Quantum Ciphertext Dimension Reduction Scheme for Homomorphic Encrypted Data

TL;DR

This paper introduces a quantum ciphertext dimension reduction scheme for homomorphically encrypted data, enabling secure, efficient quantum data processing in cloud environments with experimental validation on IBM's platform.

Contribution

It proposes a novel quantum homomorphic ciphertext dimension reduction scheme that ensures security and efficiency without interaction, validated through real quantum cloud experiments.

Findings

Achieves exponential speedup over classical algorithms under certain conditions

Ensures secure, interaction-free ciphertext dimension reduction in quantum cloud computing

Successfully verified the scheme's correctness with experimental results on IBM quantum platform

Abstract

At present, in the face of the huge and complex data in cloud computing, the parallel computing ability of quantum computing is particularly important. Quantum principal component analysis algorithm is used as a method of quantum state tomography. We perform feature extraction on the eigenvalue matrix of the density matrix after feature decomposition to achieve dimensionality reduction, proposed quantum principal component extraction algorithm (QPCE). Compared with the classic algorithm, this algorithm achieves an exponential speedup under certain conditions. The specific realization of the quantum circuit is given. And considering the limited computing power of the client, we propose a quantum homomorphic ciphertext dimension reduction scheme (QHEDR), the client can encrypt the quantum data and upload it to the cloud for computing. And through the quantum homomorphic encryption scheme to ensure security. After the calculation is completed, the client updates the key locally and decrypts the ciphertext result. We have implemented a quantum ciphertext dimensionality reduction scheme implemented in the quantum cloud, which does not require interaction and ensures safety. In addition, we have carried out experimental verification on the QPCE algorithm on IBM's real computing platform, and given a simple example of executing hybrid quantum circuits in the cloud to verify the correctness of our scheme. Experimental results show that the algorithm can perform ciphertext dimension reduction safely and effectively.