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

TL;DR

This paper presents a method to simulate complex many-body Hamiltonians with bounded interactions using a two-body interaction Hamiltonian, maintaining ground-state energy accuracy through a novel perturbation theory approach.

Contribution

It introduces a new technique based on Schrieffer-Wolff transformation to effectively reduce many-body Hamiltonians to two-body interactions with controlled error.

Findings

Ground-state energies are preserved up to O(epsilon n) error.

Interaction strengths in the simulator depend on epsilon and k, not on system size n.

The method enables efficient simulation of complex quantum systems.

Abstract

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(epsilon n) for arbitrary small epsilon. The strength of interactions in the simulator Hamiltonian depends on epsilon 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.