Hamiltonian simulation of minimal holographic sparsified SYK model - Raghav G. Jha (Nuclear Physics B)
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≪N3/24 (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˜(kαN3/2log⁡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) 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 106 gates, it might be possible to achieve an advantage in this model and simulate real-time dynamics.