Bulletin of the American Physical Society
APS March Meeting 2024
Monday–Friday, March 4–8, 2024; Minneapolis & Virtual
Session F31: Topology and Quantum Chaos in Many-Body Systems
8:00 AM–10:24 AM,
Tuesday, March 5, 2024
Room: 102C
Sponsoring
Units:
GSNP DQI DCMP
Chair: Tan Van Vu, Riken Center for Quantum Computing
Abstract: F31.00009 : Mixed-state Quantum Phases: Renormalization and Quantum Error Correction
9:36 AM–9:48 AM
Presenter:
Shengqi Sang
(Perimeter Inst for Theo Phys)
Authors:
Shengqi Sang
(Perimeter Inst for Theo Phys)
Yijian Zou
(Perimeter Inst for Theo Phys)
Timothy Hsieh
(Perimeter Institute for Theoretical Physics)
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.
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