Simulation of Quantum Homomorphic Encryption

Abstract

When interacting with a cloud server, two ideals we could aim for, among others, are performing computation and ensuring the privacy of the data. Quantum homomorphic encryption is a cryptographic primitive that seeks to address these two objectives in the quantum setting, allowing for quantum computation on encrypted quantum data. In this work, we provide a software simulation of a quantum homomorphic encryption scheme, known as the "EPR scheme", for universal quantum circuits, developed by Broadbent and Jeffery.

We demonstrate the near-term viability of this scheme and provide evidence that the computational cost of classical subroutines in the simulation is negligible compared to the cost of simulating the quantum operations. The simulation package is an open-source Python implementation, called "py-qhe-epr", with a focus on extensive documentation and ease of use for educational, verification and adaptability purposes, supporting future research and development. Furthermore, this implementation serves as a step towards further hardware applications of quantum homomorphic encryption between networked quantum devices.