Quantum states in the trivial phase can be efficiently learned from measurements and regenerated using shallow circuits, providing a theoretical foundation for quantum generative models without needing the original preparation circuit.
This paper shows how to learn and generate quantum mixed states that belong to the 'trivial phase'—states preparable by shallow quantum circuits that preserve local reversibility. The algorithm learns from measurement data alone and outputs a shallow circuit that recreates the state, with polynomial sample complexity and runtime. The work also extends to classical diffusion models.