Deterministic Quantum Search for Index Retrieval: Algorithm Design and Implementation

Searching for index corresponding to a given data in an unsorted database represents a nontrivial unstructured search problem with wide-ranging applications in fields like data mining, cryptography, and bio-informatics. Unlike the reverse query, where the data can be trivially obtained from a known index, retrieving the index from data lacks order preservation, making efficient classical search infeasible without linear traversal. To address this problem, we propose a deterministic quantum search algorithm, which provides a solution for the database having any arbitrary number of entries while always guaranteeing success in a single execution. The algorithm is formulated within the quantum circuit model, employing amplitude manipulation techniques that eliminate probabilistic outcomes and ensure exact retrieval of the location of data. We present a scalable circuit construction adaptable to databases of varying sizes, without constraints such as number of entries equal to power-of-two. Because of its adaptability, the proposed algorithm is directly applicable to real-world datasets without the need for costly pre-processing or ineffective data padding. The proposed work presents a resilient and exact technique for the quantum index retrieval problem by providing a solution offering wide applicability and dependable outputs. Our findings shows a clear way towards quantum primitives that can be easily included into deterministic computing workflows, bridging the gap between theoretical speedup and the real-world requirement for dependable outputs.