Continuous quantum correction on Markovian and Non-Markovian models

TL;DR

This paper compares the effectiveness of continuous quantum error correction under Markovian and non-Markovian noise models, finding improved performance against non-Markovian noise due to the quantum Zeno effect.

Contribution

It introduces and systematically compares two distinct non-Markovian error models with the Markovian case in the context of quantum error correction, highlighting the role of the quantum Zeno effect.

Findings

Fidelity decays slower in non-Markovian models than in Markovian.

Non-Markovian noise models show enhanced quantum error correction performance.

Presence of quantum Zeno regime explains improved fidelity in non-Markovian cases.

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.