Fault-tolerant blind quantum computing using GHZ states over depolarization channel

Blind quantum computing (BQC) allows a client with limited quantum technology to delegate her quantum computational tasks to a server who can perform universal quantum computation while retaining the client’s secret information. Firstly, in qubits transmission between the server and the client, the loss of qubits is inevitable due to the channel noise. Thus, we propose a fault-tolerant framework for blind quantum computing using logical GHZ states over depolarization channels. In our protocol, an encoded GHZ state by 7-qubit Calderbank–Shor–Steane code is sent by the quantum channel as a medium of quantum teleportation. The client only makes a single-qubit measurement on the third qubit of the logical GHZ state, and the remaining Bell state is shared between the client and the server. After decoding logical Bell state, the client and the server perform the measurement-based blind quantum computing protocol. Secondly, there are two classes of collective noises in the channel, which will affect the blind quantum computing. We modify our BQC protocol to overcome the collective-dephasing noise and the collective-rotating noise with logical states \(|H_{dp}\rangle \), \(|V_{dp}\rangle \), \(|H_{r}\rangle \) and \(|V_{r}\rangle \). Our protocol is robust against channel noise and qubits loss.