Continuous quantum correction on Markovian and Non-Markovian models

• URL: http://arxiv.org/abs/2505.18400v3
• Date: Tue, 24 Jun 2025 23:54:38 GMT
• Title: Continuous quantum correction on Markovian and Non-Markovian models
• Authors: Juan Garcia Nila, Todd A. Brun,
• Abstract summary: We compare performance under a Markovian error model to two distinct non-Markovian models.<n>We find that continuous quantum error correction has enhanced performance against non-Markovian noise.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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