Jij

Jij is part of the Strangeworks Syndicate and is working on developing quantum annealing devices.

Solvers

Model	Solvers
Quadratic Unconstrained Binary Optimization (QUBO)	`jij.SA`, `jij.SQA`
Constrained Quadratic Model (CQM)	`jij.LeapHybridCQM`

note

The maximum calculation time before solver timeout is 600.0s.

Simulated Annealing

QUBO

import strangeworks as sw
from strangeworks_optimization import StrangeworksOptimizer
from strangeworks_optimization_models.parameter_models import JijSAParameterModel
from dimod import BinaryQuadraticModel

sw.authenticate(api_key)

linear = {1: -2, 2: -2, 3: -3, 4: -3, 5: -2}
quadratic = {(1, 2): 2, (1, 3): 2, (2, 4): 2, (3, 4): 2, (3, 5): 2, (4, 5): 2}
model = BinaryQuadraticModel(linear, quadratic, "BINARY")

solver = "jij.SA"
options = JijSAParameterModel(num_sweeps=2000, num_reads=100)

so = StrangeworksOptimizer(
    model=model,
    solver=solver,
    options=options)
sw_job = so.run()

print(f"Job slug: {sw_job.slug}")
print(f"Job status: {so.status(sw_job.slug)}")

results = so.results(sw_job.slug)

Parameters

from strangeworks_optimization_models.parameter_models import JijSAParameterModel

options = JijSAParameterModel(.....)

Name	Description	Default Value
feed_dict	Dictionary of coefficients for jm.Problem.	None
num_search	Number of times algorithm will be run.	1
multipliers	Multipliers for any constraints in jm.Problem	None
beta_min	Inverse temperature.	None
beta_max	Inverse temperature.	None
num_sweeps	The number of Monte-Carlo steps.	1000
num_reads	The number of samples. If `None`, 1 will be set.	1
initial_state	Initial state.	None
updater	Updater algorithm. "single spin flip" or "swendsen wang".	single spin flip
sparse	If `True`, only non-zero matrix elements are stored, which will save memory.	False
reinitialize_state	If `True`, reinitialize state for each run.	True
seed	Seed for Monte Carlo algorithm.	None
needs_square_constraints	This dictionary object is utilized to determine whether to square the constraint condition while incorporating it into the QUBO/HUBO penalty term. Here, the constraint's name is used as the key. If the value is set to True, the corresponding constraint is squared upon its addition to the QUBO/HUBO penalty term.	True for linear constraints, and to False for non-linear ones.
relax_as_penalties	This dictionary object is designed to regulate the incorporation of constraint conditions into the QUBO/HUBO penalty term, with the constraint's name functioning as the key. If the key's value is True, the respective constraint is added to the QUBO/HUBO penalty term. If the value is False, the constraint is excluded from the penalty term, though it remains subject to evaluation to verify if it meets the constraint conditions.	True

Solvers

jij.SA

Simulated Quantum Annealing

QUBO

import strangeworks as sw
from strangeworks_optimization import StrangeworksOptimizer
from strangeworks_optimization_models.parameter_models import JijSQAParameterModel
from dimod import BinaryQuadraticModel

sw.authenticate(api_key)

linear = {1: -2, 2: -2, 3: -3, 4: -3, 5: -2}
quadratic = {(1, 2): 2, (1, 3): 2, (2, 4): 2, (3, 4): 2, (3, 5): 2, (4, 5): 2}
model = BinaryQuadraticModel(linear, quadratic, "BINARY")

solver = "jij.SQA"
options = JijSQAParameterModel(num_sweeps=2000, num_reads=100)

so = StrangeworksOptimizer(
    model=model, 
    solver=solver, 
    options=options)
sw_job = so.run()

print(f"Job slug: {sw_job.slug}")
print(f"Job status: {so.status(sw_job.slug)}")

results = so.results(sw_job.slug)

Parameters

from strangeworks_optimization_models.parameter_models import JijSQAParameterModel

options = JijSQAParameterModel(.....)

Name	Description	Default Value
feed_dict	Dictionary of coefficients for jm.Problem.	None
num_search	Number of times algorithm will be run.	1
multipliers	Multipliers for any constraints in jm.Problem	None
beta	Inverse temperature.	None
gamma	Strength of transverse field.	None
num_sweeps	The number of Monte-Carlo steps.	1000
num_reads	The number of samples.	1
sparse	If `True`, only non-zero matrix elements are stored, which will save memory.	False
reinitialize_state	If `True`, reinitialize state for each run.	True
seed	Seed for Monte Carlo algorithm.	None
needs_square_constraints	This dictionary object is utilized to determine whether to square the constraint condition while incorporating it into the QUBO/HUBO penalty term. Here, the constraint's name is used as the key. If the value is set to True, the corresponding constraint is squared upon its addition to the QUBO/HUBO penalty term.	True for linear constraints, and to False for non-linear ones.
relax_as_penalties	This dictionary object is designed to regulate the incorporation of constraint conditions into the QUBO/HUBO penalty term, with the constraint's name functioning as the key. If the key's value is True, the respective constraint is added to the QUBO/HUBO penalty term. If the value is False, the constraint is excluded from the penalty term, though it remains subject to evaluation to verify if it meets the constraint conditions.	True

Solvers

jij.SQA

Name	Description	Default Value
feed_dict	Dictionary of coefficients for jm.Problem.	`None`
num_search	Number of times algorithm will be run.	`1`
multipliers	Multipliers for any constraints in jm.Problem	`None`
beta	Inverse temperature.	`None`
gamma	Strength of transverse field.	`None`
num_sweeps	The number of Monte-Carlo steps.	`1000`
num_reads	The number of samples.	`1`
sparse	If `True`, only non-zero matrix elements are stored, which will save memory.	`False`
reinitialize_state	If `True`, reinitialize state for each run.	`True`
seed	Seed for Monte Carlo algorithm.	`None`
needs_square_constraints	This dictionary object is utilized to determine whether to square the constraint condition while incorporating it into the QUBO/HUBO penalty term. Here, the constraint's name is used as the key. If the value is set to True, the corresponding constraint is squared upon its addition to the QUBO/HUBO penalty term.	`True` for linear constraints, and to `False` for non-linear ones.
relax_as_penalties	This dictionary object is designed to regulate the incorporation of constraint conditions into the QUBO/HUBO penalty term, with the constraint's name functioning as the key. If the key's value is True, the respective constraint is added to the QUBO/HUBO penalty term. If the value is False, the constraint is excluded from the penalty term, though it remains subject to evaluation to verify if it meets the constraint conditions.	`True`

Leap Hybrid CQM

CQM

To submit a constrained quadratic model to the LeapHybridCQM solver through Jij, we must use JijModeling to define the problem.

import strangeworks as sw
from strangeworks_optimization import StrangeworksOptimizer
from strangeworks_optimization_models.parameter_models import JijLeapHybridCQMParameterModel
import jijmodeling as jm

d = jm.Placeholder("d", ndim=1)  # Define variable d
d.len_at(0, latex="N")  # Set latex expression of the length of d
x = jm.BinaryVar("x", shape=(d.shape[0],))  # Define binary variable
i = jm.Element("i", belong_to=(0, d.shape[0]))  # Define dummy index in summation
model = jm.Problem("simple problem")  # Create problem instance
model += jm.sum(i, d[i] * x[i])  # Add objective function
model += jm.Constraint("one hot", jm.sum(i, x[i]) == 1)  # Add constraint condition
model  # Display the problem

solver = "jij.LeapHybridCQM"
options = JijLeapHybridCQMParameterModel(feed_dict={"d": [1.0, 0.1, -2.0, 1.0]}, time_limit=10)

so = StrangeworksOptimizer(
    model=model, 
    solver=solver, 
    options=options)
sw_job = so.run()

print(f"Job slug: {sw_job.slug}")
print(f"Job status: {so.status(sw_job.slug)}")

results = so.results(sw_job.slug)

Parameters

from strangeworks_optimization_models.parameter_models import JijLeapHybridCQMParameterModel

options = JijLeapHybridCQMParameterModel(.....)

Name	Description	Default Value
feed_dict	Dictionary of coefficients for jm.Problem. If `None`, an empty dictionary will be set.	{}
num_search	Number of times algorithm will be run. If `None`, 1 will be set.	1
time_limit	Time limit in seconds. If `None`, this will be set automatically.	None

Solvers

jij.LeapHybridCQM

Jij

Solvers​

Simulated Annealing​

QUBO​

Parameters​

Solvers

Simulated Quantum Annealing​

QUBO​

Parameters​

Solvers

Leap Hybrid CQM​

CQM​

Parameters​

Solvers

Solvers

Simulated Annealing

QUBO

Parameters

Simulated Quantum Annealing

QUBO

Parameters

Leap Hybrid CQM

CQM

Parameters