Noise-adapted Quantum Error Correction for Non-Markovian Noise

TL;DR

This paper extends quantum error correction techniques to non-Markovian noise, demonstrating that adapted Petz maps can effectively protect quantum information even under complex noise conditions.

Contribution

It generalizes approximate quantum error correction conditions for non-Markovian noise and introduces practical Petz maps that outperform standard codes.

Findings

Petz map can safeguard code space in non-Markovian regimes

Non-Markovian Petz map outperforms stabilizer codes

Markovian approximation retains high fidelity

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.