Quantum data and processing can make classically intractable learning tasks feasible. However, quantum capabilities will only be available to a select few. Thus, reliable schemes that allow classical clients to delegate learning to untrusted quantum servers are required. Building on a recently introduced framework of interactive proofs for classical machine learning, we develop a framework for classical verification of quantum learning. We exhibit learning problems that a classical learner cannot efficiently solve on their own, but that they can efficiently and reliably solve when interacting with an untrusted quantum prover, based on a new quantum data access model that we call "mixture-of-superpositions" examples. We also showcase two scenarios in learning and verification in which these examples do not outperform classical data. Our results demonstrate that the power of quantum data for learning tasks, while not unlimited, can be utilized by classical agents through interaction with untrusted quantum entities.
Copyright. All Rights Reserved.