  The Sachdev-Ye-Kitaev (SYK) model incorporates rich physics, ranging from
exotic non-Fermi liquid states without quasiparticle excitations, to
holographic duality and quantum chaos. However, its experimental realization
remains a daunting challenge due to various unnatural ingredients of the SYK
Hamiltonian such as its strong randomness and fully nonlocal fermion
interaction. At present, constructing such a nonlocal Hamiltonian and exploring
its dynamics is best through digital quantum simulation, where state-of-the-art
techniques can already handle a moderate number of qubits. Here we demonstrate
a first step towards simulation of the SYK model on a nuclear-spin-chain
simulator. We observed the fermion paring instability of the non-Fermi liquid
state and the chaotic-nonchaotic transition at simulated temperatures, as was
predicted by previous theories. As the realization of the SYK model in
practice, our experiment opens a new avenue towards investigating the key
features of non-Fermi liquid states, as well as the quantum chaotic systems and
the AdS/CFT duality.
