Verifiable Measurement-Only Blind Quantum Computing with Stabilizer Testing

Abstract

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 learn 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 stabilizers of some copies.Blind quantum computing is a quantum cryptographic protocol that enables Alice (a client), who does not have any sophisticated quantum technology, to delegate her quantum computing to Bob (a server), who has a sufficiently powerful quantum computer, without leaking any her privacy. The first protocol of blind quantum computing that uses the measurement-based quantum computing [1] was proposed by Broadbent, Fitzsimons, and Kashefi [2], and a proof-of-principle experiment was demonstrated with photonic qubits [3]. In the protocol of Ref. [2], Alice generates many randomly-rotated singlequbit states, and sends them to Bob. Bob generates a universal resource state of the measurement-based quantum computing by applying entangling gates on qubits sent from Alice. Then, they do two-way classical communications: Alice instructs Bob how to measure each qubit, and Bob returns measurement results so that Alice can perform the feed-forward calculations. It was shown in Ref.[2] that if Bob is honest, Alice can obtain the correct quantum computing result (which we call the correctness), and that whatever evil Bob does, he cannot learn anything about Alice's input, output, and program (which we call the blindness) [4]. (See also Ref.[5] for a precise proof of the security.) Inspired by the seminal result, plenty of improvements have been done [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. For example, it was shown that instead of single-qubit states generation, single-qubit measurements [6] or coherent states generation [7] are sufficient for Alice. In the protocol of Ref. [6], so called the measurement-only blind quantum computing, Bob generates a universal resource state of measurement-based quantum computing (Fig 1(a)), and sends each qubit of the resource state one by one to Alice (Fig. 1(b)). Alice adaptively measures each qubit according to her program ( Fig. 1(b)). Since adaptive single-qubit measurements on certain states are universal [1,[21][22][23], Alice with only single-qubit measurements ability can perform universal quantum computing if Bob prepares the correct resource state. Furthermore, since this protocol is a o...

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