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.
In practical situations, the reliability of quantum resources can be compromised due to complex generation processes or adversarial manipulations during transmission. Consequently, the trials generated sequentially in an experiment may exhibit non-independent and non-identically distributed (non-i.i.d.) behavior. This non-i.i.d. behavior can introduce security concerns and result in faulty estimates when performing information tasks such as quantum key distribution, self-testing, verifiable quantum computation, and resource allocation in quantum networks. To certify the performance of such tasks, one can make a random decision in each trial, either spot-checking some desired property or utilizing the quantum resource for the given task. However, a general method for certification with a sequence of non-i.i.d. spot-checking trials is still missing. Here, we develop such a method. This method not only works efficiently with a finite number of trials but also yields asymptotically tight certificates of performance. Our analysis shows that even as the total number of trials approaches infinity, only a constant number of trials needs to be spot-checked on average to certify the average performance of the remaining trials at a specified confidence level.
Intermediate-scale quantum devices are becoming more reliable and may soon be harnessed to solve useful computational tasks. At the same time, common classical methods used to verify their computational output become intractable due to a prohibitive scaling of required resources with system size. Inspired by recent experimental progress, here we describe and analyze efficient cross-platform verification protocols for quantum states and show how these can be used to verify computations. We focus on the pairwise comparison between distant nodes of a quantum network, identify the most promising protocols, and discuss possible implementations in laboratory settings. As a proof of principle, we implement basic versions of these schemes on available quantum processors.