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 N³/24 (where k is the total number of interaction terms per N) using second-order Trotter method and Jordan-Wigner encoding is found to be O(kᵖN² log N (Jt)3/2ε-1/2) where t is the simulation time, ε is the desired error in the implementation of the unitary U = exp(-iHt), J is the disorder strength, and $p < 1$. This complexity implies that with less than a hundred logical qubits and about 10⁵ two-qubit or Clifford+T-gates, it will be possible to achieve an advantage in this model.