Measuring a topological transition in an artificial spin 1/2 system

We present measurements of a topological property, the Chern number (\(C_\mathrm{1}\)), of a closed manifold in the space of two-level system Hamiltonians, where the two-level system is formed from a superconducting qubit. We manipulate the parameters of the Hamiltonian of the superconducting qubit along paths in the manifold and extract \(C_\mathrm{1}\) from the nonadiabitic response of the qubit. By adjusting the manifold such that a degeneracy in the Hamiltonian passes from inside to outside the manifold, we observe a topological transition \(C_\mathrm{1} = 1 \rightarrow 0\). Our measurement of \(C_\mathrm{1}\) is quantized to within 2 percent on either side of the transition.