# Simulation qutrit-based quantum computing

**URL:** <https://discuss.pennylane.ai/t/simulation-qutrit-based-quantum-computing/8675>\
**Category:** PennyLane Help\
**Created:** [June 27, 2025, 10:12am UTC](https://discuss.pennylane.ai/t/simulation-qutrit-based-quantum-computing/8675 "2025-06-27T10:12:31Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![MirandaCarou](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/mirandacarou/32/4247_2.png) [@MirandaCarou](https://discuss.pennylane.ai/u/MirandaCarou)\
**Post date:** [June 27, 2025, 10:12am UTC](https://discuss.pennylane.ai/t/simulation-qutrit-based-quantum-computing/8675/1 "2025-06-27T10:12:31Z")

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Hi,

I’ven been working these weekS with the devices `qml.default_qutrit` and `qml.default.qutrit.mixed` and I was wondering about how Pennylane applied this simulations. I mean, what I read when i’m searching about this devices is for example:

```auto
The default.qutrit device is PennyLane’s standard qutrit-based device.
It implements the [`Device`](https://docs.pennylane.ai/en/stable/code/api/pennylane.devices._legacy_device.Device.html) methods as well as some built-in `qutrit operations`, and provides simple pure state simulation of qutrit-based quantum computing.

```

But there’s no specification about how you implement the qutrits simulation. **¿Which papers inspire you?**  **¿Which geometrical representation did you choose?**. I would really love it if I can obtain more information ❤.

Thank you .

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**Author:** ![CatalinaAlbornoz](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/catalinaalbornoz/32/1196_2.png) [@CatalinaAlbornoz](https://discuss.pennylane.ai/u/CatalinaAlbornoz)\
**Post date:** [June 27, 2025, 9:49pm UTC](https://discuss.pennylane.ai/t/simulation-qutrit-based-quantum-computing/8675/2 "2025-06-27T21:49:12Z")

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Hi @MirandaCarou ,

Welcome to the Forum!

I’ve asked the person who built our qutrit simulator to get back to you next week on this.

In the meantime you can take a look at the [code](https://docs.pennylane.ai/en/stable/_modules/pennylane/devices/default_qutrit.html#DefaultQutrit) if you want to learn about some of the functions implemented there.

I hope this helps!

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**Author:** ![glassnotes\_alt](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/glassnotes_alt/32/2043_2.png) [@glassnotes\_alt](https://discuss.pennylane.ai/u/glassnotes_alt)\
**Post date:** [June 28, 2025, 1:13pm UTC](https://discuss.pennylane.ai/t/simulation-qutrit-based-quantum-computing/8675/3 "2025-06-28T13:13:07Z")

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(@CatalinaAlbornoz hope you don’t mine me jumping in here!)

Hi @MirandaCarou, the operations are based primarily on two papers:

- [[1105.5485] Elementary gates for ternary quantum logic circuit](https://arxiv.org/abs/1105.5485)
- [[2204.00552] Constructing all qutrit controlled Clifford+T gates in Clifford+T](https://arxiv.org/abs/2204.00552)

The observables are the Gell-Mann matrices (they’re like generalized Pauli matrices, and are the Hermitian generators of the standard rotations `TRX`, `TRY`, and `TRZ`.

There are also the operations for noise channels. One of the key references for those is arXiv 2003.03307, “Quantum Information Scrambling in a Superconducting Qutrit Processor”.

Hope that helps - if you have more specific questions, happy to pass them on to a student in my group who helped with the device development.

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<div class="post-metadata">

**Author:** ![CatalinaAlbornoz](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/catalinaalbornoz/32/1196_2.png) [@CatalinaAlbornoz](https://discuss.pennylane.ai/u/CatalinaAlbornoz)\
**Post date:** [July 3, 2025, 3:37am UTC](https://discuss.pennylane.ai/t/simulation-qutrit-based-quantum-computing/8675/4 "2025-07-03T03:37:58Z")

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Thanks for jumping in @glassnotes_alt !

Jump in any time you want. Your insights are always very welcome ❤ .