RT Journal Article
T1 Implementing the Grover algorithm in homomorphic encryption schemes
A1 Fernández Ortiz, Pablo
A1 Martín-Delgado Alcántara, Miguel Ángel
AB We 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.
PB American Physical Society
YR 2024
FD 2024-11-06
LK https://hdl.handle.net/20.500.14352/137119
UL https://hdl.handle.net/20.500.14352/137119
LA eng
NO Fernández, 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.
NO PRE2019-090517;W911NF14-1-0103
NO Ministerio de Ciencia, Innovación y Universidades (España)
NO Agencia Estatal de Investigación (España)
NO European Commission
NO Comunidad de Madrid
NO Ministerio de Transformación Digital y Función Pública (España)
NO Army Research Office (US)
DS Docta Complutense
RD 8 jun 2026