Verifiable Measurement-Only Blind Quantum Computing with Stabilizer Testing

We introduce a simple protocol for verifiable measurement-only blind quantum computing. Alice, a client, can perform only single-qubit measurements, whereas Bob, a server, can generate and store entangled many-qubit states. Bob generates copies of a graph state, which is a universal resource state for measurement-based quantum computing, and sends Alice each qubit of them one by one. Alice adaptively measures each qubit according to her program. If Bob is honest, he generates the correct graph state, and, therefore, Alice can obtain the correct computation result. Regarding the security, whatever Bob does, Bob cannot get any information about Alice’s computation because of the no-signaling principle. Furthermore, malicious Bob does not necessarily send the copies of the correct graph state, but Alice can check the correctness of Bob’s state by directly verifying the stabilizers of some copies.

Figure 1

The measurement-only blind quantum computing. (a) Bob generates a resource state. (b) Bob sends Alice each qubit of the resource state one by one. Alice adaptively measures each qubit.

Figure 2

(a) The RHG lattice. (b) An example of bipartite graphs: the two-dimensional square lattice. Black and white colors indicate the bipartitions $B$ and $W$, respectively. (c) An example for $n=3$, $k=2$. Two blocks go to the first group, and the other two blocks go to the second group. The left block goes to the third group.

Figure 3

An example for the two-dimensional square lattice. The measurement pattern for the first group (a) and the second group (b).