In 2018, Mahadev showed that quantum computation in the cloud can be run under fully-homomorphic encryption (QFHE). This scheme requires evaluation of a claw-free trapdoor function per “AND” gate and more general non-Clifford gates. In this work, we focus on protecting results of the computation from insiders such as Administrators. We extend the usual honest-but-curious model to allow the Adversary to make arbitrary measurements. Since the workloads that run on the cloud quantum computer are signed by the client, the Adversary can also be assumed to be classical. In this case, we show that typical O (n^3) claw-free quantum evaluations of Mahadev’s QFHE can be reduced to O(n) evaluations, while still protecting quantum-advantageous computations . The talk will be introductory.