Exploring the topology of a non-Hermitian qubit using shortcuts to adiabaticity

Open quantum systems described by a non-Hermitian Hamiltonian exhibit intriguing dynamics due to their complex energy spectrum. The complex energy around the exceptional point degeneracies allows for topological state transport, chiral geometric phases, and eigenvalue braiding. To access these features, it is desirable to drive the system adiabatically along the Riemann surface. However, the imaginary part of the energy corresponds to gain or loss which makes it challenging to perform adiabatic evolution. Previous experiments have shown that slowly driving the system can transport the quantum state across the Riemann surface. This is observed for the quantum state with relative gain, whereas the other state is subject to loss and therefore does not evolve adiabatically. In this work, we harness the notion of shortcuts to adiabaticity to drive the system faster, avoiding the effects of loss while maintaining trajectories that follow the instantaneous eigenstates. We study the robustness of this control method using a superconducting transmon circuit with engineered dissipation around the 2nd order exceptional point of its effective non-Hermitian Hamiltonian. This method can be extended to explore the more complicated energy structures of higher order exceptional points.