Realizing lattice topological insulators and higher-order topological insulators on a quantum computer

The ascendency of quantum computing technologies, particularly cloud quantum computing, has made the physical realization of various elusive quantum Hamiltonians possible. In this talk, I shall discuss recent realizations of various topological states with the IBM quantum computer, including but not limited to the Kitaev chain, Chern states and higher-order topological states. To circumvent the limited qubit numbers of present-day NISQ devices, higher-dimensional noninteracting lattices are mapped onto a 1D interacting chain. This technique takes advantage of the quantum many-body nature of the quantum hardware in realizing higher-dimensional states of unprecedented complexity.