  Variational quantum algorithms (VQAs) are considered as one of the most
promising candidates for achieving quantum advantages on quantum devices in the
noisy intermediate-scale quantum (NISQ) era. They have been developed for
numerous applications such as image processing and solving linear systems of
equations. The application of VQAs can be greatly enlarged if users with
limited quantum capabilities can run them on remote powerful quantum computers.
But the private data of clients may be leaked to quantum servers in such a
quantum cloud model. To solve the problem, a novel quantum homomorphic
encryption (QHE) scheme which is client-friendly and suitable for VQAs is
constructed for quantum servers to calculate encrypted data. Then delegated
VQAs are proposed based on the given QHE scheme, where the server can train the
ansatz circuit using the client's data even without knowing the real input and
the output of the client. Furthermore, 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 its feasibility.
