Quantum search using non-Hermitian adiabatic evolution

Alexander I. Nesterov, Gennady P. Berman

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.

Quantum Physics (quant-ph); Mathematical Physics (math-ph); Computational Physics (physics.comp-ph)

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