  Grover's algorithm is a well-known contribution to quantum computing. It
searches one value within an unordered sequence faster than any classical
algorithm. A fundamental part of this algorithm is the so-called oracle, a
quantum circuit that marks the quantum state corresponding to the desired
value. A generalization of it is the oracle for Amplitude Amplification, that
marks multiple desired states. In this work we present a classical algorithm
that builds a phase-marking oracle for Amplitude Amplification. This oracle
performs a less-than operation, marking states representing natural numbers
smaller than a given one. Results of both simulations and experiments are shown
to prove its functionality. This less-than oracle implementation works on any
number of qubits and does not require any ancilla qubits. Regarding depth, the
proposed implementation is compared with the one generated by Qiskit automatic
method, UnitaryGate. We show that the depth of our less-than oracle
implementation is always lower. This difference is significant enough for our
method to outperform UnitaryGate on real quantum hardware.
