Perturbative gadgets at arbitrary orders
Stephen P. Jordan, Edward Farhi · Physical Review A · 2008
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 $\mathit{k}$-body effective interactions from two-body Hamiltonians. These effective interactions arise from the $\mathit{k}$th order in perturbation theory.