  Toward an alternative approach to the quantum mechanic ground state search,
we theoretically introduce a protocol in which energy of two identical systems
are deterministically exchanged. The protocol utilizes a quantum interference
between "forward" and "backward" time evolved states with respect to a given
Hamiltonian. In addition, to make use the protocol for the ground state search,
we construct a network with which we may be able to efficiently apply the
protocol successively among multiple systems so that energy of one of them is
gradually approaching the lowest one. Although rigorous analysis on the
validity of the network is left as a future challenge, some properties of the
network are also investigated.
