Fig. 1

A schematic circuit representation illustrating the key stages of GSA. The process includes initialization, where the qubits are prepared in a superposition state; marking, where the target item (items) in the database are identified and marked by the oracle; amplification, where the amplitude(s) of the marked item(s) are increased; and measurement, where the final result is obtained. Here, \(\left| 0\right\rangle\), H, and X represent the initialization of the qubit to the \(\left| 0\right\rangle\) state, the Hadamard gate, and Pauli’s X gate, respectively.