CSS codes for Quantum Metrology with Discrete-time Error Correction
Abstract
The goal of quantum metrology is to estimate an unknown parameter with better-than-classical precision and, ideally, to attain Heisenberg scaling. In realistic settings, however, noise can substantially reduce this advantage and, in many cases, restore standard-quantum-limit-like performance. Preserving the quantum enhancement therefore requires noise-robust strategies, which can be implemented using quantum error correction. In this work, we develop and analyze a quantum-metrology protocol based on Calderbank-Shor-Steane (CSS) codes. The main result is that, for noise perpendicular to the sensing Hamiltonian, discrete-time error correction preserves Heisenberg-like temporal scaling over a finite interrogation-time window whose duration depends on the correction frequency. It is further shown that recovery applied only after the sensing evolution provides no metrological advantage over the corresponding uncorrected noisy protocol in the setup considered here. An analytical framework is developed for arbitrary CSS codes and applied to the Steane and Shor codes, for which the discrete-time corrected dynamics, the Heisenberg-like-to-SQL-like crossover, and the optimal interrogation time are determined and numerically analysed.
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BibTeX
@misc{liaubaitė2026codes,
title = {{CSS codes for Quantum Metrology with Discrete-time Error Correction}},
author = {Ugnė Liaubaitė and Debora Ramacciotti and Robert Raußendorf},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40022},
eprint = {2609.40022},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40022},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - CSS codes for Quantum Metrology with Discrete-time Error Correction
AU - Ugnė Liaubaitė
AU - Debora Ramacciotti
AU - Robert Raußendorf
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40022
UR - https://arxiv.org/abs/2609.40022
AB - The goal of quantum metrology is to estimate an unknown parameter with better-than-classical precision and, ideally, to attain Heisenberg scaling. In realistic settings, however, noise can substantially reduce this advantage and, in many cases, restore standard-quantum-limit-like performance. Preserving the quantum enhancement therefore requires noise-robust strategies, which can be implemented using quantum error correction. In this work, we develop and analyze a quantum-metrology protocol based on Calderbank-Shor-Steane (CSS) codes. The main result is that, for noise perpendicular to the sensing Hamiltonian, discrete-time error correction preserves Heisenberg-like temporal scaling over a finite interrogation-time window whose duration depends on the correction frequency. It is further shown that recovery applied only after the sensing evolution provides no metrological advantage over the corresponding uncorrected noisy protocol in the setup considered here. An analytical framework is developed for arbitrary CSS codes and applied to the Steane and Shor codes, for which the discrete-time corrected dynamics, the Heisenberg-like-to-SQL-like crossover, and the optimal interrogation time are determined and numerically analysed.
ER -