Learning to Concatenate Quantum Codes
This work addresses the problem of efficient quantum error correction for early fault-tolerant quantum computers by reducing qubit overhead through adaptive code selection.
The authors automate the selection of quantum error correction codes in a concatenated scheme by learning the effective noise channel at each level, achieving target logical error rates with up to two orders of magnitude fewer qubits compared to standard stabilizer codes for structured noise.
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an optimal code sequence. We automate this choice by estimating the effective noise channel after each level and selecting the next code accordingly. In particular, we use learning-based methods to tailor small, non-additive encoders when the noise exhibits sufficient structure, then switch to standard codes once the noise is nearly uniform. In simulations, this level-wise adaptation achieves a target logical error rate with far fewer qubits than concatenating stabilizer codes alone--reducing qubit counts by up to two orders of magnitude for strongly structured noise. Therefore, this hybrid, learning-based strategy offers a promising tool for early fault-tolerant quantum computing.