Learning unknown stabilizer codes using product measurements
Abstract
Efficiently characterizing quantum error correcting codes is a key challenge on the path to fault-tolerant quantum computation. Stabilizer codes, a central class of such codes, are defined by a set of stabilizer generators. Here, we present an algorithm that uses random single-qubit measurements to learn the stabilizer generators of any stabilizer code from N copies of stabilizer states in its codespace, requiring no prior knowledge of the code's structure. This also enables verification that a device implements its intended code. We derive a lower bound on N needed to recover the stabilizer generators with high probability, together with a bound on the algorithm's overall probability of success. When applied to quantum low-density parity-check (qLDPC) codes, a leading candidate for practical fault-tolerant architectures, our approach requires a number of states that scales polylogarithmically with n, the number of qubits.
Related
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- Efficient quantum Gibbs sampling of stabilizer codes using hybrid computation
- Complexity and Applications of Nearest Stabilizer Product State Problems
- Local decoders for fault-tolerant quantum computation and translation-invariant stabilizer codes
BibTeX
@misc{leitch2026learning,
title = {{Learning unknown stabilizer codes using product measurements}},
author = {Heather Leitch and Sri. S. Tirukkovalluri and Yingkai Ouyang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04997},
eprint = {2609.04997},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04997},
}
RIS
TY - UNPB
TI - Learning unknown stabilizer codes using product measurements
AU - Heather Leitch
AU - Sri. S. Tirukkovalluri
AU - Yingkai Ouyang
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.04997
UR - https://arxiv.org/abs/2609.04997
AB - Efficiently characterizing quantum error correcting codes is a key challenge on the path to fault-tolerant quantum computation. Stabilizer codes, a central class of such codes, are defined by a set of stabilizer generators. Here, we present an algorithm that uses random single-qubit measurements to learn the stabilizer generators of any stabilizer code from N copies of stabilizer states in its codespace, requiring no prior knowledge of the code's structure. This also enables verification that a device implements its intended code. We derive a lower bound on N needed to recover the stabilizer generators with high probability, together with a bound on the algorithm's overall probability of success. When applied to quantum low-density parity-check (qLDPC) codes, a leading candidate for practical fault-tolerant architectures, our approach requires a number of states that scales polylogarithmically with n, the number of qubits.
ER -