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Anti-Forging Quantum Data: Cryptographic Verification of Quantum Computational Power

Quantum cloud computing is emerging as a popular model for users to experience the power of quantum computing through the internet, enabling quantum computing as a service. The question is, when the scale of the computational problems becomes out of reach of classical computers, how can users be sure that the output strings sent by the server are really from a quantum hardware? In 2008, Shepherd and Bremner proposed a cryptographic verification protocol based on a simplified circuit model called IQP (instantaneous quantum polynomial-time), which can potentially be applied to most existing quantum cloud platforms. However, the Shepherd-Bremner protocol has recently been shown to be insecure by Kahanamoku-Meyer. Here we present an extended model of IQP-based cryptographic verification protocol, where the Shepherd-Bremner construction can be regarded as a special case. This protocol not only can avoid the attack by Kahanamoku-Meyer but also provide several additional security measures for anti-forging quantum data. In particular, our protocol admits a simultaneous encoding of multiple secret strings, strengthening significantly the hardness for classical hacking. Furthermore, we provide methods for estimating the correlation functions associated with the secret strings, which are the key elements in our verification protocol.