A method for performing thermal annealing with quantum fluctuations, the method performed by an annealing system comprising a quantum computer in communication with a classical chip, wherein a ground state of the quantum computer encodes the solution to an optimization task, the method comprising: obtaining an initial input state, wherein the initial input state describes a state of the classical chip; performing simulated annealing followed by quantum annealing on the initial input state and subsequent input states until a completion of a first event to determine a final evolved state; and measuring the final evolved state to determine a solution to the optimization task, wherein the simulated annealing and quantum annealing comprises: performing simulated annealing on the initial input state or subsequent input state with a temperature reduction schedule to determine a first evolved state; performing quantum annealing on the first evolved state with a transversal field increase schedule at a minimum temperature until a completion of a second event occurs to determine a second evolved state, the quantum annealing comprising: creating a list of connected subgraphs that represents the qubits of the quantum computer and their interactions; computing a lowest achievable energy value of the quantum computer for each connected subgraph; computing the difference between a current energy value and the lowest achievable energy value for each connected subgraph; determining that at least one difference is positive; selecting the subgraph and corresponding state transition of the quantum computer that achieves an overall largest positive difference; performing the corresponding state transition of the quantum computer that achieves the overall largest positive difference; and outputting the second evolved state as a subsequent input state for simulated annealing. obtaining an initial input state, wherein the initial input state describes a state of the classical chip; performing simulated annealing followed by quantum annealing on the initial input state and subsequent input states until a completion of a first event to determine a final evolved state; and measuring the final evolved state to determine a solution to the optimization task, wherein the simulated annealing and quantum annealing comprises: performing simulated annealing on the initial input state or subsequent input state with a temperature reduction schedule to determine a first evolved state; performing quantum annealing on the first evolved state with a transversal field increase schedule at a minimum temperature until a completion of a second event occurs to determine a second evolved state, the quantum annealing comprising: creating a list of connected subgraphs that represents the qubits of the quantum computer and their interactions; computing a lowest achievable energy value of the quantum computer for each connected subgraph; computing the difference between a current energy value and the lowest achievable energy value for each connected subgraph; determining that at least one difference is positive; selecting the subgraph and corresponding state transition of the quantum computer that achieves an overall largest positive difference; performing the corresponding state transition of the quantum computer that achieves the overall largest positive difference; and outputting the second evolved state as a subsequent input state for simulated annealing. performing simulated annealing on the initial input state or subsequent input state with a temperature reduction schedule to determine a first evolved state; performing quantum annealing on the first evolved state with a transversal field increase schedule at a minimum temperature until a completion of a second event occurs to determine a second evolved state, the quantum annealing comprising: creating a list of connected subgraphs that represents the qubits of the quantum computer and their interactions; computing a lowest achievable energy value of the quantum computer for each connected subgraph; computing the difference between a current energy value and the lowest achievable energy value for each connected subgraph; determining that at least one difference is positive; selecting the subgraph and corresponding state transition of the quantum computer that achieves an overall largest positive difference; performing the corresponding state transition of the quantum computer that achieves the overall largest positive difference; and outputting the second evolved state as a subsequent input state for simulated annealing. creating a list of connected subgraphs that represents the qubits of the quantum computer and their interactions; computing a lowest achievable energy value of the quantum computer for each connected subgraph; computing the difference between a current energy value and the lowest achievable energy value for each connected subgraph; determining that at least one difference is positive; selecting the subgraph and corresponding state transition of the quantum computer that achieves an overall largest positive difference; performing the corresponding state transition of the quantum computer that achieves the overall largest positive difference; and outputting the second evolved state as a subsequent input state for simulated annealing.