Optimization of Initial States for Adiabatic Quantum Computing in a Quantum Algorithm

In any adiabatic quantum computation, there exist an initial state that must be used in the corresponding quantum algorithm. In this paper, the relation between an initial state and allowed energy level of an implemented generalized Deutsch’s algorithm is investigated. To study the generalized Deutsch’s algorithm, a compacted form for the output states of the algorithm is obtained. It has been shown that one can prepare the initial states in such a way that control the minimum of energy. By using numerical methods, the minimum values of allowed energy levels for the initial state are obtained. Also, to study the dynamics of the system is chosen. The corresponding Hamiltonian for the algorithm is obtained and it has been shown that one of the energy levels describes a binding state.