Tensorial tools for quantum computing

Tensorial methods have been playing an increasingly important role in the context of spin models and lattice gauge theory. In most examples, the variables of integration are compact and character expansion (for instance Fourier analysis for U(1) models) can be used to rewrite the partition function and average observables as discrete sums of contracted tensors. This reformulations have been used for RG coarse-graining but they are also very useful for quantum computing. Their build-in Trotter procedure allows us to write quantum circuit or propose analog simulations. We discuss recent applications and FAQs about the tensor reformulations such as boundary conditions, Grassmann variables, Ward identities, effects of truncations and gauge invariance.