Hamiltonian simulation of minimal holographic sparsified SYK model

Abstract

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 the second-order Trotter method and Jordan-Wigner encoding is found to be $\tilde{O}(k^{\alpha }{N}^{3/2}\log N{\left(Jt\right)}^{3/2}{\epsilon }^{-1/2})$ 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 $\alpha <1$. 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.