Physicists are accustomed to learning about the world by solving models. Usually, in the field of quantum materials, we start with a quantum model of a material and solve it to find wave functions that tell us about the material’s properties. Here, we propose an alternative “inverse method” for studying quantum materials in which we work backwards: We start with a wave function with a desired property and find many new models with that wave function as a solution. This approach fits into a broader class of techniques, such as machine learning approaches, for automating physical understanding, which previously required significant insight.

We develop a novel algorithm that carries out this inverse method automatically and efficiently for general quantum systems and that can be readily implemented with existing numerical tools. The key step of the algorithm is the evaluation and analysis of the quantum covariance matrix, a quantum mechanical generalization of a statistical covariance matrix. We test our algorithm on numerous wave functions and find a myriad of new models.

Because quantum models are essential for building our understanding of quantum mechanics, our algorithm could be an important tool for future advances in quantum physics. For example, new models discovered by our algorithm could potentially aid in the synthesis of new materials or the simulation of new types of quantum systems.