Simplifying the simulation of local Hamiltonian dynamics

Abstract

Local Hamiltonians Hk 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 Hk′ 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 Hk and Hk′ 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 Hk 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 Hk Hamiltonian. Published by the American Physical Society 2024