Variational secure cloud quantum computing

Variational quantum algorithms (VQAs) have been considered useful applications of noisy intermediate-scale quantum (NISQ) devices. Typically, in VQAs, a parametrized ansatz circuit generates a trial wave function, and the parameters are optimized to minimize a cost function. On the other hand, blind quantum computing (BQC) has been studied to provide quantum algorithms with security by using cloud networks. A client with a limited ability to perform quantum operations hopes to have access to a quantum computer of a server, and BQC allows the client to use the server's computer without leakage of the client's information (such as input, running quantum algorithms, and output) to the server. However, BQC is designed for fault-tolerant quantum computing, and this requires many ancillary qubits, which may not be suitable for NISQ devices. Here, we propose an efficient way to implement NISQ computing with guaranteed security for the client. In our method, only  N + 1  qubits are required, under the assumption that the form of ansätze is known to the server, where  N  denotes the necessary number of the qubits in the original NISQ algorithms. The client only performs single-qubit measurements on an ancillary qubit sent from the server, and the measurement angles can specify the parameters for the ansätze of the NISQ algorithms. The no-signaling principle guarantees that neither the parameters chosen by the client nor the outputs of the algorithm are leaked to the server.