Monolithic Quantum Error Correction in the Presence of Distinguishability
Abstract
Quantum error-correcting codes require that the environment cannot distinguish relevant error processes acting on different codewords. In practice, residual Zeeman, Stark, or anharmonic interactions shift the underlying states, making errors distinguishable and weakening the conditions for perfect recovery. We study this effect with an analytically solvable four-level model and a canonical spontaneous-emission noise model for atoms and molecules. Distinguishability raises the effective Kraus rank of the noise channel, lowers the recovered fidelity, and sets an operational checking time that shortens as the frequency separation between the emitted photons increases. We find that rapid syndrome checking suppresses the buildup of distinguishability and quantify how fast one needs to check to restore near-perfect recovery. Error distinguishability is thus a practical limitation of monolithic error correction, and our analysis identifies fast syndrome extraction as a route to mitigating it.
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BibTeX
@misc{jain2026monolithic,
title = {{Monolithic Quantum Error Correction in the Presence of Distinguishability}},
author = {Shubham P. Jain and Eric R. Hudson and Wesley C. Campbell and Alexey V. Gorshkov and Victor V. Albert},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26946},
eprint = {2609.26946},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26946},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Monolithic Quantum Error Correction in the Presence of Distinguishability
AU - Shubham P. Jain
AU - Eric R. Hudson
AU - Wesley C. Campbell
AU - Alexey V. Gorshkov
AU - Victor V. Albert
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26946
UR - https://arxiv.org/abs/2609.26946
AB - Quantum error-correcting codes require that the environment cannot distinguish relevant error processes acting on different codewords. In practice, residual Zeeman, Stark, or anharmonic interactions shift the underlying states, making errors distinguishable and weakening the conditions for perfect recovery. We study this effect with an analytically solvable four-level model and a canonical spontaneous-emission noise model for atoms and molecules. Distinguishability raises the effective Kraus rank of the noise channel, lowers the recovered fidelity, and sets an operational checking time that shortens as the frequency separation between the emitted photons increases. We find that rapid syndrome checking suppresses the buildup of distinguishability and quantify how fast one needs to check to restore near-perfect recovery. Error distinguishability is thus a practical limitation of monolithic error correction, and our analysis identifies fast syndrome extraction as a route to mitigating it.
ER -