Experimental learning of quantum states

The number of parameters describing a quantum state is well known to grow exponentially with the number of particles. This scaling limits our ability to characterize and simulate the evolution of arbitrary states to systems, with no more than a few qubits. However, from a computational learning theory perspective, it can be shown that quantum states can be approximately learned using a number of measurements growing linearly with the number of qubits. Here, we experimentally demonstrate this linear scaling in optical systems with up to 6 qubits. Our results highlight the power of the computational learning theory to investigate quantum information, provide the first experimental demonstration that quantum states can be "probably approximately learned" with access to a number of copies of the state that scales linearly with the number of qubits, and pave the way to probing quantum states at new, larger scales.