  Entanglement properties are routinely used to characterize phases of quantum
matter in theoretical computations. For example the spectrum of the reduced
density matrix, or so-called "entanglement spectrum", has become a widely used
diagnostic for universal topological properties of quantum phases. However,
while being convenient to calculate theoretically, it is notoriously hard to
measure in experiments. Here we use the IBM quantum computer to make the first
ever measurement of the entanglement spectrum of a symmetry-protected
topological state. We are able to distinguish its entanglement spectrum from
those we measure for trivial and long-range ordered states.
