  Rydberg atom arrays have recently emerged as one of the most promising
platforms for quantum simulation and quantum information processing. However,
as is the case for other experimental platforms, the longer-term success of the
Rydberg atom arrays in implementing quantum algorithms depends crucially on
their robustness to gate-induced errors. Here we show that, for an idealized
biased error model based on Rydberg atom dynamics, the implementation of QSP
protocols can be made error-robust, in the sense that the asymptotic scaling of
the gate-induced error probability is slower than that of gate complexity.
Moreover, using experimental parameters reported in the literature, we show
that QSP iterates made out of up to a hundred gates can be implemented with
constant error probability. To showcase our approach, we provide a concrete
blueprint to implement QSP-based near-optimal Hamiltonian simulation on the
Rydberg atom platform. Our protocol substantially improves both the scaling and
the overhead of gate-induced errors in comparison to those protocols that
implement a fourth-order product-formula.
