QUROPE Quantum Information Processing and Communication in Europe

One of the main challenges in the field of quantum simulation and computation is to identify ways to certify the correct functioning of a device when a classical efficient simulation is not available. In such a situation one cannot simply classically keep track of the dynamics of the device. In this note, we discuss weak-membership notions of the certification for ground state preparations of frustration-free Hamiltonians based on simple energy measurements of local Hamiltonian terms. These considerations have applications to classically intractable analog quantum simulations: for example, using Feynman-Kitaev Hamiltonians, one can realise universal quantum computers. Our certification approach is non-interactive and thus avoids challenges arising from interactive proof systems. Moreover, our certification protocol is applicable to recent results on so-called IQP circuits aiming at the demonstration of quantum supremacy.