Continuous quantum error correction on non-Markovian models

We study quantum error correction by a continuous quantum-jump process, comparing performance with a Markovian error model to two different non-Markovian models: an interaction Hamiltonian between the system and an environment qubit coupled to a “cooling” bath—a model that has been shown to have abrupt transitions between Makovian and non-Markovian behavior—and the post-Markovian master equation (PMME). For the PMME, we consider an exponential kernel with underdamped and overdamped behavior. We compare these two non-Markovian error models both to the Markovian case and to each other.

This work starts with a one-qubit system being maintained in a particular state against noise. This case allows a analytical solutions. We then generalize the study to the three-qubit repetition code. The fidelity in the Markovian case decays more abruptly than when a non-Markovian model is used: the performance of error correction is enhanced against a non-Markovian error model enhances. In particular, for the one-qubit model we observe a linear decay in time of fidelity for the Markovian case, while the non-Markovian cases exhibit a quadratic time decay at short times. Analogously, for the three-qubit code, the fidelity decays quadratically in the Markovian case and as the cube in the non-Markovian case. We attribute this difference to the existence of a quantum Zeno regime in both non-Markovian models.