Enhancing simulated annealing with quantum annealing
Methods and apparatus for enhancing simulated annealing with quantum fluctuations. In one aspect, a method includes obtaining an 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; outputting a first evolved state and first temperature value; reducing the temperature to a minimum 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; outputting a second evolved state as a subsequent input state for the simulated annealing, and determining that the completion of the first event has occurred.
1 . A method for implementing an annealing schedule, the method comprising:
iteratively:
performing, on an input state for the iteration, simulated annealing with a temperature reduction schedule to obtain a first evolved state, comprising reducing the temperature until a decrease in energy is below a first minimum value;
determining whether a reduced temperature that causes the decrease in energy to be below the first minimum value is higher than a predetermined minimum temperature; and
in response to determining that the reduced temperature is higher than the predetermined minimum temperature, performing quantum annealing on the first evolved state to obtain a subsequent input state for the simulated annealing; or
in response to determining that the reduced temperature is lower or equal to the predetermined minimum temperature, outputting the first evolved state as a final state.
2 . The method of claim 1 , wherein an input state for an initial iteration is a state of a physical system whose ground state encodes a solution to an optimization task.
3 . The method of claim 2 , further comprising performing a measurement on the final state to determine the solution to the optimization task.
4 . The method of claim 2 , wherein performing simulated annealing on the input state with a temperature reduction schedule comprises performing a Metropolis algorithm.
5 . The method of claim 1 , wherein an input state for an initial iteration is a randomly chosen state.
6 . The method of claim 1 , wherein an input state for an initial iteration is a classical state and preparing the classical state comprises setting the temperature to a predetermined maximum value.
7 . The method of claim 1 , wherein performing quantum annealing comprises repeating a number of sweeps of quantum annealing until a decrease in energy is below a second minimum value, wherein the second minimum value is different from the first minimum value.
8 . The method of claim 7 , wherein performing quantum annealing comprises:
creating a list of connected subgraphs;
computing a lowest achievable energy value for each connected subgraph;
computing a 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 transition that achieves an overall largest positive difference; and
performing the corresponding transition that achieves the overall largest positive difference.
9 . The method of claim 8 , wherein the connected subgraphs are of size K.
10 . The method of claim 9 , wherein the number of repeated sweeps is at most Q s N/K, wherein Q s is a predetermined number of quantum sweeps and N is a system size.
11 . The method of claim 8 , wherein selecting the subgraph and corresponding transition that achieves the overall largest positive difference further comprises:
calculating a Hamming distance for each connected subgraph in a set of connected subgraphs that achieves an overall lowest achievable energy value;
determining that there is one subgraph with a shortest Hamming distance relative to a Hamming distance of other subgraphs; and
choosing the transition that has the shortest Hamming distance in response to determining that there is one subgraph with the shortest Hamming distance.
12 . The method of claim 11 , further comprising:
determining that there is more than one subgraph with a shortest Hamming distance; and
choosing the transition from the set of subgraphs that achieve the overall lowest achievable energy value and that have the shortest Hamming distance at random.
13 . An apparatus comprising:
an annealing system comprising a quantum system in communication with an auxiliary system, the annealing system configured to:
iteratively:
perform, on an input state for the iteration, simulated annealing with a temperature reduction schedule to obtain a first evolved state, comprising reducing the temperature until a decrease in energy is below a first minimum value:
determine whether a reduced temperature that causes the decrease in energy to be below the first minimum value is higher than a predetermined minimum temperature; and
in response to determining that the reduced temperature is higher than the predetermined minimum temperature, perform quantum annealing on the first evolved state to obtain a subsequent input state for the simulated annealing: or
in response to determining that the reduced temperature is lower or equal to the predetermined minimum temperature, output the first evolved state as a final state.
14 . The apparatus of claim 13 , wherein the auxiliary system acts as a thermal bath for the quantum system.
15 . The apparatus of claim 13 , wherein an input state for an initial iteration is a state of a physical system whose ground state encodes a solution to an optimization task and the annealing system is further configured to perform a measurement on the final state to determine the solution to the optimization task.
16 . The apparatus of claim 13 , wherein performing simulated annealing on the input state with a temperature reduction schedule comprises performing a Metropolis algorithm.
17 . An apparatus comprising:
an annealing system comprising a quantum integrated circuit in communication with a classical integrated circuit, the annealing system configured to:
iteratively:
perform, on an input state for the iteration, simulated annealing with a temperature reduction schedule to obtain a first evolved state, comprising reducing the temperature until a decrease in energy is below a first minimum value:
determine whether a reduced temperature that causes the decrease in energy to be below the first minimum value is higher than a predetermined minimum temperature; and
in response to determining that the reduced temperature is higher than the predetermined minimum temperature, perform quantum annealing on the first evolved state to obtain a subsequent input state for the simulated annealing: or in response to determining that the reduced temperature is lower or equal to the predetermined minimum temperature, output the first evolved state as a final state.
18 . The apparatus of claim 17 , wherein an input state for an initial iteration is a state of a physical system whose ground state encodes a solution to an optimization task and the annealing system is further configured to perform a measurement on the final state to determine the solution to the optimization task.
19 . The apparatus of claim 17 , wherein performing simulated annealing on the input state with a temperature reduction schedule comprises performing a Metropolis algorithm.
20 . The apparatus of claim 17 , wherein an input state for an initial iteration is a classical state and preparing the classical state comprises setting the temperature to a predetermined maximum value.