Generating quantum error correcting codes from topological pre-thermal scars
Abstract
Quantum many-body scars are rare nonthermal states embedded within otherwise thermalizing spectra, making them promising candidates for storing and manipulating quantum information. However, a general framework that can both identify such states without prior knowledge of their microscopic scarring mechanism and determine when they enable a quantum error correcting code has remained elusive. Here, we develop an end-to-end framework connecting nonthermal-state discovery to certifiable quantum error correction using a many-body spectral localizer. By searching for states jointly localized in energy and a diagnostic observable in systems with a many-body grading symmetry, the spectral localizer identifies candidate scars within dense many-body spectra in tandem with a topological index whose shifts determine their graded subspace. For suitable pairs of same-graded scars, the grading renders grading-odd errors exactly detectable, while their localization can suppress the logical action of sufficiently local grading-even error products, yielding an approximate Knill--Laflamme condition and an operator-algebra quantum error-correction structure. We demonstrate the scar-identification framework in one- and two-dimensional density-difference-dependent bosonic models and in the PXP model, and explicitly construct the resulting approximate quantum code in the one-dimensional bosonic system. Our results establish a systematic route from identifying nonthermal many-body states to exploiting them for protecting quantum information, and position pseudospectral methods as a broadly applicable tool for discovering useful behaviors in interacting quantum systems.
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BibTeX
@misc{faugno2026generating,
title = {{Generating quantum error correcting codes from topological pre-thermal scars}},
author = {William N. Faugno and Frank Barrows and Terry A. Loring and Nathan Goldman and Alexander Cerjan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05699},
eprint = {2609.05699},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05699},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Generating quantum error correcting codes from topological pre-thermal scars
AU - William N. Faugno
AU - Frank Barrows
AU - Terry A. Loring
AU - Nathan Goldman
AU - Alexander Cerjan
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05699
UR - https://arxiv.org/abs/2609.05699
AB - Quantum many-body scars are rare nonthermal states embedded within otherwise thermalizing spectra, making them promising candidates for storing and manipulating quantum information. However, a general framework that can both identify such states without prior knowledge of their microscopic scarring mechanism and determine when they enable a quantum error correcting code has remained elusive. Here, we develop an end-to-end framework connecting nonthermal-state discovery to certifiable quantum error correction using a many-body spectral localizer. By searching for states jointly localized in energy and a diagnostic observable in systems with a many-body grading symmetry, the spectral localizer identifies candidate scars within dense many-body spectra in tandem with a topological index whose shifts determine their graded subspace. For suitable pairs of same-graded scars, the grading renders grading-odd errors exactly detectable, while their localization can suppress the logical action of sufficiently local grading-even error products, yielding an approximate Knill--Laflamme condition and an operator-algebra quantum error-correction structure. We demonstrate the scar-identification framework in one- and two-dimensional density-difference-dependent bosonic models and in the PXP model, and explicitly construct the resulting approximate quantum code in the one-dimensional bosonic system. Our results establish a systematic route from identifying nonthermal many-body states to exploiting them for protecting quantum information, and position pseudospectral methods as a broadly applicable tool for discovering useful behaviors in interacting quantum systems.
ER -