Mixed-State Quantum Phases: Renormalization and Quantum Error Correction,Physical Review X

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Mixed-State Quantum Phases: Renormalization and Quantum Error Correction
Physical Review X ( IF 11.6 ) Pub Date : 2024-09-10 , DOI: 10.1103/physrevx.14.031044
Shengqi Sang _{1,

2,

3} , Yijian Zou _{1,

4} , Timothy H. Hsieh ₁

Affiliation

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.

Published by the American Physical Society

2024

中文翻译：

混合态量子相：重整化和量子纠错

开放系统量子动力学可以产生各种长程纠缠混合态，但尚不清楚它们在什么意义上构成物质的相。为了确定两个混合态处于同一相位，由它们通过本地量子通道的双向连接来定义，我们使用了量子纠错码的重整化组（RG）和解码器。我们引入了一种基于局部通道的混合状态的实空间 RG 方案，该方案在理想情况下保持与互补系统的相关性，并且我们证明了这相当于通道动作的可逆性。作为一个应用，我们演示了有限温度复曲面码在二维到无限温度的精确 RG 流，从而证明它处于平凡相。相反，对于受局部相位控制的复曲面码，我们使用通过截断 RG 型解码器和最小权重完美匹配解码器获得的局部信道建立混合状态复曲面码相位。我们还通过证明作用于复曲面码的局部噪声无法在不将状态带出复曲面码相位的情况下破坏逻辑信息，发现了混合状态相位和可解码性之间的精确关系。美国物理学会 2024 年出版

更新日期：2024-09-10

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