  The constantly increasing dimensionality of artificial quantum systems
demands for highly efficient methods for their characterization and
benchmarking. Conventional quantum tomography fails for larger systems due to
the exponential growth of the required number of measurements. The conceptual
solution for this dimensionality curse relies on a simple idea - a complete
description of a quantum state is excessive and can be discarded in favor of
experimentally accessible information about the system. The probably
approximately correct (PAC) learning theory has been recently successfully
applied to a problem of building accurate predictors for the measurement
outcomes using a dataset which scales only linearly with the number of qubits.
Here we present a constructive and numerically efficient protocol which learns
a tensor network model of an unknown quantum system. We discuss the limitations
and the scalability of the proposed method.
