Enhancing simulated annealing with quantum annealing

An apparatus comprising:

• an annealing system comprising a quantum system in communication with an auxiliary system, the annealing system configured to:
• obtain an initial input state;
• perform simulated annealing and quantum annealing on the initial input state and subsequent input states until a completion of a first event, comprising:
• receiving an input state, the input state being one of the initial input state or a subsequent input state;
• performing simulated annealing on the input state with a temperature reduction schedule until a decrease in energy is below a first minimum value;
• terminating the simulated annealing in response to determining that the decrease in energy is below the first minimum level, comprising reducing the temperature to a minimum temperature value;
• outputting a first evolved state and first temperature value;
• performing quantum annealing on the first evolved state with a transversal field increase schedule until a completion of a second event occurs;
• terminating the quantum annealing in response to determining that a completion of the second event has occurred;
• and
• outputting a second evolved state as a subsequent input state for the simulated annealing;
• and
• determine that the completion of the first event has occurred.

An apparatus comprising:

• an annealing system comprising a quantum integrated circuit in communication with a classical integrated circuit, the annealing system configured to:
• obtain an initial input state;
• perform simulated annealing and quantum annealing on the initial input state and subsequent input states until a completion of a first event, comprising:
• receiving an input state, the input state being one of the initial input state or a subsequent input state;
• performing simulated annealing on the input state with a temperature reduction schedule until a decrease in energy is below a first minimum value;
• terminating the simulated annealing in response to determining that the decrease in energy is below the first minimum level, comprising reducing the temperature to a minimum temperature value;
• outputting a first evolved state and first temperature value;
• performing quantum annealing on the first evolved state with a transversal field increase schedule until a completion of a second event occurs;
• terminating the quantum annealing in response to determining that a completion of the second event has occurred;
• and
• outputting a second evolved state as a subsequent input state for the simulated annealing;
• and
• determine that the completion of the first event has occurred.