Fernández Ortiz, PabloMartín-Delgado Alcántara, Miguel Ángel2026-06-022026-06-022024-11-06Fernández, Pablo, y Miguel A. Martin-Delgado. «Implementing the Grover Algorithm in Homomorphic Encryption Schemes». Physical Review Research, vol. 6, n.o 4, noviembre de 2024, p. 043109. DOI.org (Crossref), https://doi.org/10.1103/PhysRevResearch.6.043109.10.1103/PhysRevResearch.6.043109https://hdl.handle.net/20.500.14352/137119PRE2019-090517; W911NF14-1-0103We apply quantum homomorphic encryption (QHE) schemes suitable for circuits with a polynomial number of 𝑇+𝑇† gates to Grover's algorithm, performing a simulation in Qiskit of a Grover circuit that contains three qubits. The 𝑇+𝑇†-gate complexity of Grover's algorithm is also analyzed in order to show that any Grover circuit can be evaluated homomorphically in an efficient manner. We discuss how to apply these QHE schemes to allow for the efficient homomorphic evaluation of any Grover circuit composed of 𝑛 qubits using 𝑛−2 extra ancilla qubits. We also show how the homomorphic evaluation of the special case where there is only one marked item can be implemented using an algorithm that makes the decryption process more efficient compared with the standard Grover algorithm.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/journal article2643-1564https://dx.doi.org/10.1103/PhysRevResearch.6.043109https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.043109open access53530.145004.7Quantum algorithmsQuantum circuitsQuantum computingQuantum criptographyFísica (Física)Teoría de los quanta2212 Física Teórica1203 Ciencia de Los Ordenadores2210.23 Teoría Cuántica