Hamiltonian and measuring time for analog quantum search

Abstract

In this work, an analog analogue of Grover's quantum search algorithm was studied. A generalized Hamiltonian driving the evolution of a quantum state in the analog search system was derived. Equations relating all parameters considered in the present problem were given according to the required maximal probability for finding the marked state. Using these equations, both the measuring time and the system energy gap suitable for a quantum search with or without certainty can thus be evaluated. Moreover, the reduction of the searching probability caused by a random and uncontrollable phase error for an initial state has been investigated. It was shown that in an efficient quantum search computation, the measuring time should be proportional to the square root of the size of the database.