Effect of quantum error correction on detection-induced coherent errors

We study the performance of quantum error correction codes (QECCs) under detection-induced coherent due to imperfectness practical implementations stabilizer measurements, after running a circuit. Considering most promising surface code, we find that will result in undetected terms, which accumulate and evolve into logical errors. However, show such errors be alleviated by increasing code size, akin eliminating other types discussed previously. also with errors, exact becomes an approximate QECC.