Perturbative Gadgets at Arbitrary Orders

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.

Corrected an error: U dagger vs. U inverse

References in corpus (2)

• Realizable Hamiltonians for Universal Adiabatic Quantum Computers
• Non-perturbative k-body to two-body commuting conversion Hamiltonians and embedding problem instances into Ising spins

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