---
sd_hide_title: true
hide-toc: true
---

# What is Amplify SDK?

```{image} ../_static/amplify-logo.svg
:alt: Fixstars Amplify
:class: only-light amplify-logo
:align: center
:target: https://amplify.fixstars.com/en/
```

```{image} ../_static/amplify-logo-dark.svg
:alt: Fixstars Amplify
:class: only-dark amplify-logo
:align: center
:target: https://amplify.fixstars.com/en/
```

[![Fixstars Amplify](https://img.shields.io/badge/-Fixstars%20Amplify-333333.svg?logo=data:image/png;base64,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&style=popout-square)](https://amplify.fixstars.com/en/) [![PyPI](https://img.shields.io/pypi/v/amplify)](https://pypi.org/project/amplify/) [![Downloads](https://static.pepy.tech/personalized-badge/amplify?period=total&units=international_system&left_color=grey&right_color=orange&left_text=Downloads)](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 use [quantum annealing machines](https://en.wikipedia.org/wiki/Quantum_annealing), Ising machines, and [quantum computers](./quantum/index.md). You can also use other hardware and software solvers, including MIP solvers, through a common interface.

```{admonition} For AI agents
:class: tip only-html

This documentation also comes in Markdown, so that an AI agent reads it without the markup of a web page. Every page has a Markdown copy next to it: `.../v1/model.html` also exists as `.../v1/model.md`. Start at [index.md](https://amplify.fixstars.com/en/docs/amplify/v1/index.md), which lists every page, or read [llms.txt](https://amplify.fixstars.com/en/docs/amplify/v1/llms.txt) and [llms-full.txt](https://amplify.fixstars.com/en/docs/amplify/v1/llms-full.txt).
```

---

```{rubric} Amplify SDK features
```

`````{grid} 1 2 2 2
:gutter: 5 5 5 5
````{grid-item-card}  🔰 Intuitive and easy to use
:link: easy-to-use
:link-type: ref
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.
+++
```{div} sd-text-right
[Learn more »](#easy-to-use)
```
````
````{grid-item-card}  ⚡ Fast processing speed
:link: blazing-fast
:link-type: ref
The Amplify SDK is extremely fast and memory-efficient in formulation.
You can develop applications for large combinatorial optimization problems.
+++
```{div} sd-text-right
[Learn more »](#blazing-fast)
```
````
````{grid-item-card} 🔱️ Multiple solver support
:link: multiple-solvers
:link-type: ref
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.
+++
```{div} sd-text-right
[Learn more »](#multiple-solvers)
```
````
````{grid-item-card}  🧑‍💻️ For broad users
:link: wide-range-users
:link-type: ref
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.
+++
```{div} sd-text-right
[Learn more »](#wide-range-users)
```
````
`````

```{admonition} Changed in version 1.0.0
:class: seealso

Version 1.0.0 gives *the Fixstars Amplify SDK* a significant makeover. It is now more intuitive and easier to use than ever before. It covers more models, and it is more flexible and faster. For a migration guide from previous versions, see [](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 [https://amplify.fixstars.com/en/docs/amplify/v0/](https://amplify.fixstars.com/en/docs/amplify/v0/).
```

---

```{rubric} How to get started with Amplify
```

`````{grid} 1 1 1 3
````{grid-item-card}  🆔 STEP 1
```{button-link} https://amplify.fixstars.com/en/register
:color: primary
:click-parent:
:expand:
**User Registration**
```
Register as a user and get a free API token for the [Amplify Annealing Engine](https://amplify.fixstars.com/en/engine) !
````
````{grid-item-card}  🛠️ STEP 2
```{button-ref} quickstart
:ref-type: doc
:color: success
:click-parent:
:expand:
**Installation**
```
Install the Amplify SDK using the pip command on Windows / Linux / MacOS!
````
````{grid-item-card}  🔍 STEP 3
```{button-link} https://amplify.fixstars.com/en/demo
:color: info
:click-parent:
:expand:
**Demos & Tutorials**
```
Check out the extensive demos and tutorials to learn how to use Amplify!
````
`````

````{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]"
    }
    ```

    [{bdg-info}`Download BibTeX`](/../_static/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]"
    }
    ```

    [{bdg-info}`Download BibTeX`](/../_static/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]"
    }
    ```

    [{bdg-info}`Download BibTeX`](/../_static/citation_amplify.bib)


````

```{toctree}
:caption: 🚀 Get Started
:hidden:
self
features.md
quickstart.md
```

```{toctree}
:caption: 🌱 Basic
:numbered:
:hidden:
overview.md
variables.md
objective.md
constraint.md
model.md
clients.md
solve.md
```

```{toctree}
:caption: 🌻 Advanced
:hidden:
conversion.md
evaluation.md
timing.md
solvers.md
serial.md
parallel.md
matrix.md
optimization.md
file_io.md
```

```{toctree}
:caption: 🧩 Examples
:hidden:
subset_sum.ipynb
maxcut.ipynb
tsp.ipynb
qap.ipynb
```

```{toctree}
:caption: 💡 Tips
:hidden:
type_hint.md
proxy.md
pprint.md
migration.md
benchmark.md
```

```{toctree}
:caption: 🎺 Cloud Solvers
:hidden:
amplify_ae.md
```

```{toctree}
:caption: ⚗️ Quantum
:hidden:
quantum/index.md
quantum/quickstart.md
quantum/samplers/index.md
quantum/algos/index.md
quantum/theories/index.md
```

```{toctree}
:caption: 🔌 Black-Box Optimization
:hidden:
amplify_bbopt.md
```

```{toctree}
:caption: 📖 Reference
:hidden:
changelog.md
reference/index.rst
genindex
```