  The circuit complexity for Hamiltonian simulation of the sparsified SYK model
with $N$ Majorana fermions and $q=4$ (quartic interactions) which retains
holographic features (referred to as `minimal holographic sparsified SYK') with
$k\ll N^{3}/24$ (where $k$ is the total number of interaction terms times
1/$N$) using second-order Trotter method and Jordan-Wigner encoding is found to
be $\widetilde{\mathcal{O}}(k^{p}N^{3/2} \log N
(\mathcal{J}t)^{3/2}\varepsilon^{-1/2})$ where $t$ is the simulation time,
$\varepsilon$ is the desired error in the implementation of the unitary $U =
\exp(-iHt)$, $\mathcal{J}$ is the disorder strength, and $p < 1$. This
complexity implies that with less than a hundred logical qubits and about
$10^{6}$ gates, it will be possible to achieve an advantage in this model and
simulate real-time dynamics up to scrambling time.
