The recent advances in qubit manufacturing and coherent control of synthetic quantum matter are leading to a new generation of intermediate scale quantum hardware, with promising progress towards simulation of quantum matter and materials. In order to enhance the capabilities of this class of quantum devices, some of the more arduous experimental tasks can be off-loaded to classical algorithms running on conventional computers. In this seminar, I will present a framework based on industry-standard machine learning algorithms to perform approximate quantum state reconstruction from qubit measurement data. The resulting neural-network wavefunctions can be deployed to perform measurements of observables not accessible in the original experimental platform. I will demonstrate this approach for extracting the entanglement entropy from experimental cold-atom data, and for quantum chemistry simulations using superconducting qubits.