Simulating highly nonlocal Hamiltonians with less nonlocal Hamiltonians

TL;DR

This paper introduces a nonperturbative method to simulate complex many-body Hamiltonians using simpler, less nonlocal Hamiltonians, enhancing quantum simulation capabilities beyond traditional perturbative approaches.

Contribution

A novel nonperturbative technique for constructing effective k-body interactions from Hamiltonians with fewer-body interactions, applicable to quantum computing models.

Findings

Effective k-body interactions can be simulated with Hamiltonians of lower locality.

The technique complements perturbative gadgets for complex Hamiltonian embedding.

Applicable to hybrid and adiabatic quantum computing schemes.

Abstract

The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with two-body interactions only. Although valid for arbitrary $k$-body interactions, their use is limited to small $k$ because the strength of interaction is $k$'th order in perturbation theory. In this paper we develop a nonperturbative technique for obtaining effective $k$-body interactions using Hamiltonians consisting of at most $l$-body interactions with $l<k$. This technique works best for Hamiltonians with a few interactions with very large $k$ and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme.