Prepare-and-Send Verifiable Universal Blind Quantum Computation

This protocol allows the client to verify the correctness of the blind delegated quantum computing with high probability. Here, the server carries out the quantum computation for the client while maintaining perfect privacy for the client, and also giving the client an ability to verify with high probability whether the server has followed the instructions of the protocol and also check if any deviations have occurred, resulting in an incorrect output state.

Tags: Two Party, Universal Task, Secure Delegated Quantum Computation, Verification of Quantum computers, Quantum Offline communication, Classical Online communication, Measurement Based Quantum Computation (MBQC), Measurement Only UBQC, Pseudo-Secret Random Qubit Generator (PSQRG).

Assumptions

• The protocol assumes perfect state preparation, transmissions, and measurements.
• The client never deviates from the protocol.
• The position of the trap qubit always remains hidden from the server.

Outline

This protocol is a modified version of prepare and send universal blind quantum computation, which is based on MBQC. An adversarial server is taken into consideration here and any computational deviations are detected with a high probability. This is achieved by insertion of randomly prepared and blindly isolated single qubits in the computation, which act as traps (trap qubits), hence assisting the client in verification.

The original brickwork state used in prepare and send universal blind quantum computation is modified to a cylinder brickwork state which allows client to embed a trap qubit surrounded by multiple dummy qubits without disrupting the computation. This state is universal and maintains privacy of client's preparation.

The dummy qubits here do not take part in the actual computation as they are disentangled from the rest of the qubits of the graph state. Hence by adding them to the neighbouring nodes of the trap qubits, they are blindly isolated and thus do not interfere with the actual computation. The dummy qubits are added next to the trap qubit in a tape format.

This protocol is dived into four stages: Client's preparation, server's preparation, interaction and measurement, verification.

• Client's preparation: The partially quantum client prepares the quantum states with embedded traps qubits and sends them to the server for creation of the cylinder brickwork state.
  • For the server to create a cylinder brickwork state, the client prepares $m*n$ single qubit states. The $n$ qubit input states are specially encoded and all the other non-input qubits except the trap qubit are prepared with randomly chosen local phase angles.
  • During this preparation, the client randomly selects one qubit as the trap qubit and corresponding to the graph of cylinder brickwork state, all the other qubits in the tape are set as the dummy qubits. The trap qubit is prepare with the local phase angle set to $0$.
  • The client then sends all the prepared qubits in the respective order so the graph state can be constructed by the server.

• Server's Preparation

The server receives the qubits in the order of $m$ rows and $n$ columns and entangles them according to the cylinder brickwork state (using CZ gate).

• Interaction and Measurement

This step is exactly the same as for Prepare and Send-Universal Blind Quantum Computation.