Mixed-State Quantum Phases: Renormalization and Quantum Error Correction

IF 11.6 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY
Shengqi Sang, Yijian Zou, Timothy H. Hsieh
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Abstract

Open system quantum dynamics can generate a variety of long-range entangled mixed states, yet it has been unclear in what sense they constitute phases of matter. To establish that two mixed states are in the same phase, as defined by their two-way connectivity via local quantum channels, we use the renormalization group (RG) and decoders of quantum error correcting codes. We introduce a real-space RG scheme for mixed states based on local channels which ideally preserve correlations with the complementary system, and we prove this is equivalent to the reversibility of the channel’s action. As an application, we demonstrate an exact RG flow of finite temperature toric code in two dimensions to infinite temperature, thus proving it is in the trivial phase. In contrast, for toric code subject to local dephasing, we establish a mixed-state toric code phase using local channels obtained by truncating an RG-type decoder and the minimum weight perfect matching decoder. We also discover a precise relation between mixed-state phase and decodability, by proving that local noise acting on toric code cannot destroy logical information without bringing the state out of the toric code phase.

Abstract Image

混合态量子相:重正化和量子纠错
开放系统量子动力学可以产生各种长程纠缠混合态,但它们在何种意义上构成物质相却一直不清楚。为了确定两个混合态处于同一相位(由它们通过局部量子通道的双向连通性定义),我们使用了重正化群(RG)和量子纠错码的解码器。我们引入了一种基于局部通道的混合态实空间 RG 方案,该方案在理想情况下保持了与互补系统的相关性,我们证明这等同于通道作用的可逆性。作为应用,我们演示了有限温度环形编码在二维到无限温度的精确 RG 流,从而证明它处于三相阶段。相反,对于受局部去相的环形码,我们利用截断 RG 型解码器和最小权重完全匹配解码器得到的局部信道,建立了混合状态环形码阶段。我们还发现了混合状态相位与可解码性之间的精确关系,证明了作用于环形码的局部噪声不会破坏逻辑信息,也不会使状态脱离环形码相位。
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来源期刊
Physical Review X
Physical Review X PHYSICS, MULTIDISCIPLINARY-
CiteScore
24.60
自引率
1.60%
发文量
197
审稿时长
3 months
期刊介绍: Physical Review X (PRX) stands as an exclusively online, fully open-access journal, emphasizing innovation, quality, and enduring impact in the scientific content it disseminates. Devoted to showcasing a curated selection of papers from pure, applied, and interdisciplinary physics, PRX aims to feature work with the potential to shape current and future research while leaving a lasting and profound impact in their respective fields. Encompassing the entire spectrum of physics subject areas, PRX places a special focus on groundbreaking interdisciplinary research with broad-reaching influence.
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