  We report an accurate and efficient classical simulation of a kicked Ising
quantum system on the heavy-hexagon lattice. A simulation of this system was
recently performed on a 127 qubit quantum processor using noise mitigation
techniques to enhance accuracy (Nature volume 618, p.~500-505 (2023)). Here we
show that, by adopting a tensor network approach that reflects the geometry of
the lattice and is approximately contracted using belief propagation, we can
perform a classical simulation that is significantly more accurate and precise
than the results obtained from the quantum processor and many other classical
methods. We quantify the tree-like correlations of the wavefunction in order to
explain the accuracy of our belief propagation-based approach. We also show how
our method allows us to perform simulations of the system to long times in the
thermodynamic limit, corresponding to a quantum computer with an infinite
number of qubits. Our tensor network approach has broader applications for
simulating the dynamics of quantum systems with tree-like correlations.
