  One of the main bottlenecks in solving combinatorial optimization problems
with quantum annealers is the qubit connectivity in the hardware. A possible
solution for larger connectivty is minor embedding. This techniques makes the
geometrical properties of the combinatorial optimization problem, encoded as a
Hamiltonian, match the properties of the quantum annealing hardware. The
embedding itself is a hard computational problem and therefore heuristic
algorithms are required. In this work, we present fixed, modular and scalable
embeddings that can be used to embed any combinatorial optimization problem
described as an Ising Hamiltonian. These embeddings are the result of an
extension of the well-known parity mapping, which has been used in the past to
map higher-order Ising Hamiltonians to quadratic Hamiltonians, which are
suitable for existing quantum hardware. We show how our new embeddings can be
mapped to existing quantum annealers and that the embedded Hamiltonian physical
properties match the original Hamiltonian properties.
