  Quantum information systems are on a path to vastly exceed the complexity of
any classical device. The number of entangled qubits in quantum devices is
rapidly increasing and the information required to fully describe these systems
scales exponentially with qubit number. This scaling is the key benefit of
quantum systems, however it also presents a severe challenge. To characterize
such systems typically requires an exponentially long sequence of different
measurements, becoming highly resource demanding for large numbers of qubits.
Here we propose a novel and scalable method to characterize quantum systems,
where the complexity of the measurement process only scales linearly with the
number of qubits. We experimentally demonstrate an integrated photonic chip
capable of measuring two- and three-photon quantum states with reconstruction
fidelity of 99.67%.
