Learning unknown stabilizer codes using product measurements

• URL: http://arxiv.org/abs/2609.04997v1
• Date: Fri, 04 Sep 2026 11:08:46 GMT
• Title: Learning unknown stabilizer codes using product measurements
• Abstract summary: We present an algorithm that learns the stabilizer generators of any stabilizer code from $N$ copies of stabilizer states in its codespace.<n>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.
• Score: 3.058685580689604
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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