Implementation and Analysis of Quantum Homomorphic Encryption

Growing interest in the field of quantum computing is fueled by quantum computers projected ”quantum supremacy” in speed and security. The potential for ultra-high speeds may produce a dramatic change in data science, machine learning, analytics, and information processing. This research study will focus on encryption algorithms where quantum computing may affect protocols and deciphering codes. Specifically, homomorphic encryption (HE) enables mathematical operations to be performed on encrypted data without having to decrypt the data in the process. Quantum homomorphic encryption (QHE) enables quantum circuits to be performed on encrypted qubits. In this research experience for undergraduates (REU) study, we design quantum circuits to implement QHE on a quantum teleportation circuit. The teleportation algorithm is profiled in terms of performance and complexity and comparative results are provided for encoded versus unencoded circuits. This work serves as a building block for encrypting more complex quantum algorithms such as Quantum Neural Networks (QNN).