  We study the quantum evolution of a non-Hermitian qubit realized as a
submanifold of a dissipative superconducting transmon circuit. Real-time tuning
of the system parameters to encircle an exceptional point results in
non-reciprocal quantum state transfer. We further observe chiral geometric
phases accumulated under state transport, verifying the quantum coherent nature
of the evolution in the complex energy landscape and distinguishing between
coherent and incoherent effects associated with exceptional point encircling.
Our work demonstrates an entirely new method for control over quantum state
vectors, highlighting new facets of quantum bath engineering enabled through
dynamical non-Hermitian control.
