Teleportation Decoheres Noise in Measurement-based Error Correction - Part 1/2

While the performance of quantum error correction (QEC) codes under incoherent Pauli noise has been studied widely, the performance under coherent or unitary errors is less understood. For example, unlike its incoherent counterpart, a constant threshold theorem for coherent noise has not yet been established. Coherent errors are also much harder to simulate, making numerical estimation of thresholds difficult. It has been shown that physical coherent noise can lead to logical coherent errors after QEC, which are undesirable as they can coherently add in a logical circuit, leading to faster accumulation of faults compared to incoherent noise. In practice, coherent errors may be converted to incoherent errors via randomized compiling. This, however, may come at the cost of extra gates and additional noise. Thus, it is important to develop a better understanding of coherent errors in QEC and ways to directly deal with them. In this work, we extend the current theoretical understanding of coherent noise and show that, remarkably, they are automatically converted to incoherent Pauli errors during teleportation-based QEC. Therefore, analytical results for QEC of incoherent Pauli noise in this model may be applied to coherent noise as well. Our work also adds to the other known features of teleportation-based QEC, distinguishing it from conventional circuit-based QEC, such as inherent mitigation of leakage and qubit loss as well as higher thresholds and code symmetry preservation for certain noise models.