Abstract: In this tutorial I will explain the fundamental principles behind the use of trapdoor claw-free functions to build a qubit certification test, which allows a classical verifier to reach into a quantum computer’s Hilbert space, and enforce a qubit structure in it. I will discuss how this leads to protocols for proofs of quantumness, certified randomness and verification of quantum computations. I will also describe refinements of these techniques for improving the efficiency of the protocols.
