  An attempt has been made in this paper to modify Grover's Algorithm to find
the binary string solutions approximating a target cost value. In that
direction, new Controlled Oracle and the Local Diffusion Operator are
suggested, apart from incorporating suitable ancilla qubits. A possible
strategy to estimate eigenvalues and eigenstates of a given cost Hamiltonian,
extending the reasoning of the methodology, is also pointed out. Typical
results and relevant discussions are captured to support the propositions.
