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We discuss the successes and limitations of statistical sampling for asequence of models studied in the context of lattice QCD and emphasize the needfor new methods to deal with finite-density and real-time evolution. We showthat these lattice models can be reformulated using tensorial methods where thefield integrations in the path-integral formalism are replaced by discretesums. These formulations involve various types of duality and provide exactcoarse-graining formulas which can be combined with truncations to obtainpractical implementations of the Wilson renormalization group program. Tensorreformulations are naturally discrete and provide manageable transfer matrices.Combining truncations with the time continuum limit, we derive Hamiltonianssuitable to perform quantum simulation experiments, for instance using coldatoms, or to be programmed on existing quantum computers. We review recentprogress concerning the tensor field theory treatment of non-compact scalarmodels, supersymmetric models, economical four-dimensional algorithms,noise-robust enforcement of Gauss's law, symmetry preserving truncations andtopological considerations. We discuss connections with other tensor networkapproaches.

Tensor lattice field theory with applications to the renormalization group and quantum computing