  We analyze a model of qubits which we argue has an emergent quantum
gravitational description similar to the fermionic Sachdev-Ye-Kitaev (SYK)
model. The model we consider is known as the quantum $q$-spin model because it
features $q$-local interactions between qubits. It was previously studied as a
model of a quantum spin glass, and while we find that the model is glassy for
$q=2$, $q=3$, and likely $q=4$, we also find evidence for previously unexpected
SYK-like behavior for the quenched free energy down to the lowest temperatures
for $q \geq 5$. This SYK-like physics includes power-law correlation functions
and an extensive low temperature entropy, so we refer to the model as Spin SYK.
The model is generic in that it includes all possible $q$-body couplings, lacks
most symmetries, and has no spatial structure, so our results can be construed
as establishing a certain ubiquity of quantum holography in systems dominated
by many-body interactions. Furthermore, we discuss a generalized family of
models which includes Spin SYK and which provably exhibit SYK-like physics in
the solvable limit of large local Hilbert space dimension. We also comment on
implications of a bosonic system with SYK-like properties for the study of
holography, Hamiltonian complexity, and related topics.
