  In this paper we discuss how we can design Hamiltonians to implement quantum
algorithms, in particular we focus in Deutsch and Grover algorithms. As main
result of this paper, we show how Hamiltonian inverse quantum engineering
method allow us to obtain feasible and time-independent Hamiltonians for
implementing such algorithms. From our approach for the Deutsch algorithm,
different from others techniques, we can provide an alternative approach for
implementing such algorithm where no auxiliary qubit and additional resources
are required. In addition, by using a single quantum evolution, the Grover
algorithm can be achieved with high probability $1-\epsilon^2$, where
$\epsilon$ is a very small arbitrary parameter.
