Lattice gauge theory

Quantum mechanics

Optical lattice

Theoretical physics

Superfluidity

Quantum computer

Mathematical optimization

Acoustics

Hamiltonian (control theory)

Gauge theory

Lattice (music)

Reciprocal lattice

Physics

Mathematics

Fermion

Quantum

Hamiltonian lattice gauge theory

Lattice field theory

Diffraction

Quantum simulator

Quantum Science and Technology

Quantum simulators have the exciting prospect of giving access to real-time dynamics of lattice gauge theories, in particular in regimes that are difficult to compute on classical computers. Future progress towards scalable quantum simulation of lattice gauge theories, however, hinges crucially on the efficient use of experimental resources. As we argue in this work, due to the fundamental non-uniqueness of discretizing the relativistic Dirac Hamiltonian, the lattice representation of gauge theories allows for an optimization that up to now has been left unexplored. We exemplify our discussion with lattice quantum electrodynamics in two-dimensional space-time, where we show that the formulation through Wilson fermions provides several advantages over the previously considered staggered fermions. Notably, it enables a strongly simplified optical-lattice setup and it reduces the number of degrees of freedom required to simulate dynamical gauge fields. Exploiting the optimal representation, we propose an experiment based on a mixture of ultracold atoms trapped in a tilted optical lattice. Using numerical benchmark simulations, we demonstrate that a state-of-the-art quantum simulator may access the Schwinger mechanism and map out its non-perturbative onset.

Quantum simulation of lattice gauge theories using Wilson fermions