  Bias-tailoring allows quantum error correction codes to exploit qubit noise
asymmetry. Recently, it was shown that a modified form of the surface code, the
XZZX code, exhibits considerably improved performance under biased noise. In
this work, we demonstrate that quantum low density parity check codes can be
similarly bias-tailored. We introduce a bias-tailored lifted product code
construction that provides the framework to expand bias-tailoring methods
beyond the family of 2D topological codes. We present examples of bias-tailored
lifted product codes based on classical quasi-cyclic codes and numerically
assess their performance using a belief propagation plus ordered statistics
decoder. Our Monte Carlo simulations, performed under asymmetric noise, show
that bias-tailored codes achieve several orders of magnitude improvement in
their error suppression relative to depolarising noise.
