A computer implemented method comprising: obtaining information representing energy states of a total Hamiltonian H tot, wherein the total Hamiltonian H tot characterizes dynamics of a quantum system having controllable quantum states, the quantum system being controlled such that the total Hamiltonian H tot evolves from an initial quantum Hamiltonian H i over time t to a problem quantum Hamiltonian H p at time t T; calculating an average phonon energy of a bath in which the quantum system is located; assigning a probability, using a probability mass function, to each energy state that a quantum annealing subsystem of the quantum system may adopt at time t T such that a final state of the quantum annealing subsystem at time t T has a maximum overlap with the ground state of H p; wherein the quantum annealing subsystem comprises a plurality of superconducting units, the plurality of superconducting units comprising superconducting qubits; determining a distribution for a Hamiltonian term, H QG, with respect to controllable parameters of the quantum annealing subsystem, the parameters comprising the coupling between the superconducting qubits, such that H tot = I(t) H i + G(t) H QG + P(t) H p, where I(t), G(t), and P(t) are time-dependent control parameters of H i, H QG, and H p respectively, based on i) the information representing the energy states of the total Hamiltonian, ii) the average phonon energy, and iii) the probability mass function; and selecting a H QG from the distribution of H QG for programming the quantum annealing subsystem to configure the couplings between the superconducting qubits. obtaining information representing energy states of a total Hamiltonian H tot, wherein the total Hamiltonian H tot characterizes dynamics of a quantum system having controllable quantum states, the quantum system being controlled such that the total Hamiltonian H tot evolves from an initial quantum Hamiltonian H i over time t to a problem quantum Hamiltonian H p at time t T; calculating an average phonon energy of a bath in which the quantum system is located; assigning a probability, using a probability mass function, to each energy state that a quantum annealing subsystem of the quantum system may adopt at time t T such that a final state of the quantum annealing subsystem at time t T has a maximum overlap with the ground state of H p; wherein the quantum annealing subsystem comprises a plurality of superconducting units, the plurality of superconducting units comprising superconducting qubits; determining a distribution for a Hamiltonian term, H QG, with respect to controllable parameters of the quantum annealing subsystem, the parameters comprising the coupling between the superconducting qubits, such that H tot = I(t) H i + G(t) H QG + P(t) H p, where I(t), G(t), and P(t) are time-dependent control parameters of H i, H QG, and H p respectively, based on i) the information representing the energy states of the total Hamiltonian, ii) the average phonon energy, and iii) the probability mass function; and selecting a H QG from the distribution of H QG for programming the quantum annealing subsystem to configure the couplings between the superconducting qubits.