How can quantum computers be classically tested? This challenging question is interesting as a novel question about interactive proofs, as a practical question about the testing of near-term quantum devices, and as a philosophical question about the testing of quantum mechanics in the limit of high complexity.

In this talk, I will show that classical cryptography provides an elegant solution to this question: I will show that it is possible to classically verify quantum computations through interaction by relying on the assumption that quantum machines cannot break the cryptographic problem of learning with errors. This is achieved by constructing a commitment protocol in which a classical string serves as a commitment to an exponentially complex quantum state.