  Recent advances in quantum technology have led to the development and
manufacturing of experimental programmable quantum annealers that promise to
solve certain combinatorial optimization problems of practical relevance faster
than their classical analogues. The applicability of such devices for many
theoretical and real-world optimization problems, which are often constrained,
is severely limited by the sparse, rigid layout of the devices' quantum bits.
Traditionally, constraints are addressed by the addition of penalty terms to
the Hamiltonian of the problem, which in turn requires prohibitively increasing
physical resources while also restricting the dynamical range of the
interactions. Here, we propose a method for encoding constrained optimization
problems on quantum annealers that eliminates the need for penalty terms and
thereby reduces the number of required couplers and removes the need for minor
embedding, greatly reducing the number of required physical qubits. We argue
the advantages of the proposed technique and illustrate its effectiveness. We
conclude by discussing the experimental feasibility of the suggested method as
well as its potential to appreciably reduce the resource requirements for
implementing optimization problems on quantum annealers, and its significance
in the field of quantum computing.
