NEC

NEC 🔗 is developing quantum annealers using superconducting parametron qubits with a greater number of all-to-all connected qubits.

Solver

Model	Solvers
Quadratic Unconstrained Binary Optimization (QUBO)	nec.vector_annealer, nec_3.vector_annealer

Quadratic Unconstrained Binary Optimization (QUBO)

Binary Quadratic Model (BQM)

import strangeworks as sw
from strangeworks_optimization import StrangeworksOptimizer
from strangeworks_optimization_models.parameter_models import NEC2ParameterModel
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")

options = NEC2ParameterModel(offset=0, num_reads=2, num_results=2, timeout=100)

solver = "nec.vector_annealer"

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)

QUBO Dictionary

The NEC QUBO Dictionary is a data structure used to represent a Quadratic Unconstrained Binary Optimization (QUBO) problem. In this dictionary, each key-value pair corresponds to a term in the QUBO problem. The keys are tuples representing the variables involved in the term, while the values are the coefficients of those terms.

For instance, a QUBO Dictionary might look like this:

QuboDict({("x1", "x1"): 1.0, ("x1", "x2"): -2.0})

In this case, the QUBO problem has two variables, x1 and x2. The first term (x1, x1) has a coefficient of 1.0, and the second term (x1, x2) has a coefficient of -2.0.

import strangeworks as sw
from strangeworks_optimization import StrangeworksOptimizer
from strangeworks_optimization_models.parameter_models import NECParameterModel
from strangeworks_optimization_models.problem_models import QuboDict

sw.authenticate(api_key)

model = QuboDict({("x1", "x1"): 1.0, ("x1", "x2"): -2.0})

options = NECParameterModel(offset=0, num_reads=2, num_results=2, timeout=100)

solver = "nec.vector_annealer"

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)

Results

NEC includes additional sampleset data in the vectors field, an array-like structure containing data fields for spin constraint satisfaction (constraint), memory usage (memory_usage), and Vector Annealer operation time (time). This allows for detailed analysis and aggregation using dimod.SampleSet methods.

sampleset = so.results(sw_job.slug).solution
for datum in sampleset.data(fields=["vectors"]):
    print(datum)

Notebooks

Launch the following notebooks in Google Colab to see examples of how to use the NEC solver. Remember to set your API key as an environment variable.

Traveling Salesman Problem

Number Problem

Vector Annealing 2.0

Parameters

from strangeworks_optimization_models.parameter_models import NEC2ParameterModel

options = NEC2ParameterModel(.....)

Solvers

• nec.vector_annealer

Name	Description	Default	Values (Range)
offset	Offset to normalize weights in the QUBO formulation.	0.0	[-3.402823E+38, 3.402823E+38]
num_reads	Number of annealing sweeps to perform, determining solution attempts.	1	[1, 20]
num_results	Number of top solutions to retrieve from the annealing process.	1	[1, num_reads]
num_sweeps	Number of sweeps per annealing.	500	[1, 100000]
beta_range	Beta value range for VA in [start, end, steps].	[10.0, 100.0, 200]	start: [1.1754945E-38, 3.402823E+38], end: [1.1754945E-38, 3.402823E+38], steps: [1, 100000]
beta_list	Array of beta values for the annealing schedule.	None	[1.1754945E-38, 3.402823E+38]
dense	Matrix mode for VA. True for dense, False for sparse.	None	[None, True, False]
vector_mode	Mode during VA annealing: speed or accuracy.	speed	[speed, accuracy]
timeout	Time limit in seconds for job execution.	1800	[1, 7200]
Ve_num	Number of Vector Engines (VEs) engaged in the annealing process.	1	[1, max VE available]
onehot	One-hot encoding constraints.	[]	Example: [["x[0]", "x[1]"], ["x[2]", "x[3]"]]
fixed	Fixed value constraints for variables.	{}	Example: {"x[0]": 1, "x[1]": 0}
andzero	Constraints ensuring combinations result in zero.	[]	Example: [["x[0]", "x[1]"], ["x[2]", "x[3]"]]
orone	Constraints ensuring at least one variable equals one.	[]	Example: [["x[0]", "x[1]"], ["x[2]", "x[3]"]]
supplement	Additional constraints for solution space exploration.	[]	Example: [["x[0]", "x[1]"], ["x[2]", "x[3]"]]
maxone	Max number of ones in a solution subset.	[]	Example: [[1, ["x[0]", "x[1]"]], [2, ["x[2]", "x[3]"]]]
minmaxone	Min limit on max number of ones in a subset.	[]	Example: [[1, ["x[0]", "x[1]"]], [2, ["x[2]", "x[3]"]]]
init_spin	Initial spin settings for the annealing process.	{}	Example: {"x[0]": 1, "x[1]": 0}
spin_list	List of initial spin values used to define constraints or initial conditions.	[]	Example: ["x[0]", "x[1]", "x[2]"]

Vector Annealing 3.0

Parameters

from strangeworks_optimization_models.parameter_models import NEC3ParameterModel

options = NEC3ParameterModel(.....)

Solvers

• nec_3.vector_annealer

Name	Description	Default	Values (Range)
offset	Offset to normalize weights in the QUBO formulation.	0.0	[-3.402823E+38, 3.402823E+38]
num_reads	Number of annealing sweeps to perform, determining solution attempts.	1	[1, 20]
num_results	Number of top solutions to retrieve from the annealing process.	1	[1, num_reads]
timeout	Time limit in seconds for job execution.	1800	[1, 7200]
num_sweeps	Number of sweeps per annealing.	500	[1, 100000]
beta_range	Beta value range for VA in [start, end, steps].	[10.0, 100.0, 200]	start: [1.1754945E-38, 3.402823E+38], end: [1.1754945E-38, 3.402823E+38], steps: [1, 100000]
beta_list	Array of beta values for the annealing schedule.	None	[1.1754945E-38, 3.402823E+38]
dense	Matrix mode for VA. True for dense, False for sparse.	None	[None, True, False]
num_threads	Number of threads for computation.	None	[1, 128]
vector_mode	Mode during VA annealing: speed or accuracy.	speed	[speed, accuracy]
precision	Precision level for computations.	None	[1, 64]
onehot	One-hot encoding constraints.	None	Example: [["x[0]", "x[1]"], ["x[2]", "x[3]"]]
fixed	Fixed value constraints for variables.	{}	Example: {"x[0]": 1, "x[1]": 0}
andzero	Constraints ensuring combinations result in zero.	[]	Example: [["x[0]", "x[1]"], ["x[2]", "x[3]"]]
orone	Constraints ensuring at least one variable equals one.	[]	Example: [["x[0]", "x[1]"], ["x[2]", "x[3]"]]
supplement	Additional constraints for solution space exploration.	[]	Example: [["x[0]", "x[1]"], ["x[2]", "x[3]"]]
maxone	Max number of ones in a solution subset.	[[2, ["1", "2"]]]	Example: [[1, ["x[0]", "x[1]"]], [2, ["x[2]", "x[3]"]]]
minmaxone	Min limit on max number of ones in a subset.	[]	Example: [[1, ["x[0]", "x[1]"]], [2, ["x[2]", "x[3]"]]]
high_order	High-order constraints for the problem.	None	Example: {"x[0]": 1, "x[1]": 0}
pattern	Pattern constraints for the problem.	None	Example: [["x[0]", "x[1]"], ["x[2]", "x[3]"]]
weighted_sum	Weighted sum constraints for the problem.	None	Example: [["x[0]", "x[1]"], ["x[2]", "x[3]"]]
init_spin	Initial spin settings for the annealing process.	{}	Example: {"x[0]": 1, "x[1]": 0}