Implementing Semiclassical Szegedy Walks in Classical-Quantum Circuits for Homomorphic Encryption

TL;DR

This paper advances quantum homomorphic encryption by implementing semiclassical Szegedy walks in classical-quantum circuits, reducing key complexity and enabling efficient secure quantum data processing in cloud environments.

Contribution

It introduces a novel approach to quantum homomorphic encryption using semiclassical Szegedy walks, eliminating exponential key preparation and demonstrating practical implementation with simulations.

Findings

Efficient real-time key computation reduces complexity

Successful simulation of QHE for standard and semiclassical walks

Introduction of CQC-QHE library for circuit construction

Abstract

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, 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 classical-quantum circuits tailored for quantum homomorphic encryption. Future work will focus on optimizing classical functions within this framework and exploring broader graph types to enhance QHE applications in practical scenarios.