Automatic generation of efficient oracles: The less-than case

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 generalisation 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, Diagonal. We show that the depth of our less-than oracle implementation is always lower. In addition, a comparison with another method for oracle generation in terms of gate count is also conducted to prove the efficiency of our method. The result presented here is part of a research work that aims to achieve reusable quantum operations that can be composed to perform more complex ones. The final aim is to provide Quantum Developers with tools that can be easily integrated in their programs/circuits.