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arXiv · 2609.04997

Learning unknown stabilizer codes using product measurements

Heather Leitch·Sowmya Tirukkovalluri·Yingkai Ouyang
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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.

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Heather Leitch, Sowmya Tirukkovalluri, Yingkai Ouyang. 2026-09-04. Learning unknown stabilizer codes using product measurements. https://arxiv.org/abs/2609.04997

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