General Hamiltonian for quantum searching with certainty

A general consideration to the Hamiltonian for quantum searching is undertaken in this work. We have established the matching condition to a certaint searching and derived an ideal Hamiltonian. We also show that this Hamiltonian can be resuced to all known quantum searching Hamiltonians. A quantum mechanical algorithm is a complete and straightforward set of directions, based on the quntum physical process which possess the unique features of superpositions and entanglement, to accomplish a computation in a finite number of steps. Each step in the algorithm is designed by a sequence of unitary operators that transform the initial state to a desired one. We usually consider that these transformations are composed of several universal quantum logic gates. Therefore, this way to think about the construction of a quantum mechanical algorithm is called the quantum circuit model for quantum computing. Famous examples include the quantum factorizing algorithm discorvered by Shor[1] and the quantum searching algorithm well developed by Grover[2]. The latter is what we intend to discuss in this work. Quantum circuit model is a conventional way to consider the quantum algorithm. However, there exists another picture, based on a fundamental postulate, to quantum computation. The quantum postulate states that the time evolution of the state vector of a closed quantum system is described by the Schrödinger equation[3], ih̄ d |Ψ(t)〉 dt = H(t) |Ψ(t)〉 , (1)