Perturbative Gadgets at Arbitrary Orders

TL;DR

This paper generalizes perturbative gadgets to arbitrary orders, enabling the simulation of complex many-body interactions using only two-body Hamiltonians, which is crucial for practical quantum computing implementations.

Contribution

The authors extend perturbative gadgets to arbitrary order, allowing direct simulation of k-body interactions from two-body Hamiltonians, advancing quantum simulation techniques.

Findings

Generalized gadgets for arbitrary order k

Effective k-body interactions from two-body Hamiltonians

Perturbation theory at order k used for simulation

Abstract

Adiabatic quantum algorithms are often most easily formulated using many-body interactions. However, experimentally available interactions are generally two-body. In 2004, Kempe, Kitaev, and Regev introduced perturbative gadgets, by which arbitrary three-body effective interactions can be obtained using Hamiltonians consisting only of two-body interactions. These three-body effective interactions arise from the third order in perturbation theory. Since their introduction, perturbative gadgets have become a standard tool in the theory of quantum computation. Here we construct generalized gadgets so that one can directly obtain arbitrary k-body effective interactions from two-body Hamiltonians. These effective interactions arise from the kth order in perturbation theory.