<p>Artificial intelligence can solve complex scientific problems beyond human capabilities, but the resulting solutions offer little insight into the underlying physical principles. One prominent example is quantum physics, where computers can discover experiments for the generation of specific quantum states, but it is unclear how finding general design concepts can be automated. Here we address this challenge by training a transformer-based language model to create human-readable Python code that generates entire families of experiments. The model is trained on millions of synthetic examples of quantum states and their corresponding experimental blueprints, enabling it to infer general construction rules rather than isolated solutions. This strategy, which we call meta-design, enables scientists to gain a deeper understanding and to extrapolate to larger experiments without additional optimization. We demonstrate that the approach can rediscover known design principles and uncover previously unknown generalizations of important quantum states, such as those from condensed-matter physics. Beyond quantum optics, the methodology provides a blueprint for applying language models to interpretable, generalizable scientific discovery across disciplines such as materials science and engineering.</p>