Logical-qubit fidelity under coherent and incoherent noise injection

The performance of quantum error correction (QEC) codes is limited by the underlying physical noise. Theoretical studies show that coherent and stochastic noise have different effects when performing QEC with either surface or repetition code. In this work we experimentally inject coherent and stochastic noise into bit-flip repetition codes and study the impact on the logical fidelity. We adapt a subset sampling technique to efficiently sample stochastic noise within the quantum circuit, allowing the estimation of logical fidelity for any injected physical error probability using only a subset of noisy circuit evaluations. We observe a difference in logical error probability depending on the noise coherence applied for the distance-3 code but not at distance-5. Both a density matrix simulation, as well as a scalable, phenomenological simulation are used to investigate this discrepancy. The density matrix simulation reproduces the discrepancy using noise parameters extracted from experiment, while the phenomenological simulation follows theoretical predictions. Our results provide insight into the specific parameter regimes in which coherent and stochastic noise impact the logical fidelity differently, and what is needed to capture this behavior in quantum simulation.