Quantum dynamics of complex energies: non-Hermitian quantum evolution of a single dissipative qubit

The evolution of a quantum system is governed by its discrete energies. These energies are almost always assumed to be real, as is guaranteed by Hermiticity of the system Hamiltonian. Utilizing a dissipative submanifold of a superconducting circuit we realize effective non-Hermitian dynamics, revealing novel features arising from the topology of the Riemann manifolds that describe complex energies. The degeneracies that occur with these non-Hermitian Hamiltonians are known as exceptional points. We employ quasi-static dynamical tuning of Hamiltonian parameters to encircle the exceptional point degeneracies, leading to coherent evolution between quantum states. Our work demonstrates a wholly new method for control over quantum state vectors, highlighting new facets of quantum bath engineering enabled non-Hermitian control.