Storage medium, solution search method, and information processing device

1 . A non-transitory computer-readable storage medium storing a solution search program that causes at least one computer to execute a process, the process comprising:

searching for a ground state of an Ising model that represents a problem by obtaining a state change of the Ising model;

reducing, from an initial state of the Ising model, a strength of a magnetic field applied to the Ising model according to a first annealing schedule; and

reducing, after a quantum phase transition occurs in the Ising model, the strength of the magnetic field according to a second annealing schedule, wherein

the second annealing schedule has fewer updates of the magnetic field up to a minimum value of the magnetic field than a first number, the first number being a number of updates of the magnetic field in a case where the strength of the magnetic field is reduced according to the first annealing schedule even after the quantum phase transition occurs in the Ising model.

2 . The non-transitory computer-readable storage medium according to claim 1 , the process further comprising:

searching for a ground state of the Ising model for each of a plurality of solution conditions with different values of a parameter in the Ising model; and

determining a value of the parameter, based on the ground state obtained by the searching, with which the strength of the magnetic field when the quantum phase transition occurs is within a certain range.

3 . The non-transitory computer-readable storage medium according to claim 2 , wherein the determining the value of the parameter includes

determining the value based on a frequency at which a spin arrangement in a lowest energy state is obtained for each of a plurality of solution conditions with different values of the parameter.

4 . The non-transitory computer-readable storage medium according to claim 1 , wherein the process further comprising

determining whether the quantum phase transition occurs based on a change in energy in each state in a process of obtaining a state change of the Ising model when the magnetic field is reduced.

5 . The non-transitory computer-readable storage medium according to claim 1 , wherein a Hamiltonian of the Ising model includes a term that indicates a nonlinear external magnetic field of a certain order.

6 . The non-transitory computer-readable storage medium according to claim 1 , wherein the searching for the ground state of the Ising model includes:

reducing the strength of the magnetic field with a real number time evolution; and

reducing energy of the Ising model based on an imaginary time propagation each time when the strength of the magnetic field is updated in the reducing the strength of the magnetic field with a real number time evolution.

7 . The non-transitory computer-readable storage medium according to claim 6 , wherein

when reducing the strength of the magnetic field with a real number time evolution after the reducing energy of the Ising model based on the imaginary time propagation,

determining that an end state of the reducing energy of the Ising model is an initial state of the reducing the strength of the magnetic field; and

changing the strength of the magnetic field within a range where an energy difference between the end state and the initial state is smaller than a certain threshold.

8 . A solution search method implemented by a computer, the solution search method comprising:

searching for a ground state of an Ising model that represents a problem by obtaining a state change of the Ising model;

reducing, from an initial state of the Ising model, a strength of a magnetic field applied to the Ising model according to a first annealing schedule; and

reducing, after a quantum phase transition occurs in the Ising model, the strength of the magnetic field according to a second annealing schedule, wherein

the second annealing schedule has fewer updates of the magnetic field up to a minimum value of the magnetic field than a first number, the first number being a number of updates of the magnetic field in a case where the strength of the magnetic field is reduced according to the first annealing schedule even after the quantum phase transition occurs in the Ising model.

9 . The solution search method according to claim 8 , further comprising:

searching for a ground state of the Ising model for each of a plurality of solution conditions with different values of a parameter in the Ising model; and

determining a value of the parameter, based on the ground state obtained by the searching, with which the strength of the magnetic field when the quantum phase transition occurs is within a certain range.

10 . The solution search method according to claim 9 , wherein the determining the value of the parameter includes

determining the value of based on a frequency at which a spin arrangement in a lowest energy state is obtained for each of a plurality of solution conditions with different values of the parameter.

11 . The solution search method according to claim 8 , further comprising

determining whether the quantum phase transition occurs based on a change in energy in each state in a process of obtaining a state change of the Ising model when the magnetic field is reduced.

12 . The solution search method according to claim 8 , wherein a Hamiltonian of the Ising model includes a term that indicates a nonlinear external magnetic field of a certain order.

13 . The solution search method according to claim 8 , wherein the searching for the ground state of the Ising model includes:

reducing the strength of the magnetic field with a real number time evolution; and

reducing energy of the Ising model based on an imaginary time propagation each time when the strength of the magnetic field is updated in the reducing the strength of the magnetic field with a real number time evolution.

14 . The solution search method according to claim 13 , wherein

when reducing the strength of the magnetic field with a real number time evolution after the reducing energy of the Ising model based on the imaginary time propagation,

determining that an end state of the reducing energy of the Ising model is an initial state of the reducing the strength of the magnetic field; and

changing the strength of the magnetic field within a range where an energy difference between the end state and the initial state is smaller than a certain threshold.

15 . An information processing device comprising:

one or more memories; and

one or more processors coupled to the one or more memories and the one or more processors configured to:

search for a ground state of an Ising model that represents a problem by obtaining a state change of the Ising model;

reduce, from an initial state of the Ising model, a strength of a magnetic field applied to the Ising model according to a first annealing schedule, and

reduce, after a quantum phase transition occurs in the Ising model, the strength of the magnetic field according to a second annealing schedule, wherein

the second annealing schedule has fewer updates of the magnetic field up to a minimum value of the magnetic field than a first number, the first number being a number of updates of the magnetic field in a case where the strength of the magnetic field is reduced according to the first annealing schedule even after the quantum phase transition occurs in the Ising model.