Topological codes revisited: Hamiltonian learning and topological phase transitions

The efficient validation of quantum devices is critical for emerging technological applications. The precise engineering of a Hamiltonian is required both for the implementation of quantum information processing as well as for quantum memories. Inferring the experimentally realized Hamiltonian through a scalable number of measurements constitutes the challenging task of Hamiltonian learning. In particular, assessing the quality of the implementation of topological codes is essential for quantum error correction. We introduce a neural net based approach to this challenge. We capitalize on a family of exactly solvable models to train our algorithm and generalize to a broad class of experimentally relevant sources of errors. We discuss how our algorithm scales with system size and analyze its resilience towards noise. A related issue regarding topological codes is to ensure that the system does not leave the topological manifold due to experimental noise. We present an unsupervised machine learning technique that is able to detect topological order from experimentally accessible data.