Quantum error as an emergent magnetic field

• URL: http://arxiv.org/abs/2106.09635v1
• Date: Thu, 17 Jun 2021 16:24:58 GMT
• Title: Quantum error as an emergent magnetic field
• Authors: Shao-Kai Jian, Chunxiao Liu, Xiao Chen, Brian Swingle, Pengfei Zhang
• Abstract summary: We investigate the effect of quantum errors on a monitored Brownian Sachdev-Ye-Kitaev (SYK) model. Errors describe the loss of information about the measurement outcomes and are applied during the non-unitary evolution or at the end of the evolution.
• Score: 16.533265279392772
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the effect of quantum errors on a monitored Brownian Sachdev-Ye-Kitaev (SYK) model featuring a measurement-induced phase transition that can be understood as a symmetry-breaking transition of an effective $Z_4$ magnet in the replica space. The errors describe the loss of information about the measurement outcomes and are applied during the non-unitary evolution or at the end of the evolution. In the former case, we find that this error can be mapped to an emergent magnetic field in the $Z_4$ magnet, and as a consequence, the symmetry is explicitly broken independent of the measurement rate. R\'enyi entropies computed by twisting boundary conditions now generate domain walls even in the would-be symmetric phase at a high measurement rate. The entropy is therefore volume-law irrespective of the measurement rate. In the latter case, the error-induced magnetic field only exists near the boundary of the magnet. Varying the magnetic field leads to a pinning transition of domain walls, corresponding to error threshold of the quantum code prepared by the non-unitary SYK dynamics.

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