3D Ising Spin Glass Solutions

Description

This dataset provides ground states and energies for three-dimensional Ising spin glass instances with system sizes
N=263,678,958,1312,2084,5627.

All configurations were obtained using a cyclic quantum annealing protocol implemented on the D-Wave quantum annealer, followed by a digital cooling method.

The dataset is associated with the results reported in:

H. Zhang & A. Kamenev, "Computational complexity of three-dimensional Ising spin glass: Lessons from D-Wave annealer", Phys. Rev. Research 7, 033098 (2025).
https://journals.aps.org/prresearch/abstract/10.1103/3bkn-v5rd

Applications

• Benchmarking quantum and classical optimization algorithms on large-scale optimization problems

• Studying 3D Ising spin glasses

• Providing reference ground states for testing quantum annealing and hybrid quantum-classical methods

Data Structure

For each system size N:

SpinGlassData/N_{N}_realization_{r}/
 ├── J.npz         # Coupling matrix J (dictionary format)
 └── solution.npz  # Contains:
                   #   - "solution": ground state spin configuration
                   #   - "energy": ground state energy

Loading Data

Method 1: Load individual instances

import numpy as np

number_of_nodes_list = [263, 678, 958, 1312, 2084, 5627]
realization_number = 1
solution_list, energy_list = [], []

for N in number_of_nodes_list:
    directory = f'SpinGlassData/N_{N}_realization_{realization_number}/'
    J = np.load(directory + "J.npz", allow_pickle=True)["J"].item()
    sol = np.load(directory + "solution.npz", allow_pickle=True)["solution"].item()
    E = np.load(directory + "solution.npz", allow_pickle=True)["energy"].item()
    solution_list.append(sol)
    energy_list.append(E)

Method 2: Load all-in-one file

import numpy as np

data = np.load("SpinGlassData/all_data.npz", allow_pickle=True)
J_list = data["J_list"]
ground_energy_list = np.array(data["ground_energy_list"])
ground_state_list = data["ground_state_list"]
N_list = np.array(data["N_list"])

Citation

If you use this dataset, please cite the related publication:

H. Zhang & A. Kamenev, "Computational complexity of three-dimensional Ising spin glass: Lessons from D-Wave annealer", Phys. Rev. Research 7, 033098 (2025).
https://journals.aps.org/prresearch/abstract/10.1103/3bkn-v5rd

BibTex

@article{zhangComputationalComplexityThreedimensional2025,
  title = {Computational Complexity of Three-Dimensional Ising Spin Glass: Lessons from D-wave Annealer},
  author = {Zhang, Hao and Kamenev, Alex},
  year = {2025},
  month = jul,
  journal = {Physical Review Research},
  volume = {7},
  number = {3},
  pages = {033098},
  publisher = {American Physical Society},
  doi = {10.1103/3bkn-v5rd},
  url = {https://link.aps.org/doi/10.1103/3bkn-v5rd}
}