# Fixstars Amplify SDK documentation
This is the Markdown edition of the documentation. It holds the same content as the HTML edition at , and it exists so that an AI agent can read the documentation without the markup of a web page.
Every page below is a Markdown file, and every link inside those pages points to another Markdown file. `llms.txt` holds this index with absolute addresses, and `llms-full.txt` holds every page in one file.
[](https://amplify.fixstars.com/en/)
[](https://amplify.fixstars.com/en/)
[](https://amplify.fixstars.com/en/) [](https://pypi.org/project/amplify/) [](https://pepy.tech/project/amplify)
The *Fixstars Amplify SDK* (Amplify SDK) is a Python library for formulating combinatorial optimization problems and running external optimization solvers.
The Amplify SDK provides a simple and intuitive way to formulate combinatorial optimization problems. Once the problem is formulated, you can easily use [quantum annealing machines](https://en.wikipedia.org/wiki/Quantum_annealing), Ising machines, [quantum computers](quantum/index.md), and various hardware and software solvers including MIP solvers, through a common interface.
---
**Amplify SDK features**
**🔰 Intuitive and easy to use**
The easiest and most intuitive library to formulate and solve combinatorial optimization problems! [Amplify Annealing Engine](https://amplify.fixstars.com/en/engine), a solver that requires no further installation, is also provided free of charge.
[Learn more »](features.md#easy-to-use)
**⚡ Fast processing speed**
The Amplify SDK is extremely fast and memory-efficient in formulation.
You can develop applications for large combinatorial optimization problems.
[Learn more »](features.md#blazing-fast)
**🔱️ Multiple solver support**
A wide range of solvers are available in the Amplify SDK, including quantum annealing machines, Ising machines, quantum computers, and MIP solvers.
You can choose the solver that best suits your problems.
[Learn more »](features.md#multiple-solvers)
**🧑💻️ For broad users**
The Amplify SDK can be used by a wide range of users engaged in combinatorial optimization. It is designed to support a variety of user groups, from application software development to academic research.
[Learn more »](features.md#wide-range-users)
> [!NOTE]
>
> **Changed in version 1.0.0**
>
> *The Fixstars Amplify SDK* has undergone a significant makeover in version 1.0.0, making it more intuitive and easier to use than ever before, expanding the models covered, and making it more flexible and faster. For a migration guide from previous versions, see [Migrating from Previous Versions](migration.md). A compatibility layer with the earlier version is also provided to ensure a smooth transition.
> You can find documentation for previous versions at .
---
**How to get started with Amplify**
**🆔 STEP 1**
[**User Registration**](https://amplify.fixstars.com/en/register)
Register as a user and get a free API token for the [Amplify Annealing Engine](https://amplify.fixstars.com/en/engine) !
**🛠️ STEP 2**
[Installation](quickstart.md)
Install the Amplify SDK using the pip command on Windows / Linux / MacOS!
**🔍 STEP 3**
[**Demos & Tutorials**](https://amplify.fixstars.com/en/demo)
Check out the extensive demos and tutorials to learn how to use Amplify!
> [!NOTE]
>
> **Note**
>
> *The Fixstars Amplify SDK* is proprietary software.
> It is free for non-commercial and academic use. See [Fixstars Amplify Terms of Service](https://amplify.fixstars.com/en/termsofuse) for more information.
> When citing in an academic publication, please use the BibTeX formats below.
>
> * Fixstars Amplify SDK
>
> ```
> @misc{fixstarsamplifysdkdoc,
> author = "{Fixstars Amplify Corporation}",
> title = {{Fixstars Amplify SDK documentation}},
> howpublished = "\url{https://amplify.fixstars.com/en/docs/amplify/v1/}",
> year = {2024},
> note = "[Accessed: 7-March-2024]"
> }
> ```
>
> [Download BibTeX](_downloads/eed8f336eaf8b121a975320d27df34f2/citation_sdk.bib)
> * Fixstars Amplify Annealing Engine (AE)
>
> ```
> @misc{fixstarsamplifyaedoc,
> author = "{Fixstars Amplify Corporation}",
> title = {{API Reference - Fixstars Amplify Annealing Engine}},
> howpublished = "\url{https://amplify.fixstars.com/en/docs/amplify/v1/amplify_ae.html}",
> year = {2025},
> note = "[Accessed: 30-September-2025]"
> }
> ```
>
> [Download BibTeX](_downloads/fa40222046f6d5b3cc720832fc4384a9/citation_ae.bib)
> * Fixstars Amplify
>
> Please use this if you want to cite both the Fixsatrs Amplify SDK and AE together.
>
> ```
> @misc{fixstarsamplify,
> author = "{Fixstars Amplify Corporation}",
> title = {{Fixstars Amplify}},
> howpublished = "\url{https://amplify.fixstars.com/en/}",
> year = {2020},
> note = "[Accessed: 7-March-2024]"
> }
> ```
>
> [Download BibTeX](_downloads/586ec087abf5502e07c22b264faf8aeb/citation_amplify.bib)
## Table of contents
### 🚀 Get Started
* [What is Amplify SDK?](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](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. To…
* [Quickstart](quickstart.md) — You can run the Amplify SDK in any of the following ways.
### 🌱 Basic
* [1. Amplify SDK Overview](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](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 step…
* [3. Polynomials and Objective Functions](objective.md) — The objective function is a mathematical expression expressing the degree to which the objective in a combinatorial optimization problem is achieved; in the…
* [4. Constructing Constraints](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 you…
* [5. Model Formulation](model.md) — A combinatorial optimization problem comprises decision variables, objective functions, and constraints. In “2. Creating Decision Variables,” “3. Polynomials…
* [6. Solver Client](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 execution…
* [7. Solving a Combinatorial Optimization Problem](solve.md) — This page explains how to solve a combinatorial optimization problem using the model Model and solver client created in “Model Formulation” and “Solver Client.”
### 🌻 Advanced
* [Model Conversions](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, combinatorial…
* [Variable Conversion and Degree Reduction](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, combinatorial…
* [Constraints and Penalty Functions](penalty.md) — The Amplify SDK allows you to create models with any variable and polynomial degree constraints. However, each combinatorial optimization solver handles…
* [Graph Embedding](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 the…
* [Evaluation of Execution Results](evaluation.md) — The execution result returned by the solve() function contains various information about the solutions, model conversion, and execution time. This page…
* [Execution Time information](timing.md) — The Amplify SDK provides an interface to obtain information of various execution times when solving combinatorial optimization problems.
* [Client details](solvers.md) — The Amplify SDK provides client classes for the solvers that you can run from the SDK. The client classes wrap each solver’s API and provide an interface for…
* [Fixstars Amplify](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,…
* [D-Wave Systems](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 problem…
* [TOSHIBA](clients/toshiba.md) — SQBM+ is a TOSHIBA-developed quantum-inspired optimization solution with a simulated bifurcation machine at its core.
* [Fujitsu](clients/fujitsu.md) — Fujitsu DA4 is Fujitsu’s QUBO solver with the 4th-generation Digital Annealing Unit (DAU (GPU)).
* [NEC](clients/nec.md) — NEC provides the QUBO solver, which runs on the vector supercomputer SX-Aurora TSUBASA.
* [Hitachi](clients/hitachi.md) — The CMOS annealing machine provided by Hitachi.
* [Gurobi](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, including…
* [Quantum Computers](clients/quantum_algorithm.md) — Clients for quantum computers run optimization with quantum algorithms such as QAOA.
* [Serial Solver Execution](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 running…
* [Parallel Solver Execution](parallel.md) — parallel_solve() can send queries to multiple clients and models simultaneously. Such parallel execution may hide processing times for model transformations…
* [Objective Function with a Coefficient Matrix](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-valued…
* [Speedup Formulation](optimization.md) — Formulating a large combinatorial optimization problem using Python’s for statements can be very time-consuming. The Amplify SDK provides a fast way to…
* [File input/output of the model](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.
### 🧩 Examples
* [Subset Sum Problem](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](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 solve…
* [Traveling Salesperson Problem](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 combinatorial…
* [Quadratic Assignment Problem](qap.md) — Quadratic assignment problem (QAP) is the following problem.
### 💡 Tips
* [Type Hint Support](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 to…
* [Proxy Server Settings](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](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 and…
* [Migrating from Previous Versions](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 it…
* [Formulation Benchmarks](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 time…
### 🎺 Cloud Solvers
* [Fixstars Amplify AE](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,…
* [Solving Algorithms](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 Amplify…
* [Advanced Usage](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 for…
* [Performance of Amplify AE](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](amplify_ae/changelog.md) — Improve performance for linear problems containing only integer-coefficient constraints.
* [API Reference](amplify_ae/api_reference.md)
### ⚗️ Quantum
* [Amplify Quantum](quantum/index.md) — The Amplify SDK provides features for researching and validating combinatorial optimization using quantum computers.
* [Quickstart](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 following…
* [List of Supported Devices](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 method…
* [IBM Quantum](quantum/samplers/ibm.md) — Uses IBM Quantum QPUs for circuit evaluation.
* [Qiskit Aer Simulator](quantum/samplers/aer.md) — Uses the Qiskit Aer Simulator for circuit evaluation.
* [Qulacs Simulator](quantum/samplers/qulacs.md) — A local simulator that uses Qulacs for circuit evaluation.
* [Amazon Braket Simulator](quantum/samplers/aws.md) — Uses Amazon Braket simulators for circuit evaluation. Both local and cloud simulators are supported.
* [AQT](quantum/samplers/aqt.md) — Uses AQT (Alpine Quantum Technologies) trapped-ion quantum computers for circuit evaluation via Amazon Braket.
* [IonQ](quantum/samplers/ionq.md) — Uses IonQ’s trapped-ion quantum computers for circuit evaluation.
* [IQM](quantum/samplers/iqm.md) — Uses IQM superconducting quantum computers for circuit evaluation via Amazon Braket.
* [Rigetti](quantum/samplers/rigetti.md) — Uses Rigetti superconducting quantum computers for circuit evaluation via Amazon Braket.
* [QUDORA](quantum/samplers/qudora.md) — Uses QUDORA trapped-ion quantum computers and their cloud simulators for circuit evaluation.
* [OQTOPUS Cloud](quantum/samplers/oqtopus.md) — Uses cloud quantum computers and simulators available via OQTOPUS Cloud for circuit evaluation.
* [List of Supported Algorithms](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 algorithm…
* [QAOA / Constrained QAOA](quantum/algos/QAOA.md) — QAOA (Quantum Approximate Optimization Algorithm) is a quantum-classical hybrid algorithm that alternates between quantum circuit operations on a quantum…
* [Recursive QAOA](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 the…
* [Algorithm Details](quantum/theories/index.md) — This section introduces the theoretical framework of the quantum optimization algorithms supported by the Amplify SDK.
* [QAOA Algorithm](quantum/theories/QAOA_algo.md) — This page describes the mathematical framework of QAOA (Quantum Approximate Optimization Algorithm)[1].
* [Constrained QAOA Algorithm](quantum/theories/NHOT_QAOA_algo.md) — Some optimization problems require finding the optimum subject to certain constraints on the variables.
* [Recursive QAOA Algorithm](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 identify…
### 🔌 Black-Box Optimization
* [Amplify-BBOpt](amplify_bbopt.md) — An extension library for performing Black-Box Optimization (BBO) using the features of the Amplify SDK.
### 📖 Reference
* [Changelog](changelog.md) — Support quantum computers via the Amplify Quantum extension.
* [API Reference](reference/index.md)
* [Algebra](reference/algebra.md) — amplify.Poly
* [Poly](reference/generated/amplify.Poly.md) — The polynomial class used for representing objective functions and constraints.
* [PolyArray](reference/generated/amplify.PolyArray.md) — A NumPy-like multidimensional array of polynomials. Supports indexing, slicing, broadcast-compatible arithmetic, and utility methods for building optimization…
* [Matrix](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](reference/generated/amplify.Variable.md) — Class for variable information. Instances are typically obtained via as_variable() or variables.
* [VariableGenerator](reference/generated/amplify.VariableGenerator.md) — Provides functionality to generate a decision variable or an array of decision variables.
* [sum](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. Deprecated…
* [einsum](reference/generated/amplify.einsum.md) — Einstein summation for polynomial arrays and NumPy arrays.
* [dot](reference/generated/amplify.dot.md) — Compute dot product for polynomial arrays and NumPy arrays.
* [matmul](reference/generated/amplify.matmul.md) — Matrix multiplication for polynomial arrays and NumPy arrays.
* [newaxis](reference/generated/amplify.newaxis.md)
* [VariableType](reference/generated/amplify.VariableType.md) — Enum of decision variable types: Binary, Ising, Integer, and Real.
* [Dim](reference/generated/amplify.Dim.md) — Base class for PolyArray dimension types.
* [Dim0](reference/generated/amplify.Dim0.md) — A 0D PolyArray.
* [Dim1](reference/generated/amplify.Dim1.md) — A 1D PolyArray.
* [Dim2](reference/generated/amplify.Dim2.md) — A 2D PolyArray.
* [Dim3](reference/generated/amplify.Dim3.md) — A 3D PolyArray.
* [Dim4](reference/generated/amplify.Dim4.md) — A 4D PolyArray.
* [Constraint](reference/constraint.md) — amplify.Constraint
* [Constraint](reference/generated/amplify.Constraint.md) — Constraint class representing equality or inequality conditions on polynomial expressions.
* [ConstraintList](reference/generated/amplify.ConstraintList.md) — List-like container of Constraint objects.
* [equal_to](reference/generated/amplify.equal_to.md) — Create an equality constraint.
* [one_hot](reference/generated/amplify.one_hot.md) — Create a one-hot constraint.
* [less_equal](reference/generated/amplify.less_equal.md) — Create a less-than-or-equal constraint.
* [greater_equal](reference/generated/amplify.greater_equal.md) — Create a greater-than-or-equal constraint.
* [clamp](reference/generated/amplify.clamp.md) — Create a range constraint.
* [domain_wall](reference/generated/amplify.domain_wall.md) — Create domain wall constraints for a variable array.
* [PenaltyFormulation](reference/generated/amplify.PenaltyFormulation.md) — Penalty function formulation strategy used for constraint conversion.
* [Model](reference/model.md) — amplify.Model
* [Model](reference/generated/amplify.Model.md) — Combinatorial optimization model containing objective and constraints.
* [IntegerEncodingMethod](reference/generated/amplify.IntegerEncodingMethod.md) — Encoding method for integer variables during model conversion.
* [RealEncodingMethod](reference/generated/amplify.RealEncodingMethod.md) — Encoding method for real variables during model conversion.
* [QuadratizationMethod](reference/generated/amplify.QuadratizationMethod.md) — Method used to reduce higher-order terms during conversion.
* [Graph Embedding](reference/graph.md) — amplify.Graph
* [Graph](reference/generated/amplify.Graph.md) — Physical graph information used by graph-embedding solvers.
* [embed](reference/generated/amplify.embed.md) — Perform graph embedding and return embedding information.
* [to_edges](reference/generated/amplify.to_edges.md) — Convert a polynomial to its graph edge list.
* [EmbeddingMethod](reference/generated/amplify.EmbeddingMethod.md) — Graph embedding algorithm to apply.
* [Client](reference/client.md) — amplify.BaseClient
* [BaseClient](reference/generated/amplify.BaseClient.md) — Base class of all clients in the Amplify SDK
* [AmplifyAEClient](reference/generated/amplify.AmplifyAEClient.md) — __init__
* [FixstarsClient](reference/generated/amplify.FixstarsClient.md) — __init__
* [DWaveSamplerClient](reference/generated/amplify.DWaveSamplerClient.md) — __init__
* [LeapHybridSamplerClient](reference/generated/amplify.LeapHybridSamplerClient.md) — __init__
* [LeapHybridCQMSamplerClient](reference/generated/amplify.LeapHybridCQMSamplerClient.md) — __init__
* [FujitsuDA4Client](reference/generated/amplify.FujitsuDA4Client.md) — __init__
* [FujitsuDA3cClient](reference/generated/amplify.FujitsuDA3cClient.md) — __init__
* [ToshibaSQBM2Client](reference/generated/amplify.ToshibaSQBM2Client.md) — __init__
* [GurobiClient](reference/generated/amplify.GurobiClient.md) — __init__
* [NECVA2Client](reference/generated/amplify.NECVA2Client.md) — __init__
* [HitachiClient](reference/generated/amplify.HitachiClient.md) — __init__
* [AcceptableDegrees](reference/generated/amplify.AcceptableDegrees.md) — Container of acceptable polynomial degrees by variable type for objective and constraints.
* [Degree](reference/generated/amplify.Degree.md) — Polynomial degree enumeration.
* [Solve](reference/solve.md) — amplify.Result
* [Result](reference/generated/amplify.Result.md) — Container of optimization solutions and conversion/runtime metadata.
* [Values](reference/generated/amplify.Values.md) — Mapping from variables to numeric values in a solution.
* [solve](reference/generated/amplify.solve.md) — Solve a combinatorial optimization problem.
* [parallel_solve](reference/generated/amplify.parallel_solve.md) — Solve multiple problems in parallel.
* [Misc.](reference/misc.md) — amplify.set_num_threads
* [set_num_threads](reference/generated/amplify.set_num_threads.md) — Set the number of threads used for parallel computation.
* [load_lp](reference/generated/amplify.load_lp.md) — Load an LP file and construct a model.
* [save_lp](reference/generated/amplify.save_lp.md) — Save a model to an LP file.
* [load_qplib](reference/generated/amplify.load_qplib.md) — Load a QPLIB file and construct a model.
* [save_qplib](reference/generated/amplify.save_qplib.md) — Save a model to a QPLIB file.
* [set_seed](reference/generated/amplify.set_seed.md) — Set the seed for random number generation.
* [__version__](reference/generated/amplify.__version__.md) — The version of the SDK.
* [Quantum](reference/quantum/index.md)
* [Client](reference/quantum/client.md) — QuantumBaseClient
* [QuantumBaseClient](reference/generated/amplify.QuantumBaseClient.md) — Abstract base class for clients that target a specific backend sampler.
* [AerClient](reference/generated/amplify.AerClient.md) — Client that executes quantum circuits using the Qiskit Aer simulator.
* [AQTClient](reference/generated/amplify.AQTClient.md) — Client that executes quantum circuits on AQT hardware via Amazon Braket.
* [BraketSimulatorClient](reference/generated/amplify.BraketSimulatorClient.md) — Client that executes quantum circuits on Amazon Braket simulators.
* [IBMClient](reference/generated/amplify.IBMClient.md) — Client that executes quantum circuits on IBM Quantum hardware.
* [IonQClient](reference/generated/amplify.IonQClient.md) — Client that executes quantum circuits on IonQ hardware.
* [IQMClient](reference/generated/amplify.IQMClient.md) — Client that executes quantum circuits on IQM hardware via Amazon Braket.
* [QulacsClient](reference/generated/amplify.QulacsClient.md) — Client that executes quantum circuits using the Qulacs simulator.
* [RigettiClient](reference/generated/amplify.RigettiClient.md) — Client that executes quantum circuits on Rigetti hardware via Amazon Braket.
* [QUDORAClient](reference/generated/amplify.QUDORAClient.md) — Client that executes quantum circuits on QUDORA hardware.
* [OqtopusClient](reference/generated/amplify.OqtopusClient.md) — Client that executes quantum circuits on OQTOPUS Cloud.
* [Algorithm](reference/quantum/algorithm.md) — QAOA
* [QAOA](reference/generated/amplify.QAOA.md) — Quantum Approximate Optimization Algorithm (QAOA).
* [QAOAType](reference/generated/amplify.QAOAType.md) — Selects the QAOA circuit construction strategy.
* [QAOAResult](reference/generated/amplify.QAOAResult.md) — Raw result produced by a single QAOA run.
* [QAOADurations](reference/generated/amplify.QAOADurations.md) — Total timing breakdown for a QAOA run.
* [QAOAHistoryItem](reference/generated/amplify.QAOAHistoryItem.md) — Record of a single objective function evaluation during QAOA optimization.
* [RQAOA](reference/generated/amplify.RQAOA.md) — Recursive Quantum Approximate Optimization Algorithm (RQAOA).
* [RQAOAType](reference/generated/amplify.RQAOAType.md) — Selects the QAOA circuit construction strategy used within each RQAOA iteration.
* [RQAOAResult](reference/generated/amplify.RQAOAResult.md) — Raw result produced by a single RQAOA run.
* [RQAOADurations](reference/generated/amplify.RQAOADurations.md) — Total timing breakdown for an RQAOA run.
* [RQAOAHistoryItem](reference/generated/amplify.RQAOAHistoryItem.md) — Record of a single iteration during RQAOA optimization.
* [NormalElimination](reference/generated/amplify.NormalElimination.md) — Record of a variable explicitly eliminated during an RQAOA iteration.
* [UnintentionalElimination](reference/generated/amplify.UnintentionalElimination.md) — Record of a variable eliminated as a side effect of another variable’s elimination.
* [QuantumAlgoProtocol](reference/generated/amplify.QuantumAlgoProtocol.md) — Protocol for quantum optimization algorithms.
* [Minimize](reference/quantum/minimize.md) — ScipyMinimize
* [ScipyMinimize](reference/generated/amplify.ScipyMinimize.md) — Classical optimizer for QAOA circuit parameters using scipy.optimize.minimize().
* [ScipyMinimizeOptions](reference/generated/amplify.ScipyMinimizeOptions.md) — Optional keyword arguments for scipy.optimize.minimize().
* [ScipyMinimizeResult](reference/generated/amplify.ScipyMinimizeResult.md) — Result of a ScipyMinimize optimization run.
* [NoOpMinimize](reference/generated/amplify.NoOpMinimize.md) — Classical optimizer that evaluates the objective at a fixed set of parameters.
* [NoOpMinimizeResult](reference/generated/amplify.NoOpMinimizeResult.md) — Result of a NoOpMinimize run.
* [MinimizeProtocol](reference/generated/amplify.MinimizeProtocol.md) — Protocol for classical optimizers used to tune QAOA circuit parameters.
* [MinimizeResult](reference/generated/amplify.MinimizeResult.md) — Protocol for the result of a classical minimization run.
* [Sampler](reference/quantum/sampler.md) — SamplerProtocol
* [SamplerProtocol](reference/generated/amplify.SamplerProtocol.md) — Protocol for quantum circuit samplers.
* [SamplingDurations](reference/generated/amplify.SamplingDurations.md) — Timing breakdown for a single quantum circuit sampling call.
* [AerDeviceType](reference/generated/amplify.AerDeviceType.md) — alias of Literal[‘CPU’, ‘GPU’, ‘Thrust’]
* [QiskitJobMeta](reference/generated/amplify.QiskitJobMeta.md) — Metadata for a single Qiskit quantum job.
* [QulacsJobMeta](reference/generated/amplify.QulacsJobMeta.md) — Metadata for a single Qulacs simulation run.
* [BraketJobMeta](reference/generated/amplify.BraketJobMeta.md) — Metadata for a single Braket quantum job.
* [Circuit](reference/quantum/circuit.md) — QiskitCircuit
* [QiskitCircuit](reference/generated/amplify.QiskitCircuit.md) — Qiskit-based quantum circuit implementation.
* [QulacsCircuit](reference/generated/amplify.QulacsCircuit.md) — Qulacs-based quantum circuit implementation.
* [Misc.](reference/quantum/misc.md) — IsingSeqFreqList
* [IsingSeqFreqList](reference/generated/amplify.IsingSeqFreqList.md) — alias of list[tuple[list[int], int]]
* [Deprecated](reference/deprecated.md) — amplify.BinaryPoly
* [BinaryPoly](reference/generated/amplify.BinaryPoly.md) — alias of Poly
* [IsingPoly](reference/generated/amplify.IsingPoly.md) — alias of Poly
* [BinaryPolyArray](reference/generated/amplify.BinaryPolyArray.md) — __init__
* [IsingPolyArray](reference/generated/amplify.IsingPolyArray.md) — __init__
* [BinarySymbolGenerator](reference/generated/amplify.BinarySymbolGenerator.md) — __init__
* [IsingSymbolGenerator](reference/generated/amplify.IsingSymbolGenerator.md) — __init__
* [IsingSymbolGenerator](reference/generated/amplify.IsingSymbolGenerator.md) — __init__
* [BinaryMatrix](reference/generated/amplify.BinaryMatrix.md) — __init__
* [IsingMatrix](reference/generated/amplify.IsingMatrix.md) — __init__
* [QuadraticModel](reference/generated/amplify.QuadraticModel.md) — __init__
* [BinaryQuadraticModel](reference/generated/amplify.BinaryQuadraticModel.md) — __init__
* [IsingQuadraticModel](reference/generated/amplify.IsingQuadraticModel.md) — __init__
* [Solver](reference/generated/amplify.Solver.md) — __init__
* [SolverResult](reference/generated/amplify.SolverResult.md) — __init__
* [SolverSolution](reference/generated/amplify.SolverSolution.md) — __init__
* [SymbolGenerator](reference/generated/amplify.SymbolGenerator.md)
* [sum_poly](reference/generated/amplify.sum_poly.md)
* [decode_solution](reference/generated/amplify.decode_solution.md)
* [penalty](reference/generated/amplify.constraint.penalty.md) — alias of constructor of Constraint
* [InequalityFormulation](reference/generated/amplify.InequalityFormulation.md) — An enumeration.
### Other pages
* [quantum_algorithm_table](quantum/quantum_algorithm_table.md) — The variable types and polynomial degree accepted for the input problem depend on the chosen algorithm.