# Fixstars Amplify SDK documentation > The Fixstars Amplify SDK (Amplify SDK) is a Python library for formulating combinatorial optimization problems and running external optimization solvers. ## šŸš€ Get Started - [What is Amplify SDK?](https://amplify.fixstars.com/en/docs/amplify/v1/index.md): The Fixstars Amplify SDK (Amplify SDK) is a Python library for formulating combinatorial optimization problems and running external optimization solvers. - [Amplify SDK Features](https://amplify.fixstars.com/en/docs/amplify/v1/features.md): The Amplify SDK aims to formulate combinatorial optimization problems in a simple and intuitive way and solve them using a variety of machines and solvers. Toā€¦ - [Quickstart](https://amplify.fixstars.com/en/docs/amplify/v1/quickstart.md): You can run the Amplify SDK in any of the following ways. ## šŸŒ± Basic - [1. Amplify SDK Overview](https://amplify.fixstars.com/en/docs/amplify/v1/overview.md): Before we go into the functionality details, let us summarize the overall picture and execution flow of the Amplify SDK. - [2. Creating Decision Variables](https://amplify.fixstars.com/en/docs/amplify/v1/variables.md): You must express the problem formulation in the program code to solve a combinatorial optimization problem with Amplify SDK. This page describes the first stepā€¦ - [3. Polynomials and Objective Functions](https://amplify.fixstars.com/en/docs/amplify/v1/objective.md): The objective function is a mathematical expression expressing the degree to which the objective in a combinatorial optimization problem is achieved; in theā€¦ - [4. Constructing Constraints](https://amplify.fixstars.com/en/docs/amplify/v1/constraint.md): Constraints are the conditions that must be satisfied by the values of the decision variables in a combinatorial optimization problem. In the Amplify SDK youā€¦ - [5. Model Formulation](https://amplify.fixstars.com/en/docs/amplify/v1/model.md): A combinatorial optimization problem comprises decision variables, objective functions, and constraints. In ā€œ2. Creating Decision Variables,ā€ ā€œ3. Polynomialsā€¦ - [6. Solver Client](https://amplify.fixstars.com/en/docs/amplify/v1/clients.md): To run a solver from the Amplify SDK, you must create a solver client that abstracts each solver and specifies the connection point, API token, and executionā€¦ - [7. Solving a Combinatorial Optimization Problem](https://amplify.fixstars.com/en/docs/amplify/v1/solve.md): This page explains how to solve a combinatorial optimization problem using the model Model and solver client created in ā€œModel Formulationā€ and ā€œSolver Client.ā€ ## šŸŒ» Advanced - [Model Conversions](https://amplify.fixstars.com/en/docs/amplify/v1/conversion.md): The Amplify SDK allows you to create models that contain real and integer variables and polynomials of any degree. On the other hand, combinatorialā€¦ - [Variable Conversion and Degree Reduction](https://amplify.fixstars.com/en/docs/amplify/v1/intermediate.md): The Amplify SDK allows you to create models that include real and integer variables and polynomials of any degree. On the other hand, combinatorialā€¦ - [Constraints and Penalty Functions](https://amplify.fixstars.com/en/docs/amplify/v1/penalty.md): The Amplify SDK allows you to create models with any variable and polynomial degree constraints. However, each combinatorial optimization solver handlesā€¦ - [Graph Embedding](https://amplify.fixstars.com/en/docs/amplify/v1/graph.md): Some QUBO and Ising solvers do not accept arbitrary second-order polynomials and are limited in the number of second-order terms that you can pass to theā€¦ - [Evaluation of Execution Results](https://amplify.fixstars.com/en/docs/amplify/v1/evaluation.md): The execution result returned by the solve() function contains various information about the solutions, model conversion, and execution time. This pageā€¦ - [Execution Time information](https://amplify.fixstars.com/en/docs/amplify/v1/timing.md): The Amplify SDK provides an interface to obtain information of various execution times when solving combinatorial optimization problems. - [Client details](https://amplify.fixstars.com/en/docs/amplify/v1/solvers.md): The Amplify SDK provides client classes for the solvers that you can run from the SDK. The client classes wrap each solverā€™s API and provide an interface forā€¦ - [Fixstars Amplify](https://amplify.fixstars.com/en/docs/amplify/v1/clients/fixstars.md): Fixstars Amplify Annealing Engine (Amplify AE) is a solver provided by Fixstars Amplify. It uses heuristic algorithms based on simulated annealing on GPUs,ā€¦ - [D-Wave Systems](https://amplify.fixstars.com/en/docs/amplify/v1/clients/dwave.md): D-Wave Systems offers a quantum annealing machine (quantum processing unit; QPU) that allows you to input QUBO or a combinatorial optimization problemā€¦ - [TOSHIBA](https://amplify.fixstars.com/en/docs/amplify/v1/clients/toshiba.md): SQBM+ is a TOSHIBA-developed quantum-inspired optimization solution with a simulated bifurcation machine at its core. - [Fujitsu](https://amplify.fixstars.com/en/docs/amplify/v1/clients/fujitsu.md): Fujitsu DA4 is Fujitsuā€™s QUBO solver with the 4th-generation Digital Annealing Unit (DAU (GPU)). - [NEC](https://amplify.fixstars.com/en/docs/amplify/v1/clients/nec.md): NEC provides the QUBO solver, which runs on the vector supercomputer SX-Aurora TSUBASA. - [Hitachi](https://amplify.fixstars.com/en/docs/amplify/v1/clients/hitachi.md): The CMOS annealing machine provided by Hitachi. - [Gurobi](https://amplify.fixstars.com/en/docs/amplify/v1/clients/gurobi.md): Gurobi Optimizer is a Mixed Integer Programming (MIP) solver provided by Gurobi that can handle quadratic problems in integer and real variables, includingā€¦ - [Quantum Computers](https://amplify.fixstars.com/en/docs/amplify/v1/clients/quantum_algorithm.md): Clients for quantum computers run optimization with quantum algorithms such as QAOA. - [Serial Solver Execution](https://amplify.fixstars.com/en/docs/amplify/v1/serial.md): You may want to run the solver several times iteratively when evaluating performance. Also, some solvers are more likely to find a good solution by runningā€¦ - [Parallel Solver Execution](https://amplify.fixstars.com/en/docs/amplify/v1/parallel.md): parallel_solve() can send queries to multiple clients and models simultaneously. Such parallel execution may hide processing times for model transformationsā€¦ - [Objective Function with a Coefficient Matrix](https://amplify.fixstars.com/en/docs/amplify/v1/matrix.md): One way to represent the objective function is by using a multidimensional polynomial coefficient array. This is a convenient formulation when a real-valuedā€¦ - [Speedup Formulation](https://amplify.fixstars.com/en/docs/amplify/v1/optimization.md): Formulating a large combinatorial optimization problem using Pythonā€™s for statements can be very time-consuming. The Amplify SDK provides a fast way toā€¦ - [File input/output of the model](https://amplify.fixstars.com/en/docs/amplify/v1/file_io.md): You can load an LP or QPLIB file and create Model from it, and vice versa, you can save Model and output to an LP or QPLIB file. ## šŸ§© Examples - [Subset Sum Problem](https://amplify.fixstars.com/en/docs/amplify/v1/subset_sum.md): This page discuss the subset sum problem as a simple example of formulation and solving with the Amplify SDK. - [Max-Cut Problem](https://amplify.fixstars.com/en/docs/amplify/v1/maxcut.md): The Max-Cut problem is one of the most well-known combinatorial optimization problems. In this tutorial, we will walk through the problem definition and solveā€¦ - [Traveling Salesperson Problem](https://amplify.fixstars.com/en/docs/amplify/v1/tsp.md): As an example of using the Amplify SDK, we will explain how to solve the traveling salesperson problem (TSP) with the Amplify SDK. The TSP is a combinatorialā€¦ - [Quadratic Assignment Problem](https://amplify.fixstars.com/en/docs/amplify/v1/qap.md): Quadratic assignment problem (QAP) is the following problem. ## šŸ’” Tips - [Type Hint Support](https://amplify.fixstars.com/en/docs/amplify/v1/type_hint.md): The Amplify SDK defines type hints for all functions, methods, and attributes. This feature allows IDEs such as Visual Studio Code and Google Colaboratory toā€¦ - [Proxy Server Settings](https://amplify.fixstars.com/en/docs/amplify/v1/proxy.md): If you want to connect to the Internet through a proxy server, you must configure the proxy server in the code that runs the Amplify SDK cloud service. - [Formatted Formula View](https://amplify.fixstars.com/en/docs/amplify/v1/pprint.md): The Amplify SDK formulas are automatically rendered in LaTeX in IPython front-end environments that support LaTeX formula display, such as Jupyter Notebook andā€¦ - [Migrating from Previous Versions](https://amplify.fixstars.com/en/docs/amplify/v1/migration.md): The Amplify SDK v1 has lost some compatibility with v0. If you have been using an older version, this section explains how to maintain your code so that itā€¦ - [Formulation Benchmarks](https://amplify.fixstars.com/en/docs/amplify/v1/benchmark.md): We have benchmarked the formulation of mathematical optimization models provided as a library in Python against the Amplify SDK. We measured the execution timeā€¦ ## šŸŽŗ Cloud Solvers - [Fixstars Amplify AE](https://amplify.fixstars.com/en/docs/amplify/v1/amplify_ae.md): Fixstars Amplify Annealing Engine (Amplify AE) is a solver provided by Fixstars Amplify. It uses heuristic algorithms based on simulated annealing on GPUs,ā€¦ - [Solving Algorithms](https://amplify.fixstars.com/en/docs/amplify/v1/amplify_ae/algorithm.md): Fixstars Amplify Annealing Engine (Amplify AE) utilizes an optimization algorithm based on simulated annealing. This page provides an overview of the Amplifyā€¦ - [Advanced Usage](https://amplify.fixstars.com/en/docs/amplify/v1/amplify_ae/advanced.md): Leveraging the information obtained from the response data can significantly enhance your use of Amplify AE. This section details advanced techniques forā€¦ - [Performance of Amplify AE](https://amplify.fixstars.com/en/docs/amplify/v1/amplify_ae/benchmark.md): To evaluate the performance of Amplify AE, we are obtaining benchmark results from two perspectives: (1) solution performance and (2) annealing speed. - [Changelog](https://amplify.fixstars.com/en/docs/amplify/v1/amplify_ae/changelog.md): Improve performance for linear problems containing only integer-coefficient constraints. - [API Reference](https://amplify.fixstars.com/en/docs/amplify/v1/amplify_ae/api_reference.md) ## āš—ļø Quantum - [Amplify Quantum](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/index.md): The Amplify SDK provides features for researching and validating combinatorial optimization using quantum computers. - [Quickstart](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/quickstart.md): Quantum computing features are provided as an add-on to the Amplify SDK. To use them, install the package with the extra dependencies using the followingā€¦ - [List of Supported Devices](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/samplers/index.md): A list of quantum computers and their simulators supported by the Amplify SDK. All clients share a common interface, and you can switch the optimization methodā€¦ - [IBM Quantum](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/samplers/ibm.md): Uses IBM Quantum QPUs for circuit evaluation. - [Qiskit Aer Simulator](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/samplers/aer.md): Uses the Qiskit Aer Simulator for circuit evaluation. - [Qulacs Simulator](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/samplers/qulacs.md): A local simulator that uses Qulacs for circuit evaluation. - [Amazon Braket Simulator](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/samplers/aws.md): Uses Amazon Braket simulators for circuit evaluation. Both local and cloud simulators are supported. - [AQT](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/samplers/aqt.md): Uses AQT (Alpine Quantum Technologies) trapped-ion quantum computers for circuit evaluation via Amazon Braket. - [IonQ](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/samplers/ionq.md): Uses IonQā€™s trapped-ion quantum computers for circuit evaluation. - [IQM](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/samplers/iqm.md): Uses IQM superconducting quantum computers for circuit evaluation via Amazon Braket. - [Rigetti](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/samplers/rigetti.md): Uses Rigetti superconducting quantum computers for circuit evaluation via Amazon Braket. - [QUDORA](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/samplers/qudora.md): Uses QUDORA trapped-ion quantum computers and their cloud simulators for circuit evaluation. - [OQTOPUS Cloud](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/samplers/oqtopus.md): Uses cloud quantum computers and simulators available via OQTOPUS Cloud for circuit evaluation. - [List of Supported Algorithms](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/algos/index.md): A list of algorithms that use quantum computers supported by the Amplify SDK. Clients that handle quantum computers are used by specifying one of the algorithmā€¦ - [QAOA / Constrained QAOA](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/algos/QAOA.md): QAOA (Quantum Approximate Optimization Algorithm) is a quantum-classical hybrid algorithm that alternates between quantum circuit operations on a quantumā€¦ - [Recursive QAOA](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/algos/RQAOA.md): Recursive QAOA is a quantum-classical hybrid algorithm that repeatedly executes QAOA as a subroutine, progressively reducing the problem size to identify theā€¦ - [Algorithm Details](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/theories/index.md): This section introduces the theoretical framework of the quantum optimization algorithms supported by the Amplify SDK. - [QAOA Algorithm](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/theories/QAOA_algo.md): This page describes the mathematical framework of QAOA (Quantum Approximate Optimization Algorithm)[1]. - [Constrained QAOA Algorithm](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/theories/NHOT_QAOA_algo.md): Some optimization problems require finding the optimum subject to certain constraints on the variables. - [Recursive QAOA Algorithm](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/theories/RQAOA_algo.md): Recursive QAOA[1] (hereafter RQAOA) is a method that repeatedly executes QAOA with shallow ansatz circuits, progressively reducing the problem size to identifyā€¦ ## šŸ”Œ Black-Box Optimization - [Amplify-BBOpt](https://amplify.fixstars.com/en/docs/amplify/v1/amplify_bbopt.md): An extension library for performing Black-Box Optimization (BBO) using the features of the Amplify SDK. ## šŸ“– Reference - [Changelog](https://amplify.fixstars.com/en/docs/amplify/v1/changelog.md): Support quantum computers via the Amplify Quantum extension. - [API Reference](https://amplify.fixstars.com/en/docs/amplify/v1/reference/index.md) - [Algebra](https://amplify.fixstars.com/en/docs/amplify/v1/reference/algebra.md): amplify.Poly - [Poly](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.Poly.md): The polynomial class used for representing objective functions and constraints. - [PolyArray](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.PolyArray.md): A NumPy-like multidimensional array of polynomials. Supports indexing, slicing, broadcast-compatible arithmetic, and utility methods for building optimizationā€¦ - [Matrix](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.Matrix.md): This class represents a quadratic objective in coefficient-matrix form, expressed as \(x^\top Q x + p^\top x + c\). - [Variable](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.Variable.md): Class for variable information. Instances are typically obtained via as_variable() or variables. - [VariableGenerator](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.VariableGenerator.md): Provides functionality to generate a decision variable or an array of decision variables. - [sum](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.sum.md): Sum elements of a polynomial array, sequence, or iterator. Sum a sequence or iterator efficiently. Sum a sequence or iterator of constraints. Deprecatedā€¦ - [einsum](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.einsum.md): Einstein summation for polynomial arrays and NumPy arrays. - [dot](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.dot.md): Compute dot product for polynomial arrays and NumPy arrays. - [matmul](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.matmul.md): Matrix multiplication for polynomial arrays and NumPy arrays. - [newaxis](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.newaxis.md) - [VariableType](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.VariableType.md): Enum of decision variable types: Binary, Ising, Integer, and Real. - [Dim](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.Dim.md): Base class for PolyArray dimension types. - [Dim0](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.Dim0.md): A 0D PolyArray. - [Dim1](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.Dim1.md): A 1D PolyArray. - [Dim2](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.Dim2.md): A 2D PolyArray. - [Dim3](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.Dim3.md): A 3D PolyArray. - [Dim4](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.Dim4.md): A 4D PolyArray. - [Constraint](https://amplify.fixstars.com/en/docs/amplify/v1/reference/constraint.md): amplify.Constraint - [Constraint](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.Constraint.md): Constraint class representing equality or inequality conditions on polynomial expressions. - [ConstraintList](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.ConstraintList.md): List-like container of Constraint objects. - [equal_to](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.equal_to.md): Create an equality constraint. - [one_hot](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.one_hot.md): Create a one-hot constraint. - [less_equal](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.less_equal.md): Create a less-than-or-equal constraint. - [greater_equal](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.greater_equal.md): Create a greater-than-or-equal constraint. - [clamp](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.clamp.md): Create a range constraint. - [domain_wall](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.domain_wall.md): Create domain wall constraints for a variable array. - [PenaltyFormulation](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.PenaltyFormulation.md): Penalty function formulation strategy used for constraint conversion. - [Model](https://amplify.fixstars.com/en/docs/amplify/v1/reference/model.md): amplify.Model - [Model](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.Model.md): Combinatorial optimization model containing objective and constraints. - [IntegerEncodingMethod](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.IntegerEncodingMethod.md): Encoding method for integer variables during model conversion. - [RealEncodingMethod](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.RealEncodingMethod.md): Encoding method for real variables during model conversion. - [QuadratizationMethod](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.QuadratizationMethod.md): Method used to reduce higher-order terms during conversion. - [Graph Embedding](https://amplify.fixstars.com/en/docs/amplify/v1/reference/graph.md): amplify.Graph - [Graph](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.Graph.md): Physical graph information used by graph-embedding solvers. - [embed](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.embed.md): Perform graph embedding and return embedding information. - [to_edges](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.to_edges.md): Convert a polynomial to its graph edge list. - [EmbeddingMethod](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.EmbeddingMethod.md): Graph embedding algorithm to apply. - [Client](https://amplify.fixstars.com/en/docs/amplify/v1/reference/client.md): amplify.BaseClient - [BaseClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.BaseClient.md): Base class of all clients in the Amplify SDK - [AmplifyAEClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.AmplifyAEClient.md): __init__ - [FixstarsClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.FixstarsClient.md): __init__ - [DWaveSamplerClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.DWaveSamplerClient.md): __init__ - [LeapHybridSamplerClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.LeapHybridSamplerClient.md): __init__ - [LeapHybridCQMSamplerClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.LeapHybridCQMSamplerClient.md): __init__ - [FujitsuDA4Client](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.FujitsuDA4Client.md): __init__ - [FujitsuDA3cClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.FujitsuDA3cClient.md): __init__ - [ToshibaSQBM2Client](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.ToshibaSQBM2Client.md): __init__ - [GurobiClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.GurobiClient.md): __init__ - [NECVA2Client](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.NECVA2Client.md): __init__ - [HitachiClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.HitachiClient.md): __init__ - [AcceptableDegrees](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.AcceptableDegrees.md): Container of acceptable polynomial degrees by variable type for objective and constraints. - [Degree](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.Degree.md): Polynomial degree enumeration. - [Solve](https://amplify.fixstars.com/en/docs/amplify/v1/reference/solve.md): amplify.Result - [Result](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.Result.md): Container of optimization solutions and conversion/runtime metadata. - [Values](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.Values.md): Mapping from variables to numeric values in a solution. - [solve](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.solve.md): Solve a combinatorial optimization problem. - [parallel_solve](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.parallel_solve.md): Solve multiple problems in parallel. - [Misc.](https://amplify.fixstars.com/en/docs/amplify/v1/reference/misc.md): amplify.set_num_threads - [set_num_threads](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.set_num_threads.md): Set the number of threads used for parallel computation. - [load_lp](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.load_lp.md): Load an LP file and construct a model. - [save_lp](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.save_lp.md): Save a model to an LP file. - [load_qplib](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.load_qplib.md): Load a QPLIB file and construct a model. - [save_qplib](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.save_qplib.md): Save a model to a QPLIB file. - [set_seed](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.set_seed.md): Set the seed for random number generation. - [__version__](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.__version__.md): The version of the SDK. - [Quantum](https://amplify.fixstars.com/en/docs/amplify/v1/reference/quantum/index.md) - [Client](https://amplify.fixstars.com/en/docs/amplify/v1/reference/quantum/client.md): QuantumBaseClient - [QuantumBaseClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.QuantumBaseClient.md): Abstract base class for clients that target a specific backend sampler. - [AerClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.AerClient.md): Client that executes quantum circuits using the Qiskit Aer simulator. - [AQTClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.AQTClient.md): Client that executes quantum circuits on AQT hardware via Amazon Braket. - [BraketSimulatorClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.BraketSimulatorClient.md): Client that executes quantum circuits on Amazon Braket simulators. - [IBMClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.IBMClient.md): Client that executes quantum circuits on IBM Quantum hardware. - [IonQClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.IonQClient.md): Client that executes quantum circuits on IonQ hardware. - [IQMClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.IQMClient.md): Client that executes quantum circuits on IQM hardware via Amazon Braket. - [QulacsClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.QulacsClient.md): Client that executes quantum circuits using the Qulacs simulator. - [RigettiClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.RigettiClient.md): Client that executes quantum circuits on Rigetti hardware via Amazon Braket. - [QUDORAClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.QUDORAClient.md): Client that executes quantum circuits on QUDORA hardware. - [OqtopusClient](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.OqtopusClient.md): Client that executes quantum circuits on OQTOPUS Cloud. - [Algorithm](https://amplify.fixstars.com/en/docs/amplify/v1/reference/quantum/algorithm.md): QAOA - [QAOA](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.QAOA.md): Quantum Approximate Optimization Algorithm (QAOA). - [QAOAType](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.QAOAType.md): Selects the QAOA circuit construction strategy. - [QAOAResult](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.QAOAResult.md): Raw result produced by a single QAOA run. - [QAOADurations](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.QAOADurations.md): Total timing breakdown for a QAOA run. - [QAOAHistoryItem](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.QAOAHistoryItem.md): Record of a single objective function evaluation during QAOA optimization. - [RQAOA](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.RQAOA.md): Recursive Quantum Approximate Optimization Algorithm (RQAOA). - [RQAOAType](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.RQAOAType.md): Selects the QAOA circuit construction strategy used within each RQAOA iteration. - [RQAOAResult](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.RQAOAResult.md): Raw result produced by a single RQAOA run. - [RQAOADurations](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.RQAOADurations.md): Total timing breakdown for an RQAOA run. - [RQAOAHistoryItem](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.RQAOAHistoryItem.md): Record of a single iteration during RQAOA optimization. - [NormalElimination](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.NormalElimination.md): Record of a variable explicitly eliminated during an RQAOA iteration. - [UnintentionalElimination](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.UnintentionalElimination.md): Record of a variable eliminated as a side effect of another variableā€™s elimination. - [QuantumAlgoProtocol](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.QuantumAlgoProtocol.md): Protocol for quantum optimization algorithms. - [Minimize](https://amplify.fixstars.com/en/docs/amplify/v1/reference/quantum/minimize.md): ScipyMinimize - [ScipyMinimize](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.ScipyMinimize.md): Classical optimizer for QAOA circuit parameters using scipy.optimize.minimize(). - [ScipyMinimizeOptions](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.ScipyMinimizeOptions.md): Optional keyword arguments for scipy.optimize.minimize(). - [ScipyMinimizeResult](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.ScipyMinimizeResult.md): Result of a ScipyMinimize optimization run. - [NoOpMinimize](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.NoOpMinimize.md): Classical optimizer that evaluates the objective at a fixed set of parameters. - [NoOpMinimizeResult](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.NoOpMinimizeResult.md): Result of a NoOpMinimize run. - [MinimizeProtocol](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.MinimizeProtocol.md): Protocol for classical optimizers used to tune QAOA circuit parameters. - [MinimizeResult](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.MinimizeResult.md): Protocol for the result of a classical minimization run. - [Sampler](https://amplify.fixstars.com/en/docs/amplify/v1/reference/quantum/sampler.md): SamplerProtocol - [SamplerProtocol](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.SamplerProtocol.md): Protocol for quantum circuit samplers. - [SamplingDurations](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.SamplingDurations.md): Timing breakdown for a single quantum circuit sampling call. - [AerDeviceType](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.AerDeviceType.md): alias of Literal[ā€˜CPUā€™, ā€˜GPUā€™, ā€˜Thrustā€™] - [QiskitJobMeta](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.QiskitJobMeta.md): Metadata for a single Qiskit quantum job. - [QulacsJobMeta](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.QulacsJobMeta.md): Metadata for a single Qulacs simulation run. - [BraketJobMeta](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.BraketJobMeta.md): Metadata for a single Braket quantum job. - [Circuit](https://amplify.fixstars.com/en/docs/amplify/v1/reference/quantum/circuit.md): QiskitCircuit - [QiskitCircuit](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.QiskitCircuit.md): Qiskit-based quantum circuit implementation. - [QulacsCircuit](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.QulacsCircuit.md): Qulacs-based quantum circuit implementation. - [Misc.](https://amplify.fixstars.com/en/docs/amplify/v1/reference/quantum/misc.md): IsingSeqFreqList - [IsingSeqFreqList](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.IsingSeqFreqList.md): alias of list[tuple[list[int], int]] - [Deprecated](https://amplify.fixstars.com/en/docs/amplify/v1/reference/deprecated.md): amplify.BinaryPoly - [BinaryPoly](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.BinaryPoly.md): alias of Poly - [IsingPoly](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.IsingPoly.md): alias of Poly - [BinaryPolyArray](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.BinaryPolyArray.md): __init__ - [IsingPolyArray](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.IsingPolyArray.md): __init__ - [BinarySymbolGenerator](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.BinarySymbolGenerator.md): __init__ - [IsingSymbolGenerator](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.IsingSymbolGenerator.md): __init__ - [BinaryMatrix](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.BinaryMatrix.md): __init__ - [IsingMatrix](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.IsingMatrix.md): __init__ - [QuadraticModel](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.QuadraticModel.md): __init__ - [BinaryQuadraticModel](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.BinaryQuadraticModel.md): __init__ - [IsingQuadraticModel](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.IsingQuadraticModel.md): __init__ - [Solver](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.Solver.md): __init__ - [SolverResult](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.SolverResult.md): __init__ - [SolverSolution](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.SolverSolution.md): __init__ - [SymbolGenerator](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.SymbolGenerator.md) - [sum_poly](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.sum_poly.md) - [decode_solution](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.decode_solution.md) - [penalty](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.constraint.penalty.md): alias of constructor of Constraint - [InequalityFormulation](https://amplify.fixstars.com/en/docs/amplify/v1/reference/generated/amplify.InequalityFormulation.md): An enumeration. ## Other pages - [quantum_algorithm_table](https://amplify.fixstars.com/en/docs/amplify/v1/quantum/quantum_algorithm_table.md): The variable types and polynomial degree accepted for the input problem depend on the chosen algorithm. ## Optional - [Every page in one file](https://amplify.fixstars.com/en/docs/amplify/v1/llms-full.txt): The whole documentation, concatenated in the order of the index.