Entanglement Structure and Information Protection in Noisy Hybrid Quantum Circuits

• URL: http://arxiv.org/abs/2401.01593v2
• Date: Fri, 14 Jun 2024 08:18:08 GMT
• Title: Entanglement Structure and Information Protection in Noisy Hybrid Quantum Circuits
• Authors: Shuo Liu, Ming-Rui Li, Shi-Xin Zhang, Shao-Kai Jian,
• Abstract summary: This Letter contributes to a deeper understanding of the interplay between quantum noises and measurement-induced phase transition. It also provides a new perspective to understand the effects of Markovian and non-Markovian noises on quantum computation.
• Score: 3.326868738829707
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the context of measurement-induced entanglement phase transitions, the influence of quantum noises, which are inherent in real physical systems, is of great importance and experimental relevance. In this Letter, we present a comprehensive theoretical analysis of the effects of both temporally uncorrelated and correlated quantum noises on entanglement generation and information protection. This investigation reveals that entanglement within the system follows $q^{-1/3}$ scaling for both types of quantum noises, where $q$ represents the noise probability. The scaling arises from the Kardar-Parisi-Zhang fluctuation with effective length scale $L_{\text{eff}} \sim q^{-1}$. More importantly, the information protection timescales of the steady states are explored and shown to follow $q^{-1/2}$ and $q^{-2/3}$ scaling for temporally uncorrelated and correlated noises, respectively. The former scaling can be interpreted as a Hayden-Preskill protocol, while the latter is a direct consequence of Kardar-Parisi-Zhang fluctuations. We conduct extensive numerical simulations using stabilizer formalism to support the theoretical understanding. This Letter not only contributes to a deeper understanding of the interplay between quantum noises and measurement-induced phase transition but also provides a new perspective to understand the effects of Markovian and non-Markovian noises on quantum computation.

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