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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2505.18400 |
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| _version_ | 1866910042674954240 |
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| author | Nila, Juan Garcia Brun, Todd A. |
| author_facet | Nila, Juan Garcia Brun, Todd A. |
| contents | We investigate continuous quantum error correction, comparing performance under a Markovian error model to two distinct non-Markovian models. The first non-Markovian model involves an interaction Hamiltonian between the system and an environmental qubit via an X-X coupling, with a "cooling" bath acting on the environment qubit. This model is known to exhibit abrupt transitions between Markovian and non-Markovian behavior. The second non-Markovian model uses the post-Markovian master equation (PMME), which represents the bath correlation through a memory kernel; we consider an exponentially decaying kernel and both underdamped and overdamped dynamics. We systematically compare these non-Markovian error models against the Markovian case and against each other, for a variety of different codes. We start with a single qubit, which can be solved analytically. We then consider the three-qubit repetition code and the five-qubit "perfect" code. In all cases, we find that the fidelity decays more rapidly in the Markovian case than in either non-Markovian model, suggesting that continuous quantum error correction has enhanced performance against non-Markovian noise. We attribute this difference to the presence of a quantum Zeno regime in both non-Markovian models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18400 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuous quantum correction on Markovian and Non-Markovian models Nila, Juan Garcia Brun, Todd A. Quantum Physics We investigate continuous quantum error correction, comparing performance under a Markovian error model to two distinct non-Markovian models. The first non-Markovian model involves an interaction Hamiltonian between the system and an environmental qubit via an X-X coupling, with a "cooling" bath acting on the environment qubit. This model is known to exhibit abrupt transitions between Markovian and non-Markovian behavior. The second non-Markovian model uses the post-Markovian master equation (PMME), which represents the bath correlation through a memory kernel; we consider an exponentially decaying kernel and both underdamped and overdamped dynamics. We systematically compare these non-Markovian error models against the Markovian case and against each other, for a variety of different codes. We start with a single qubit, which can be solved analytically. We then consider the three-qubit repetition code and the five-qubit "perfect" code. In all cases, we find that the fidelity decays more rapidly in the Markovian case than in either non-Markovian model, suggesting that continuous quantum error correction has enhanced performance against non-Markovian noise. We attribute this difference to the presence of a quantum Zeno regime in both non-Markovian models. |
| title | Continuous quantum correction on Markovian and Non-Markovian models |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2505.18400 |