Noise-strength-adapted approximate quantum codes inspired by machine learning

We demonstrate that machine learning provides a powerful tool for discovering new approximate quantum error-correcting (AQEC) codes beyond conventional algebraic frameworks. Building upon direct observations through hybrid quantum-classical learning, we discover two new 4-qubit amplitude damping codes with an innovative noise-strength-adaptive (NSA) feature where the codeword varies with noise strength. They are NSA self-complementary and NSA pair-complementary codes. We show that they can both outperform conventional codes for amplitude damping (AD) noise. The 4-qubit self-complementary NSA code outperforms the standard LNCY AD code in fidelity and Knill-Laflamme condition violation. The pair-complementary code, which has no known non-NSA analog, achieves even better performance with higher-order loss suppression and better fidelity. We further generalize both approaches to families of NSA AD codes for arbitrary system size, as well as an NSA variant of the 0-2-4 binomial code for single-photon loss. 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 new valuable code formalisms that may not emerge from traditional design approaches.