Non-perturbative topological gadgets for many-body coupling

Abstract Continuous-time quantum hardware implementations generally lack the native capability to implement high-order terms that would facilitate efficient compilation of quantum algorithms. This limitation has, in part, motivated the development of perturbative gadgets—multi-qubit constructions used to effect a desired Hamiltonian using engineered low-energy subspaces of a larger system constructed using simpler, usually two-body, primitives. In this work, we demonstrate how a class of non-perturbative gadgets can produce high-order multi-body interactions by taking advantage of the odd–even properties of topological defect subspaces. The simplest example uses domain-wall defects in an effective Ising spin chain with linear connectivity and three-body couplings, alongside three- or five-body driving terms depending on the intended use. We demonstrate a version of a gadget which can perform an encoded bit-flip operation on a minor embedding chain, an important task to mitigate the limitations of quasi-two-dimensional (also sometimes called quasi-planar) topology. Although this will be the main focus of the paper due to conceptual simplicity, there exist systems constructed with only two-body couplings where the boundaries determine whether there are an odd or even number of defects, namely ice-like systems which may yield more complex gadget-like constructions.