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Homomorphic encryption of the k=2 Bernstein–Vazirani algorithm Fernández Ortiz, Pablo Martín-Delgado Alcántara, Miguel Ángel ©2024 The Author(s). W911NF-14-1-0103, PRE2019-090517 We introduce a class of circuits that solve a particular case of the Bernstein-Vazirani recursive problem for second-level recursion. This class of circuits allows for the implementation of the oracle using a number of T-gates that grows linearly with the number of qubits in the problem. We find an application of this scheme to quantum homomorphic encryption (QHE), which is an important cryptographic technology useful for delegated quantum computing, allowing a remote server to perform quantum computations on encrypted quantum data, so that the server cannot know anything about the client's data. Liang's QHE schemes are suitable for circuits with a polynomial number of gates T/T† dagger. Thus, the simplified circuits we have constructed can be evaluated homomorphically in an efficient manner. 2026-06-03T18:33:24Z 2026-06-03T18:33:24Z 2024-08-22 journal article Pablo Fernández and Miguel A Martin-Delgado 2024 J. Phys. A: Math. Theor. 57 365301 1751-8113 10.1088/1751-8121/ad6c04 https://hdl.handle.net/20.500.14352/137164 1751-8121 https://doi.org/10.1088/1751-8121/ad6c04 https://iopscience.iop.org/article/10.1088/1751-8121/ad6c04 https://arxiv.org/abs/2303.17426 eng info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2021-122547NB-I00/ES/TECNOLOGIAS CLAVE PARA COMPUTACION CUANTICA/ MaDQuantum-CM S2018/TCS-4342 http://creativecommons.org/licenses/by/4.0/ open access Attribution 4.0 International IOP Publishing