Structured search algorithm: A quantum leap

Abstract: We introduce a structured quantum search algorithm that leverages entanglement maps and a fixed-point method to minimize oracle query complexity in unsorted datasets. By partitioning qubits into rows based on their entanglement order, the algorithm enables parallel subspace searches, achieving solution identification with at most two oracle calls per row. Experimental results on IBM Kyiv hardware demonstrate successful searches in datasets with up to 5 TB of unsorted data. Our findings indicate that with optimal encoding, the quantum search complexity becomes $\mathcal{O}(1)$, that is, independent of the dataset size $N$, surpassing both classical $\mathcal{O}(N)$ and Grover's $\mathcal{O}(\sqrt{N})$ scaling. Furthermore, the letter hypothesizes a scalable simulation of the said algorithm using classical means.