Hamiltonian simulation of minimal holographic sparsified SYK model

The circuit complexity for Hamiltonian simulation of the sparsified SYK model with $N$ Majorana fermions and quartic interactions which retains holographic features (referred to as `minimal holographic sparsified SYK') with $k = 8.7 \ll N^{3}/24$ (where $k$ is the total number of interaction terms per $N$) using second-order Trotter method and Jordan-Wigner encoding is found to be $\widetilde{\mathcal{O}}(k^{p}N^{2} \log N (\mathcal{J}t)^{3/2}\varepsilon^{-1/2})$ 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 $10^{5}$ two-qubit or Clifford+$T$-gates, it will be possible to achieve an advantage in this model.