Abstract Blind quantum computation (BQC) is a secure quantum computation method that protects the privacy of clients. Measurement-based quantum computation (MBQC) is a promising approach for realizing BQC. To obtain reliable results in blind MBQC, it is crucial to verify whether the resource graph states are accurately prepared in the adversarial scenario. However, previous verification protocols for this task are too resource-consuming or noise-susceptible to be applied in practice. Here, we propose a robust and efficient protocol for verifying arbitrary graph states with any prime local dimension in the adversarial scenario, which leads to a robust and efficient protocol for verifying the resource state in blind MBQC. Our protocol requires only local Pauli measurements and is thus easy to realize with current technologies. Nevertheless, it can achieve optimal scaling behaviors with respect to the system size and the target precision as quantified by the infidelity and significance level, which has never been achieved before. Notably, our protocol can exponentially enhance the scaling behavior with the significance level.
Abstract Blind quantum computation (BQC) is a secure quantum computation method that protects the privacy of clients. Measurement-based quantum computation (MBQC) is a promising approach for realizing BQC. To obtain reliable results in blind MBQC, it is crucial to verify whether the resource graph states are accurately prepared in the adversarial scenario. However, previous verification protocols for this task are too resource-consuming or noise-susceptible to be applied in practice. Here, we propose a robust and efficient protocol for verifying arbitrary graph states with any prime local dimension in the adversarial scenario, which leads to a robust and efficient protocol for verifying the resource state in blind MBQC. Our protocol requires only local Pauli measurements and is thus easy to realize with current technologies. Nevertheless, it can achieve optimal scaling behaviors with respect to the system size and the target precision as quantified by the infidelity and significance level, which has never been achieved before. Notably, our protocol can exponentially enhance the scaling behavior with the significance level.
Graph states known as the resource states for measurement-based quantum computation play an important role in quantum information processing. Verifying the correctness of graph states in an efficient way is crucial to scalable quantum computing. In this paper, we propose an efficient method for verifying two-colorable graph states with Pauli measurements, where the number of required measurement settings is a constant that is independent of the size of graph states. In addition, the number of required tests is less than the existing protocols. We also present several examples, such as the brickwork state and the two-dimensional square lattice state, to show how to get the specific verification strategy. Furthermore, we propose a robust verification of graph states for resisting the noise acting on the measurement device. Finally, based on the verification of two-colorable graph states in the adversarial scenario, we propose a verifiable blind quantum computing protocol, which can realize the less resource overhead.
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), where n 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.
Abstract Graph states are resource states for measurement‐based quantum computation. Verification of graph states aims to certify whether a quantum state prepared by an untrusted device is close to an ideal graph state or not. Existing verification methods have not considered verifying graph states under an adversarial scenario and noisy measurements. In this paper, a robust verification method for graph states is proposed to overcome this issue. First, a verification model for graph states is designed. Then, two types of verification protocols based on this model are proposed. In addition, the completeness and soundness of the verification protocols are calculated when the measurement devices are affected by noises. Afterward, the measurement strategy of the robust verification protocols is extended from the specific case to the general case. In order to obtain the soundness that scales as , the verification method only requires copies of the graph state, where is the size of the graph state. Finally, several numerical examples are presented to demonstrate the effect of noises on the completeness and soundness of the verification protocols.
Blind quantum computing (BQC) allows a client to have a server carry out a quantum computation for them such that the client's input, output, and computation remain private. A desirable property for any BQC protocol is verification, whereby the client can verify with high probability whether the server has followed the instructions of the protocol or if there has been some deviation resulting in a corrupted output state. A verifiable BQC protocol can be viewed as an interactive proof system leading to consequences for complexity theory. We previously proposed [A. Broadbent, J. Fitzsimons, and E. Kashefi, in Proceedings of the 50th Annual Symposium on Foundations of Computer Science, Atlanta, 2009 (IEEE, Piscataway, 2009), p. 517] a universal and unconditionally secure BQC scheme where the client only needs to be able to prepare single qubits in separable states randomly chosen from a finite set and send them to the server, who has the balance of the required quantum computational resources. In this paper we extend that protocol with additional functionality allowing blind computational basis measurements, which we use to construct another verifiable BQC protocol based on a different class of resource states. We rigorously prove that the probability of failing to detect an incorrect output is exponentially small in a security parameter, while resource overhead remains polynomial in this parameter. This resource state allows entangling gates to be performed between arbitrary pairs of logical qubits with only constant overhead. This is a significant improvement on the original scheme, which required that all computations to be performed must first be put into a nearest-neighbor form, incurring linear overhead in the number of qubits. Such an improvement has important consequences for efficiency and fault-tolerance thresholds.
Efficient verification of pure quantum states in the adversarial scenario is crucial to many applications in quantum information processing, such as blind measurement-based quantum computation and quantum networks. However, little is known about this topic so far. Here, we establish a general framework for verifying pure quantum states in the adversarial scenario and clarify the resource cost. Moreover, we propose a simple and general recipe to constructing efficient verification protocols for the adversarial scenario from protocols for the nonadversarial scenario. With this recipe, arbitrary pure states can be verified in the adversarial scenario with almost the same efficiency as in the nonadversarial scenario. Many important quantum states can be verified in the adversarial scenario using local projective measurements with unprecedented high efficiencies.