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arXiv:1505.07535 · Physical Review Letters

Verifiable Measurement-Only Blind Quantum Computing with Stabilizer Testing

Masahito Hayashi, Tomoyuki Morimae

Published Nov 25, 2015• 193 citations
arXivHTMLPDF

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 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.

DOI
10.1103/physrevlett.115.220502

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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.
The characteristics of BQC is that it enables a client with less quantum abilities to delegate her quantum computation to a server with strong quantum computablities while keeping the client's privacy. In this article, we study single client-server BQC based on measurement which is verifiable. In detail, the verifiability is that the client Alice can obtain the correct measurement results if the server Bob is honest, while Bob does not get nothing of Alice's secret information if he is malicious. We construct a latticed state, composed of six-qubit cluster states and eight-qubit entangled states, to realize Alice's quantum computing. In this proposed protocol, the cilent Alice prepares and sends initial single-qubit states to Bob, where the initial states include useful qubits and trap qubits. And then Bob performs controlled-Z gate to produce the entanglement and returns them to Alice. Alice will send trap qubits and useful qubits to Bob randomly and Bob returns all measurement results to her. Alice makes a comparison for trap qubits between true results and Bob's results to check the honesty of Bob. In a word, the trap qubtis have two purposes: 1) confusing Bob to keep the blindness; 2)verifying the honesty of Bob and correctness of Bob's quantum computing. There has an important feature that Alice does not need to encrypt the computing angles by rπr\pirπ (r∈{0,1}\in\{0,1\}∈{0,1}), meanwhile the blindness and correctness can also be ensured. That is, Alice's computing results don't need to flipped since Bob is not impossible know anything about the quantum computation. Our work gives a better understanding for verifiable BQC based on measurement.
Verifiable blind quantum computation provides a cloud scenario for scalable quantum information processing. However, constructing one resource-efficient verification protocol is still an open problem. In this paper, the context of verification we consider is the measurement-based model, in which the client receives the graph state prepared by the server and performs single-qubit measurements on it to drive the computation. We first utilize three entanglement witnesses to estimate the fidelity of the prepared graph state. Applying entanglement witnesses to design the test phase, we propose verification protocols. Our protocol requires overhead in terms of copies of the graph state that scales as O(n2logn)O({n}^{2}logn)O(n2logn), where nnn is the number of qubits of the graph state. Furthermore, the soundness of our protocol is improved. The advantages of our protocol are derived from the fact that each entanglement witness can be implemented by the client with a fixed number of measurement settings.
Blind quantum computing (BQC) enables a client with limited quantum capability to delegate her quantum computation to a remote quantum server and still keeps the client's input, output, and the algorithm private. One important property of BQC is verifiability, which means the client can verify the correctness of the computation or unknown quantum inputs. Recently, Morimae proposed a verifiable blind quantum computing protocol where the client can verify both the correctness of computing and the quantum input. However, the client needs much quantum memory and takes a lot of qubits to get the true result. We reduce the size of quantum memory and the number of qubits used in Morimae's protocol. Besides, we extend the resource state in Morimae's protocol from graph state to hypergraph state. For certain hypergraph states as resources states, such as Union Jack State, the client only needs Pauli measurements in the computation stage but he needs non-Clifford basis measurements if graph states are considered as resources states.
Verifiable blind quantum computing is a secure delegated quantum computing where a client with a limited quantum technology delegates her quantum computing to a server who has a universal quantum computer. The client's privacy is protected (blindness), and the correctness of the computation is verifiable by the client despite her limited quantum technology (verifiability). There are mainly two types of protocols for verifiable blind quantum computing: the protocol where the client has only to generate single-qubit states and the protocol where the client needs only the ability of single-qubit measurements. The latter is called the measurement-only verifiable blind quantum computing. If the input of the client's quantum computing is a quantum state, whose classical efficient description is not known to the client, there was no way for the measurement-only client to verify the correctness of the input. Here we introduce a protocol of measurement-only verifiable blind quantum computing where the correctness of the quantum input is also verifiable.
Abstract Blind quantum computing enables quantum-limited clients to securely access untrusted quantum servers. This paper proposes a three-party verifiable blind quantum computing protocol with separated input and function ownership, where Alice holds the private input, Bob holds the target function, and Charlie performs the delegated quantum computation, with the result released only to Alice. Alice and Bob first establish a shared key using BB84. Under the measurement-based quantum computing framework, a secure two-party computation protocol is then used to jointly generate adaptive blinded measurement instructions, eliminating the need for Bob to transmit quantum states to Charlie. A hidden dummy-trap mechanism is further incorporated to verify malicious server behavior. Under the honest-but-curious client model without client-server collusion, the protocol protects input and function privacy while ensuring computation blindness, shared-key security, and verifiability. Most quantum operations are performed by Charlie, while the clients require only limited quantum capabilities.
Blind quantum computation is a new secure quantum computing protocol which enables Alice (who does not have sufficient quantum technology) to delegate her quantum computation to Bob (who has a full-fledged quantum computer) in such a way that Bob cannot learn anything about Alice's input, output, and algorithm. In previous protocols, Alice needs to have a device which generates quantum states, such as single-photon states. Here we propose another type of blind computing protocol where Alice does only measurements, such as the polarization measurements with a threshold detector. In several experimental setups, such as optical systems, the measurement of a state is much easier than the generation of a single-qubit state. Therefore our protocols ease Alice's burden. Furthermore, the security of our protocol is based on the no-signaling principle, which is more fundamental than quantum physics. Finally, our protocols are device independent in the sense that Alice does not need to trust her measurement device in order to guarantee the security.