The Sachdev-Ye-Kitaev (SYK) model may provide us with a good starting point for the experimental study of quantum chaos and holography in the laboratory. Still, the four-local interaction of fermions makes quantum simulation challenging, and it would be good to search for simpler models that keep the essence. In this paper, we argue that the four-local interaction may not be important by introducing a few models that have two-local interactions. The first model is a generalization of the spin-SYK model, which is obtained by replacing the spin variables with $\mathrm{SU}\left(d\right)$ generators. Simulations of this class of models might be straightforward on qudit-based quantum devices. We study the case of $d=3,4,5,6$ numerically and observe quantum chaos already for two-local interactions in a wide energy range. We also introduce modifications of spin-SYK and SYK models that have similar structures as the $\mathrm{SU}\left(d\right)$ model (e.g., $H={\sum }_{p,q}{J}_{pq}{\chi }_p{\chi }_{p+1}{\chi }_q{\chi }_{q+1}$ instead of the original SYK Hamiltonian $H={\sum }_{p,q,r,s}{J}_{pqrs}{\chi }_p{\chi }_q{\chi }_r{\chi }_s$), which shows strongly chaotic features although the interaction is essentially two-local. These models may be a good starting point for the quantum simulation of the original SYK model.

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• Majorana fermions
• Quantum chaos
• Quantum simulation
• Qudits
• Quantum many-body systems
• Strongly correlated systems
• Exact diagonalization
• Random matrix theory
• SU(N) symmetries
• Sachdev-Ye-Kitaev model