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Hauptverfasser: Fernández, Pablo, Martin-Delgado, Miguel A.
Format: Preprint
Veröffentlicht: 2024
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Online-Zugang:https://arxiv.org/abs/2403.04922
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author Fernández, Pablo
Martin-Delgado, Miguel A.
author_facet Fernández, Pablo
Martin-Delgado, Miguel A.
contents We apply quantum homomorphic encryption (QHE) schemes suitable for circuits with a polynomial number of $T/T^{\dagger}$-gates to Grover's algorithm, performing a simulation in Qiskit of a Grover circuit that contains 3 qubits. The $T/T^{\dagger}$ gate complexity of Grover's algorithm is also analysed 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 to the standard Grover algorithm.
format Preprint
id arxiv_https___arxiv_org_abs_2403_04922
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Implementing the Grover Algorithm in Homomorphic Encryption Schemes
Fernández, Pablo
Martin-Delgado, Miguel A.
Quantum Physics
We apply quantum homomorphic encryption (QHE) schemes suitable for circuits with a polynomial number of $T/T^{\dagger}$-gates to Grover's algorithm, performing a simulation in Qiskit of a Grover circuit that contains 3 qubits. The $T/T^{\dagger}$ gate complexity of Grover's algorithm is also analysed 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 to the standard Grover algorithm.
title Implementing the Grover Algorithm in Homomorphic Encryption Schemes
topic Quantum Physics
url https://arxiv.org/abs/2403.04922