  The experimental interest and developments in quantum spin-1/2-chains has
increased uninterruptedly over the last decade. In many instances, the target
quantum simulation belongs to the broader class of non-interacting fermionic
models, constituting an important benchmark. In spite of this class being
analytically efficiently tractable, no direct certification tool has yet been
reported for it. In fact, in experiments, certification has almost exclusively
relied on notions of quantum state tomography scaling very unfavorably with the
system size. Here, we develop experimentally-friendly fidelity witnesses for
all pure fermionic Gaussian target states. Their expectation value yields a
tight lower bound to the fidelity and can be measured efficiently. We derive
witnesses in full generality in the Majorana-fermion representation and apply
them to experimentally relevant spin-1/2 chains. Among others, we show how to
efficiently certify strongly out-of-equilibrium dynamics in critical Ising
chains. At the heart of the measurement scheme is a variant of importance
sampling specially tailored to overlaps between covariance matrices. The method
is shown to be robust against finite experimental-state infidelities.
