Noise-adapted Quantum Error Correction for Non-Markovian Noise

• URL: http://arxiv.org/abs/2411.09637v1
• Date: Thu, 14 Nov 2024 18:03:16 GMT
• Title: Noise-adapted Quantum Error Correction for Non-Markovian Noise
• Authors: Debjyoti Biswas, Shrikant Utagi, Prabha Mandayam,
• Abstract summary: We show that conditions for approximate QEC can be easily generalized for the case of non-Markovian noise. We also construct a Markovian Petz map that achieves similar performance, with only a slight compromise on the fidelity.
• Score: 1.8799303827638123
• License:
• 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.

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