Shortcuts to adiabaticity for non-Hermitian dynamics in the vicinity of higher-order exceptional points*

The complex energy spectrum of an effective non-Hermitian Hamiltonian can possess unique topology in the space of Hamiltonian parameters. Tuning these parameters allows us to realize non-trivial phenomena and invariants associated with their special degeneracies. We investigate how real-time parameter tuning can be used to observe these topology-dependent phenomena. In practice, however, adiabatic processes require long evolution times, which are not desirable for practical purposes, nor possible in many experimental setups in open quantum systems, especially those described by effective non-Hermitian Hamiltonians. Shortcuts to adiabaticity emulate the dynamics expected from slow adiabatic evolution in a fast time-dependent process. We harness a superconducting circuit platform to realize dynamical control of the system in the vicinity of its Hamiltonian exceptional points. Additional counter-diabatic controls improve the fidelity of the system's evolution.