  Experimental progress in qubit manufacturing calls for the development of new
theoretical tools to analyze quantum data. We show how an unsupervised
machine-learning technique can be used to understand short-range entangled
many-qubit systems using data of local measurements. The method successfully
constructs the phase diagram of a cluster-state model and detects the
respective order parameters of its phases, including string order parameters.
For the toric code subject to external magnetic fields, the machine identifies
the explicit forms of its two stabilizers. Prior information of the underlying
Hamiltonian or the quantum states is not needed; instead, the machine outputs
their characteristic observables. Our work opens the door for a
first-principles application of hybrid algorithms that aim at strong
interpretability without supervision.
