Qutrits Simulator Doubts

Quantum Compilation
1

Hi!

I’ve been working for a while with the default.qutrit simulator, and I was wondering if there have been any updates on its development. I have a few questions, as well as some general curiosities.

First of all, I have some doubts regarding the current rotation gates. I checked the reference paper describing their construction, but I’m not entirely sure I fully understand their scope. As far as I can tell, they seem to be implementations of Pauli-like operators acting on specific two-dimensional subspaces of the full Hilbert space, rather than genuine rotation operators acting on the entire qutrit space.

For instance, if we look at the Gell-Mann matrices (generators of SU(3)), they also resemble Pauli matrices in the sense that each one acts non-trivially on a particular subspace. However, it should in principle be possible to combine multiple such generators, properly normalised, and construct operations that act more globally across the full space.

I understand that qutrit states naturally live on an 8-dimensional hypersphere, which makes the construction of global rotations quite involved (and sometimes impractical). However, using alternative representations, such as the Majorana stellar representation, it is possible to map pure qutrit states onto a unit-sphere-like picture, somewhat analogous to the Bloch sphere, while preserving the essential properties of quantum operations.

Recently, I submitted a paper to arXiv ( Qutrits for physics at LHC ) where I used the default.qutrit simulator in PennyLane together with this type of gate construction and the Majorana representation, in case you’d be interested in taking a look.

I also based part of this approach on another paper, which I’d be happy to share. Majorana representation, qutrit Hilbert space and NMR implementation of qutrit gates

Finally, regarding GPU support: as far as I know, the default.qubit simulator includes options for GPU acceleration to parallelise computations. However, the qutrit simulator seems to be limited to CPU execution. Are there any plans to support GPU acceleration for qutrit simulations as well?

Thanks in advance!

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Hi @MirandaCarou ,

Thank you for your questions and congrats on your paper! I’ll share it with our team, I’m sure they’ll be excited to see it.

I’ll forward your qutrit question to our qutrit expert here, hopefully they’ll be able to help you.

Regarding the question on GPU support, there are no current plans to support GPU acceleration of qutrit simulations unfortunately.

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Hi @MirandaCarou, I’m the developer that originally implemented default.qutrit. It’s always awesome to see the device being used by the community.

Your analysis of the currently available rotations is totally correct. However, the qutrit rotation gates can already be used to cover the whole “Bloch sphere-like” space that you mentioned. You can validate this by taking a look at how the generators for the rotation gates are defined (linear combinations of Gell-Mann operators). Although, admittedly, this may not be the most intuitive way to work with qutrits, as you pointed out.

This is my first time hearing about the Majorana stellar representation, so I can’t comment too much on it.

Regarding GPU support on default.qutrit, I believe that the device works seamlessly with native Autograd, PyTorch, and JAX tensors, so it should work with GPUs out-of-the-box as long as you use GPU data with the device. If this is not the case, please open an issue on the PennyLane GitHub repository and the team can check it out :blush: