Systems and methods of processing using a quantum processor are described. A method includes obtaining a problem Hamiltonian and defining a nested Hamiltonian with a plurality of logical qubits by embedding a logical KN representing the problem Hamiltonian into a larger KC×N, where N represents a number of the logical qubits and C represents a nesting level defining the amount of hardware resources for the nest Hamiltonian. The method also includes encoding the nested Hamiltonian into the plurality of physical qubits of the quantum processor; and performing a quantum annealing process with the quantum processor after the encoding.