Noise-adapted Quantum Error Correction for Non-Markovian Noise
arXiv:2411.09637 · doi:10.1103/PhysRevA.111.052413
Abstract
We consider the problem of quantum error correction (QEC) for non-Markovian noise. Using the well known Petz recovery map, we first show that conditions for approximate QEC can be easily generalized for the case of non-Markovian noise, in the strong coupling regime where the noise map becomes non-completely-positive at intermediate times. While certain approximate QEC schemes are ineffective against quantum non-Markovian noise, in the sense that the fidelity vanishes in finite time, the Petz map adapted to non-Markovian noise uniquely safeguards the code space even at the maximum noise limit. Focusing on the case of non-Markovian amplitude damping noise, we further show that the non-Markovian Petz map also outperforms the standard, stabilizer-based QEC code. Since implementing such a non-Markovian map poses practical challenges, we also construct a Markovian Petz map that achieves similar performance, with only a slight compromise on the fidelity.
15 pages, 6 figures
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