Fixstars Amplify AE¶
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.
It can handle binary variable optimization problems, which are composed of objective functions and constraints. This makes it suitable for practical applications. When combined with the Amplify SDK, it can be used to solve a broader range of general optimization problems. Furthermore, it serves as a highly accurate QUBO solver, ideal for researchers working with quantum annealing and Ising machines.
For usage with the Amplify SDK, please refer to Client Page .
Features of Amplify AE¶
Amplify AE is a solver that explores solutions to optimization problems using a heuristic algorithm based on the annealing method. A particularly unique aspect is its utilization of parallel computing technology, specifically GPUs, which are known as AI semiconductors. By highly parallelizing the solving process, it harnesses the full potential of GPUs to minimize objective functions with high speed and accuracy.
The functional specifications for the cloud-based Amplify AE are as follows:
Variable Type |
Binary |
Maximum Problem Size (Fully Connected) |
8,192 variables (Basic) / 65,536 variables (Standard) / 131,072 variables (Premium) |
Maximum Degree |
4th degree (Objective Function) / 4th degree (Constraints) |
Constraint Type |
Equality/Inequality (Constraint mode) / Penalty function (PUBO mode) |
Precision |
Input: 64-bit real number / Computation: 64-bit real number / Data: 32-bit real number |
Maximum Execution Time |
10 seconds (Basic) / Over 10 minutes (Standard, Premium) |
Supported GPUs |
NVIDIA Volta (Basic, Standard) / NVIDIA Ampere (Premium) / NVIDIA Hopper (Premium) |
Multi-GPU Support |
1 GPU (Basic) / Up to 8 GPUs (Standard, Premium) |
Endpoint URL |
https://optigan.fixstars.com |
Basic, Standard, Premium: Amplify subscription plans (Basic is free.).
The Enterprise plan offers unlimited execution time with customizable settings. Problem size limitations are contingent upon GPU memory capacity and can exceed 131,072 variables.
Supported GPUs include NVIDIA Volta / Ampere / Hopper and the latest NVIDIA Blackwell (coming soon). Access to Amplify AE with these GPUs is provided through Fixstars Amplify’s cloud service, as well as on-premises deployments.
Changed in version 1.0.0
Fixstars Amplify AE received a major update in version 1.0.0, including support for higher-order polynomials, enhanced constraint handling, and improved solving performance. While previous versions only supported quadratic objective functions and penalty functions, the new version supports objective functions up to the 4th degree and equality/inequality constraints. Additionally, version 1.0.0 improves the automatic adjustment of penalty function weights. This enables solving more complex optimization problems for a broader range of applications. A transition period keeps previous versions available for a limited time.
Input Specifications¶
Amplify AE accepts polynomials of binary variables with real-valued coefficients. It addresses problems formulated with an objective function and constraints (or penalty functions), all expressible as polynomials up to the 4th degree. It supports up to 131,072 binary variables. This is the maximum for a fully connected model (a model where variables are connected to all other variables). Input in a sparse format is possible. This lets you solve larger problems with fewer connections. Constraints support both equality and inequality constraints (Constraint mode). In the PUBO mode described later, constraints can also be set using penalty functions.
Solving requests are made as requests to the WEB API in JSON format. For API specifications, please refer to API Reference.
Solving Modes¶
Amplify AE features two solving modes: the default Constraint mode and PUBO (Polynomial Unconstrained Binary Optimization) mode. For general use, we recommend using the default Constraint mode. The PUBO mode, on the other hand, is designed for researchers using it as a simulator for quantum annealing or Ising machines. The main difference between the two lies in constraint handling. In the default Constraint mode, the solver directly handles equality and inequality constraints. In the PUBO mode, the user sets penalty functions for the desired constraints in the objective function. For technical details on these differences based on the Amplify AE operating algorithm, please refer to Solving Algorithms.
Using the functions of the Amplify SDK, the Amplify SDK can automatically set constraints and penalty functions. Switching between Constraint mode and PUBO mode is also easy. Please refer to the Clients page for details.
Changed in version 1.1.0
Version 1.1.0 adds a dense coupling mode specialized for large-scale quadratic problems with many terms.
The Amplify SDK looks at the density of the objective function and selects the format to send by itself.
It uses the dense coupling mode for an objective function that is quadratic and dense enough, and the conventional sparse coupling mode for other cases.
This rule also holds for a Matrix, because the client converts a matrix to a Poly.
Set objective_format to choose the mode yourself.
However, the choice depends on the number of terms and the problem size. If the specified mode is determined to be inefficient, the other mode will be used instead.
Parameter-Free¶
Amplify AE does not require the user to adjust any parameters for solving. When the user inputs the optimization problem, the solver automatically determines the optimal annealing strategy and performs the solution process. For example, the temperature drop schedule in simulated annealing and penalty function weights are automatically adjusted. This allows users to maximize the performance of GPU annealing without requiring complex parameter tuning.
Multi-GPU Support¶
Amplify AE supports multi-GPU environments. It performs parallel processing using multiple GPUs. Applications of multi-GPU utilization for Amplify AE include solving multiple different problems simultaneously and enhancing computational power for a single problem. The former is effective for multi-user environments or solving multiple problems concurrently. The latter allocates more computational resources to the same problem and performs inter-GPU communication to obtain a more accurate solution. In other words, higher-accuracy solutions can be obtained in a shorter time.