The interplay of quantum fluctuations and interactions can yield novel quantum phases of matter with fascinating properties. Particularly exciting physics is at play when confining systems to two spatial dimensions. For this case, it has been predicted that exotic quantum particles emerge —so-called “anyons”— that cannot exist in the three-dimensional world we live in. Understanding the physics of such system is a very challenging problem as it requires to solve quantum many body problems—which is generically exponentially hard on classical computers. 

In this context, universal quantum computers are potentially an ideal setting for simulating the emergent quantum many-body physics. In my talk, I will discuss how to use existing (noisy) quantum computers to simulate quantum phases of matter.  First, I will consider symmetry protected topological phases (SPT) in one-dimensional systems. For this case, ground states of Hamiltonians can be obtained using shallow quantum circuits and we can observe a quantum phase transition between different SPT phases on a quantum device. Second, we prepare the ground state of the toric code Hamiltonian in two-dimensions 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 characteristic braiding statistics of the emergent excitations.