Demonstrating Quantum Homomorphic Encryption Through Simulation

Cloud computing allows clients with limited computational resources to offload computations to more powerful remote servers. In this paradigm, homomorphic encryption (HE) schemes enable a server to run any computation on a client's encrypted data. These schemes are widely used in cloud computing protocols such as delegated computing, two-party secure computation, and zero-knowledge proofs. Quantum homomorphic encryption (QHE) aims to achieve the objectives of HE with quantum data and quantum circuits, enabling cloud quantum servers to compute on encrypted quantum data uploaded by clients. In this work, we consider a scenario where a client has access to a quantum “encryption/decryption device”, which allows the encryption, transmission, reception, and decryption of quantum states, but not universal quantum computation. In this setting, we provide a proof-of-concept software simulation of quantum homomorphic encryption. Our code implements the “EPR scheme” of Broadbent and Jeffery, which allows for the execution of universal quantum circuits by the server at the cost of requiring shared EPR pairs between the client and server. Our implementation explores the near-term viability of the EPR scheme. Perhaps unsurprisingly, our experiments indicate that the additional cost of homomorphic circuit evaluation is minor in comparison to the simulation cost of the quantum operations. Our simulation toolkit is implemented in Python and is open-source.