Welcome to OpenJij’s documentation!

Welcome to OpenJij’s documentation!#

OpenJij : Framework for the Ising model and QUBO.#

Introduction#

This project is still going. If you can help, please join in the OpenJij Slack Community. Then, you can participate in the project, and ask questions.

OpenJij Discord Community

What is OpenJij ?#

OpenJij is a heuristic optimization library of the Ising model and QUBO. It has a Python interface, therefore it can be easily written in Python, although the core part of the optimization is implemented with C++. Let’s install OpenJij.

Install#

pip#

$ pip install openjij

Minimum sample code#

Simulated annealing (SA)#

for the Ising model#

to get a sample that executed SA 100 times

import openjij as oj
n = 10
h, J = {}, {}
for i in range(n-1):
    for j in range(i+1, n):
        J[i, j] = -1
sampler = oj.SASampler()
response = sampler.sample_ising(h, J, num_reads=100)
# minimum energy state
print(response.first.sample)
# {0: -1, 1: -1, 2: -1, 3: -1, 4: -1, 5: -1, 6: -1, 7: -1, 8: -1, 9: -1}
# or
# {0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 8: 1, 9: 1}
# indices (labels) of state (spins)
print(response.indices)
# [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

Parameters customize#

Customize annealing schedule#

import openjij as oj
n = 10
h, J = {}, {}
for i in range(n-1):
    for j in range(i+1, n):
        J[i, j] = -1
# customized annealing schedule
# list of [beta, monte carlo steps in beta]
schedule = [
    [10, 3],
    [ 5, 5],
    [0.5, 10]
]
sampler = oj.SASampler()
response = sampler.sample_ising(h, J, schedule=schedule)
print(response)

Higher order model#

If you want to handle higher order model as follows:

\[\begin{split}H = \sum_{i}h_i\sigma_i + \sum_{i < j} J_{ij} \sigma_i \sigma_j + \sum_{i, j, k} K_{i,j,k} \sigma_i\sigma_j \sigma_k \cdots \\\end{split}\]

use .sample_hubo

HUBO: Higher order unconstraint binary optimization

Sample code#

import openjij as oj
# Only SASampler can handle HUBO.
sampler = oj.SASampler()
# make HUBO
J = {(0,): -1, (0,1): -1, (0,1,2): 1}
response = sampler.sample_hubo(J, vartype="SPIN")
print(response)
#    0  1  2 energy num_oc.
# 0 +1 +1 -1   -3.0       1
# ['SPIN', 1 rows, 1 samples, 3 variables]
response = sampler.sample_hubo(J, vartype="BINARY")
print(response)
#    0  1  2 energy num_oc.
# 0  1  1  0   -2.0       1
# ['BINARY', 1 rows, 1 samples, 3 variables]

Outline#

Tutorial