Quantum states can be described by matrices whose size grows exponentially with the size of the underlying physical system. Since storing these objects becomes infeasible already for moderate sized systems, recent work has proposed classical shadows, a framework in which allows to reuse collected measurements to predict the measurement outcome for unseen observables. The original protocol is based on measuring random Pauli observables or clifford observables and only works for local observables, i.e. observables which only act non-trivially on a small number of qubits. In this work, we aim to extend the protocol to a different class of random measurements, enabling to predict a more general class of observables. Furthermore, we may explore deep learning-based methods. In order to probe states of convincing sizes, we are planning to run simulations based on tensor-networks. Supervisor: Devdatt Dubhashi, Chalmers tekniska högskola