Quantum search using non-Hermitian adiabatic evolution
  We propose a non-Hermitian quantum annealing algorithm which can be useful for solving complex optimization problems. We demonstrate our approach on Grover's problem of finding a marked item inside of unsorted database. We show that the energy gap between the ground and excited states depends on the relaxation parameters, and is not exponentially small. This allows a significant reduction of the searching time. We discuss the relations between the probabilities of finding the ground state and the survival of a quantum computer in a dissipative environment. 
Alexander I. Nesterov and Gennady P. Berman
quant-ph math-ph math.MP physics.comp-ph