Quantum Simulation of Many-Body Hamiltonians Using Perturbation Theory with Bounded-Strength Interactions

We show how to map a given $n$-qubit target Hamiltonian with bounded-strength $k$-body interactions onto a simulator Hamiltonian with two-body interactions, such that the ground-state energy of the target and the simulator Hamiltonians are the same up to an extensive error $O(ϵn)$ for arbitrary small $ϵ$. The strength of the interactions in the simulator Hamiltonian depends on $ϵ$ and $k$ but does not depend on $n$. We accomplish this reduction using a new way of deriving an effective low-energy Hamiltonian which relies on the Schrieffer-Wolff transformation of many-body physics.