Encircling exceptional points of a single dissipative qubit*

We study the behavior of a single dissipative qubit which is described by a non-Hermitian Hamiltonian. This system exhibits a degeneracy known as an exceptional point (EP) where both eigenvalues and eigenstates coalesce. According to the adiabatic theorem, slow variation of the system parameters in a closed loop transports the system back to its initial state. Surprisingly, in a loop enclosing an EP the eigenstates of the system will switch. Moreover, this behavior is chiral due to its dependence on the encircling direction and the initial state. We experimentally explore these phenomena by varying the drive parameters in a superconducting transmon circuit, creating closed loops in parameter space with one or two EPs. Our study shows how non-Hermiticities enable novel methods of quantum control.