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This is really a question out of curiosity. I am aware that geometric algebra and geometric calculus provide simplifications in many aspects of physics. I'm wondering if this framework's usefulness extends to the realm of quantum computing.

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The algebra generated over $\mathbb{C}$ by $\sigma_{x,y,z}$ gives $\text{Cliff}(\mathbb{R}^{3,0})$. But this doesn't really use more of the general features of Clifford algebra for general $\mathbb{R}^{p,q}$. You can phrase it in terms of Clifford algebra if you want, but not necessary for small examples.

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