Parameter setting for quantum annealing

Solving a combinatorial optimization problem with the current generation of adiabatic quantum devices, as the D-Wave 2000Q, requires to express the cost function of the optimization problem in the QUBO form, which in many cases includes penalty terms to enforce hard constraints.
A similar problem appears when a minor embedding is necessary to map the QUBO Hamiltonian on a specific hardware graph.
Interestingly, the performance of both classical and quantum heuristics is very sensible to the choice of such penalty terms and an optimal choice of parameters could result in much faster computations than those ones performed with sub-optimal parameter values.
In this talk I will focus on the parameter setting problem, that is how to find the optimal weights to be used in penalty terms, as well as the values of the ferromagnetic couplings to be used in the minor embedding problem.
I will also present a method to find the minimum parameter values which guarantee that the ground state of the QUBO Hamiltonian corresponds to the solution of the original problem. Finally, benchmark results using the D-Wave 2000Q chip hosted at NASA Ames with different values of the parameters will be discussed.