Many-body physics with superconducting circuits: noisy topological states

Topological states of matter are universal resources for quantum error correction and measurement-based quantum
computation. Because topological states are insensitive to local measurements, it is often extremely hard to verify
whether a quantum state is topological. In the case of symmetry-protected topological states, the topological nature
of the state is determined by the degeneracies of an exponentially large matrix, namely the reduced density matrix.
Here, we propose and realize a quantum circuit that allows us to directly probe these degeneracies using a
polynomial number of gates only. We use this circuit to identify one dimensional symmetry-protected topological
states, and distinguish them from topologically trivial states. Remarkably, our algorithm is robust to realistic noise
sources, as long as some symmetries are preserved. In the last part of my talk, I will briefly mention a recent
collaboration with the Ivry group from Technion, involving the realization of a new superconducting device with
nontrivial properties.