The recent demonstrations of quantum advantage with superconducting and linear optics devices have highlighted both the impressive capabilities of near-term quantum computers but also the limitations in being able to verify the results in a scalable manner. This is because current experiments have focused on (classically-hard) sampling tasks which, while relatively easy to implement in hardware, require exponential time to validate their results. A way to overcome the intractability of verification is with interactive proofs of quantumness---protocols that leverage cryptographic functions as well as interactions between a prover and a verifier, to bridge the gap between verifiability and implementation.

In this talk, we present the first implementation of such an interactive test of quantum advantage on an ion-trap quantum computer. This consists of two complementary protocols---one based on the hardness of factoring, which implements a type of computational Bell test and another based on the learning with errors (LWE) problem. To perform multiple rounds of interaction, we used a split-and-shuttle approach to realize mid-circuit measurements on selected subsystems, with subsequent coherent evolution. For both protocols, the experimental results exceed the asymptotic bound for classical behavior; maintaining this fidelity at scale would conclusively demonstrate verifiable quantum advantage.