Hamiltonian simulation of minimal holographic sparsified SYK model

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 ≪ N 3 / 24 (where k is the total number of interaction terms times 1/ N ) using the second-order Trotter method and Jordan-Wigner encoding is found to be O ˜ ( k α N 3 / 2 log ⁡ N ( J t ) 3 / 2 ε − 1 / 2 ) where t is the simulation time, ε is the desired error in the implementation of the unitary U = exp ⁡ ( − i H t ) measured by the operator norm, J is the disorder strength, and constant α < 1 . This complexity implies that with less than a hundred logical qubits and about 10 6 gates, it might be possible to achieve an advantage in this model and simulate real-time dynamics.