Bias-tailoring single-shot quantum LDPC codes

Bias-tailoring improves quantum error correction codes based on the qubit noise asymmetry between X and Z noise. Single-shot error correction is a scheme that allows using only a single round of stabilizer generator measurements despite measurement noise. We combine these two ideas and propose two quantum error correction codes. The standard syndrome-encoded hypergraph product code has a high threshold under biased noise and is capable of good single-shot error correction under any bias level of the noise model. The reduced syndrome-encoded hypergraph product code, which is around 25% shorter in length and requires around 50% fewer stabilizer generator measurements than the standard version, has a high threshold under biased noise and is capable of single-shot error correction of the same level as the standard version when the noise model approaches the depolarizing model. In addition, we also show that the three-dimensional XZZX code is an instance of the reduced syndrome-encoded hypergraph product code.