Non-Hermitian Adiabatic Quantum Optimization
  We propose a novel non-Hermitian adiabatic quantum optimization algorithm. One of the new ideas is to use a non-Hermitian auxiliary "initial'' Hamiltonian that provides an effective level repulsion for the main Hamiltonian. This effect enables us to develop an adiabatic theory which determines ground state much more efficiently than Hermitian methods. 
Gennady P. Berman and Alexander I. Nesterov