  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.
