Fixstars Amplify¶

Fixstars Amplify Annealing Engine v1¶

Fixstars Amplify Annealing Engine (Amplify AE) is a solver provided by Fixstars Amplify. It uses heuristic algorithms based on simulated annealing on GPUs, leveraging their parallel computing capabilities to search for solutions with high speed and accuracy.

Tip

A free API token is available upon user registration.

Solver specification:

Client class	`amplify.AmplifyAEClient`
Execution parameters	`amplify.AmplifyAEClient.Parameters`
Execution result	`amplify.AmplifyAEClient.Result`
Execution time	`amplify.AmplifyAEClient.Result.execution_time_ms`
API Method	REST API (JSON)
API reference	📖 Documents

When the solver property is set to Constraint (default):

	Binary variable	Ising variable	Integer variable	Real variable
Objective function	4th	-	-	-
Equality constraint	4th	-	-	-
Inequality constraint	4th	-	-	-

When the solver property is set to Pubo:

	Binary variable	Ising variable	Integer variable	Real variable
Objective function	4th	-	-	-
Equality constraint	4th^*	-	-	-
Inequality constraint	4th^*	-	-	-

*: must give a penalty function.

When the solver property is set to Qubo:

	Binary variable	Ising variable	Integer variable	Real variable
Objective function	2nd	-	-	-
Equality constraint	2nd^*	-	-	-
Inequality constraint	2nd^*	-	-	-

*: must give a penalty function.

Client class:

In addition to the common interface of the client class, it has the following attributes.

Attribute	Data type	Details
`solver`	`Solver`	Set the solve mode for Amplify AE. The default is `Constraint`. By setting it to `Pubo` or `Qubo`, you can perform solves that emulate the PUBO / QUBO solvers. For details, please refer to the Amplify AE documentation.
`compression`	`bool`	Compress the requested data before sending. The default is `True`; setting it to `False` will reduce request data compression time, but may increase transmission time.

Configuration example:

Here is an example configuration. For parameter details, please refer to the Amplify AE documentation.

from amplify import AmplifyAEClient
from datetime import timedelta

client = AmplifyAEClient()

# Set API token
client.token = "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx"

# Set the solver mode
client.solver = "Constraint" # For general (Default)
# client.solver = "Pubo"  # For PUBO simulation
# client.solver = "Qubo"  # For QUBO simulation

# Set timeout to 1 second
client.parameters.time_limit_ms = timedelta(milliseconds=1000)

# Set the number of GPUs to use to 1
client.parameters.num_gpus = 1

# Get all solutions obtained during the search
client.parameters.duplicate_solutions = True

Execution example:

from amplify import Model, VariableGenerator, solve

# Define decision variables and the objective function
g = VariableGenerator()
q = g.array("Binary", 2)
f = q[0] * q[1] + q[0] - q[1] + 1

# Create a model
model = Model(f)

# Run the solver
result = solve(model, client)

Obtain the solver version and GPU name:

>>> client.version
'1.0.0+V100'

Obtain detailed execution time:

# Get GPU annealing time
>>> print(result.client_result.execution_time_ms)
0:00:01.008328
# Get queue wait time
>>> print(result.client_result.queue_time_ms)
0:00:00.000108
# Get the time of request reception
>>> print(result.client_result.submitted_at)
2025-08-25 17:37:38.553593+09:00
# Get the time when the request processing started
>>> print(result.client_result.started_at)
2025-08-25 17:37:38.553701+09:00

Obtain runtime parameter information:

# Number of GPUs used for solving
>>> result.client_result.num_gpus
1
# Total flip count of all GPUs tried until the execution result is returned
>>> result.client_result.num_flips
1567467520
# Number of solutions (samples) obtained until the execution result is returned
>>> result.client_result.num_samplings
58

[Deprecated] Fixstars Amplify Annealing Engine v0¶

Deprecated

Amplify AE v0 is now deprecated. Accordingly, amplify.FixstarsClient is also deprecated. For new usage, please use Amplify AE v1 and amplify.AmplifyAEClient.

The QUBO solver provided by Fixstars Amplify uses an algorithm based on Simulated Annealing implemented on GPUs.

Tip

A free API token is available upon user registration.

Solver specification:

Client class	`amplify.FixstarsClient`
Execution parameters	`amplify.FixstarsClient.Parameters`
Execution result	`amplify.FixstarsClient.Result`
Execution time	`amplify.FixstarsClient.Result.execution_time`
API method	REST API (JSON)
API reference	📖 API Reference

	Binary variable	Ising variable	Integer variable	Real variable
Objective function	2nd	-	-	-
Equality constraint	2nd^*	-	-	-
Inequality constraint	2nd^*	-	-	-

*: must give a penalty function.

Client class:

In addition to the common interface of the client class, it has the following attributes.

Attribute	Data type	Details
`compression`	`bool`	Compress the requested data before sending. The default is `True`; setting it to `False` will reduce request data compression time, but may increase transmission time.

Configuration example:

from amplify import FixstarsClient
from datetime import timedelta

client = FixstarsClient()

# Set API token
client.token = "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx"

# Set timeout to 1 second
client.parameters.timeout = timedelta(milliseconds=1000)

# Set the number of GPUs to use to 1
client.parameters.num_gpus = 1

# Get all solutions obtained during the search
client.parameters.outputs.num_outputs = 0

Execution example:

from amplify import Model, VariableGenerator, solve

# Define decision variables and the objective function
g = VariableGenerator()
q = g.array("Binary", 2)
f = q[0] * q[1] + q[0] - q[1] + 1

# Create a model
model = Model(f)

# Run the solver
result = solve(model, client)

Obtain the solver version:

>>> client.version
'v0.8.5-V100'

Obtain detailed execution time:

>>> result.client_result.execution_time
FixstarsClient.Result.ExecutionTime({
"annealing_time": 9988.965504,
"queue_time": 0.047615,
"cpu_time": 0.19356399999999996,
"time_stamps": [
    8.764683
]
})

Obtain runtime parameter information:

>>> result.client_result.execution_parameters
FixstarsClient.Result.ExecutionParameters({
"num_gpus": 1,
"timeout": 10000,
"num_iterations": 585,
"penalty_calibration": false,
"penalty_multipliers": [],
"version": "v0.8.7-V100"
})