Universal quantum computers are potentially an ideal setting for simulating emergent quantum many-body phenomena that are out of reach for classical computers.

Here we discuss two applications to the study of topologically ordered systems: First, we represent the ground states of Hamiltonians using shallow quantum circuits

and observe a quantum phase transition between different symmetry-protected topological phases on a quantum device.

Second, we prepare the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor.

We measure a topological entanglement entropy near the expected value of ln 2, and simulate anyon interferometry to extract the braiding statistics of the emergent excitations.