RT Journal Article
T1 Implementing semiclassical Szegedy walks in classical-quantum circuits for homomorphic encryption
A1 Ortega, Sergio A.
A1 Fernández, Pablo
A1 Martín-Delgado Alcántara, Miguel Ángel
AB As cloud services continue to expand, the security of private data stored and processed in these environments has become paramount. This work delves into quantum homomorphic encryption (QHE), an emerging technology that facilitates secure computation on encrypted quantum data without revealing the underlying information. We reinterpret QHE schemes through classical-quantum circuits (CQC), enhancing efficiency and addressing previous limitations related to key computations. Our approach eliminates the need for exponential key preparation by calculating keys in real-time during simulation, leading to a linear complexity in classically controlled gates. We also investigate the T/T dagger-gate complexity associated with various quantum walks, particularly Szegedy quantum and semiclassical algorithms, demonstrating efficient homomorphic implementations across different graph structures. Our simulations, conducted in Qiskit, validate the effectiveness of QHE for both standard and semiclassical walks. The rules for the homomorphic evaluation of the reset and intermediate measurement operations have also been included to perform the QHE of semiclassical walks. Additionally, we introduce the CQC-QHE library, a comprehensive tool that simplifies the construction and simulation of CQC tailored for QHE. Future work will focus on optimizing classical functions within this framework and exploring broader graph types to enhance QHE applications in practical scenarios.
PB IOP Publishing
SN 2632-072X
YR 2025
FD 2025-05-15
LK https://hdl.handle.net/20.500.14352/122421
UL https://hdl.handle.net/20.500.14352/122421
LA eng
NO Sergio A Ortega et al 2025 J. Phys. Complex. 6 025010
NO W911NF-14-1-0103. CT58/21-CT59/21.PRE2019-090517.
NO Ministerio de Economía, Comercio y Empresa (España)
NO Comunidad de Madrid
NO European Commission
NO Ministerio de Ciencia, Innovación y Universidades(España)
NO U.S.ArmyResearch Office
NO Universidad Complutense de Madrid
NO Banco de Santander
NO Ministerio para la Transformación Digital y de la Función Pública (España)
DS Docta Complutense
RD 19 mar 2026