Plugging Leaks in Fault-Tolerant Quantum Computation and Verification

With the advent of quantum cloud computing, the security of delegated quantum computation has become of utmost importance. While multiple statistically secure blind verification schemes in the prepare-and-send model have been proposed, none of them achieves full quantum fault-tolerance, a prerequisite for useful verification on scalable quantum computers. In this paper, we present the first fault-tolerant blind verification scheme for universal quantum computations able to handle secret-dependent noise on the verifier's quantum device. Composable security of the proposed protocol is proven in the Abstract Cryptography framework. Our main tools are two novel distillation protocols that turn secret-dependent noise into secret-independent noise. The first one is run by the verifier and acts on its noisy gates, while the second and more complex one is run entirely on the prover's device and acts on states provided by the verifier. Both are required to overcome the leakage induced by secret-dependent noise. We use these protocols to prepare states in the X-Y-plane whose noise is overwhelmingly secret-independent, which then allows us to verify with exponential confidence arbitrary fault-tolerant BQP computations.