surface codes. Specifically, we consider a Clifford deformation of the 3D surface code such that it has a layered structure made of XZZX layers. To optimize the encoding rate while maintaining the code distance, we consider the code on a rotated layout. Using the belief propagation with ordered statistics decoder, we obtain a threshold above 36% at infinite Z bias, and threshold of 33% at a moderate bias ratio of 30.