Constructing and programming driver graphs in quantum hardware for non-stoquastic quantum optimization annealing processes

A computer implemented method comprising:

• receiving, by a control system, an optimization problem expressed as a Maximum Weighted Independent Set (MWIS) on a problem graph;
• encoding, by the control system, the MWIS problem into an energy spectrum of a problem Hamiltonian;
• determining, by the control system, an XX-driver graph based on an identified independent-cliques (IC), edges in the XX-driver graph being the edges between partites in each clique of the IC, the edges in the XX-driver graph corresponding to XX-couplers of a quantum annealing hardware;
• determining, by the control system, XX-coupler strengths associated with the XX-driver graph;
• specifying, by the control system, a non-stoquastic driver Hamiltonian based on the XX-driver graph and the associated XX-coupler strengths;
• initializing and programming, by the control system, a time-dependent non-stoquastic system Hamiltonian of the quantum annealing hardware using determined values of parameters included in the problem Hamiltonian and determined values of parameters included in the non-stoquastic driver Hamiltonian;
• implementing, by the programmed quantum annealing hardware, a quantum annealing schedule;
• receiving, by the control system and from the quantum annealing hardware, an output representing eigenstates of the system Hamiltonian and corresponding energy values, wherein the eigenstates and the corresponding energy values include a solution to the optimization problem.