Secure Delegated Variational Quantum Algorithms

Variational quantum algorithms (VQAs) can train parameterized quantum circuits via classical optimizers to find approximate solutions to some important problems. They can overcome the limitations of existing quantum technologies only allowing for a few qubits and small circuit depth and are considered as one of the most promising methods for achieving quantum advantages in the noisy intermediate-scale quantum (NISQ) era. In this paper, we propose secure delegated VQAs by utilizing quantum homomorphic encryption (QHE) for users with limited quantum power to delegate the task of running VQAs to remote quantum servers while still keeping the training data private. Firstly, a client-friendly QHE scheme that allows quantum servers to perform calculation on encrypted data is proposed to be suitable for VQAs. Then, delegated VQAs based on the given QHE scheme are presented, where servers can train the ansatz circuit using the encrypted data. Finally, a delegated variational quantum classifier to identify handwritten digit images is given as a specific example of delegated VQAs and simulated on the cloud platform of Original Quantum to show the feasibility. Secure delegated VQAs will provide significant technical support for future quantum cloud services.