  We propose a frustration-free model for the Moore-Read quantum Hall state on
sufficiently thin cylinders with circumferences $\lesssim 7$ magnetic lengths.
While the Moore-Read Hamiltonian involves complicated long-range interactions
between triplets of electrons in a Landau level, our effective model is a
simpler one-dimensional chain of qubits with deformed Fredkin gates. We show
that the ground state of the Fredkin model has high overlap with the Moore-Read
wave function and accurately reproduces the latter's entanglement properties.
Moreover, we demonstrate that the model captures the dynamical response of the
Moore-Read state to a geometric quench, induced by suddenly changing the
anisotropy of the system. We elucidate the underlying mechanism of the quench
dynamics and show that it coincides with the linearized bimetric field theory.
The minimal model introduced here can be directly implemented as a first step
towards quantum simulation of the Moore-Read state, as we demonstrate by
deriving an efficient circuit approximation to the ground state and
implementing it on IBM quantum processor.
