  Quantum samplers are believed capable of sampling efficiently from
distributions that are classically hard to sample from. We consider a sampler
inspired by the classical Ising model. It is nonadaptive and therefore
experimentally amenable. Under a plausible conjecture, classical sampling upto
additive errors from this model is known to be hard. We present a trap-based
verification scheme for quantum supremacy that only requires the verifier to
prepare single-qubit states. The verification is done on the same model as the
original sampler, a square lattice, with only a constant overhead. We next
revamp our verification scheme in two distinct ways using fault tolerance that
preserves the nonadaptivity. The first has a lower overhead based on error
correction with the same threshold as universal quantum computation. The second
has a higher overhead but an improved threshold (1.97\%) based on error
detection. We show that classically sampling upto additive errors is likely
hard in both these schemes. Our results are applicable to other sampling
problems such as the Instantaneous Quantum Polynomial-time (IQP) computation
model. They should also assist near-term attempts at experimentally
demonstrating quantum supremacy and guide long-term ones.
