Simplifying the simulation of local Hamiltonian dynamics

Local Hamiltonians H k describe nontrivial k -body interactions in quantum many-body systems. Here, we address the dynamical simulatability of a k -local Hamiltonian by a simpler one H k ′ with k ′ < k , under the realistic constraint that both Hamiltonians act on the same Hilbert space. When it comes to exact simulation, we build upon known methods to derive examples of H k and H k ′ that simulate the same physics. We also address the most realistic case of approximate simulation. There, we upper-bound the error up to which a Hamiltonian can simulate another one, regardless of their internal structure, and show an example suggesting that the accuracy of a ( k ′ = 2 ) -local Hamiltonian to simulate H k with k > 2 increases with k . Finally, we propose a method to search for the k ′ -local Hamiltonian that simulates, with the highest possible precision, the short time dynamics of a given H k Hamiltonian.