Hamiltonian Simulation of Lattice Gauge Theories with Fermionic Tensor Networks and Monte Carlo

Quantum simulation is based on the Hamiltonian formulation of lattice gauge theories. Classical Monte Carlo algorithms, however, mainly focus on the action formalism due to gains in computational efficiency. At the same time, they lose the possibility to describe real-time dynamics and may suffer from the sign problem.

We present a variational Monte Carlo algorithm based on fermionic tensor network states. The algorithm works directly in the Hamiltonian formulation and cannot suffer from the sign problem. The combination of Monte Carlo techniques and tensor networks enables simulations in two and more spatial dimensions.