Bias-preserving computation with the bit-flip code

We explore the feasibility of fault-tolerant quantum computation using the bit-flip repetition code in a biased noise channel where only the bit-flip error can occur. While several logic gates can potentially produce phase-flip errors even in such a channel, we propose bias-preserving implementation of $S$, $H$, $\mathrm{CZ}$, and $R_z$ gates. We demonstrate that our scheme improves the computational precision in several tasks such as the time evolution of quantum systems and variational quantum eigensolver.