Tensor field theory with applications to quantum computing

We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these lattice models can be reformulated using tensorial methods where the field integrations in the path-integral formalism are replaced by discrete sums. These formulations involve various types of duality and provide exact coarse-graining formulas which can be combined with truncations to obtain practical implementations of the Wilson renormalization group program. Tensor reformulations are naturally discrete and provide manageable transfer matrices. Combining truncations with the time continuum limit, we derive Hamiltonians suitable to perform quantum simulation experiments, for instance using cold atoms, or to be programmed on existing quantum computers. We review recent progress concerning the tensor field theory treatment of non-compact scalar models, supersymmetric models, economical four-dimensional algorithms, noise-robust enforcement of Gausss law, symmetry preserving truncations and topological considerations.

Tensor network formulation of the massless Schwinger model

We construct a tensor network representation of the partition function for the massless Schwinger model on a two dimensional lattice using staggered fermions. The tensor network representation allows us to include a topological term. Using a particular implementation of the tensor renormalization group (HOTRG) we calculate the phase diagram of the theory. For a range of values of the coupling to the topological term $theta$ and the gauge coupling $beta$ we compare with results from hybrid Monte Carlo when possible and find good agreement.

Tensor renormalization group study of the 2d O(3) model

We present our progress on a study of the $O(3)$ model in two-dimensions using the Tensor Renormalization Group method. We first construct the theory in terms of tensors, and show how to construct $n$-point correlation functions. We then give results for thermodynamic quantities at finite and infinite volume, as well as 2-point correlation function data. We discuss some of the advantages and challenges of tensor renormalization and future directions in which to work.