We demonstrate that machine learning provides a powerful tool for discovering approximate quantum error-correcting (AQEC) codes beyond conventional algebraic frameworks. Building upon observations from hybrid quantum-classical learning, we introduce families of noise-strength-adapted (NSA) codes whose codewords vary with noise strength. In particular, through machine learning, we first identify four-qubit NSA self-complementary and pair-complementary codes that outperform standard Leung–Nielsen–Chuang–Yamamoto amplitude damping (AD) code in both worst-case fidelity and Knill–Laflamme condition violation. We then derive analytical generalizations of both forms into families of NSA AD codes for arbitrary numbers of qubits, as well as an NSA variant of the 0-2-4 binomial code for single-photon loss. We note that the pair-complementary codes, which have no known non-NSA analogs, achieve even better performance, with higher-order loss suppression and larger fidelity, than the self-complementary ones. Our results demonstrate that adaptation to noise strength can systematically lead to significant improvements in error correction capability and also showcase how machine learning can help discover valuable code formalisms that may not emerge from traditional design approaches.

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• Machine learning
• Quantum error correction