  We investigate two sparse Sachdev-Ye-Kitaev (SYK) systems coupled by a
bilinear term as a holographic quantum mechanical description of an eternal
traversable wormhole in the low temperature limit. Each SYK system consists of
$N$ Majorana fermions coupled by random $q$-body interactions. The degree of
sparseness is captured by a regular hypergraph in such a way that the
Hamiltonian contains exactly $k\,N$ independent terms. We improve on the
theoretical understanding of the sparseness property by using known measures of
hypergraph expansion. We show that the sparse version of the two coupled SYK
model is gapped with a ground state close to a thermofield double state. Using
Krylov subspace and parallelization techniques, we simulate the system for
$q=4$ and $q=8.$ The sparsity of the model allows us to explore larger values
of $N$ than the ones existing in the literature for the all-to-all SYK. We
analyze in detail the two-point functions and the transmission amplitude of
signals between the two systems. We identify a range of parameters where
revivals obey the scaling predicted by holography and signals can be
interpreted as traversing the wormhole.
