In the present work, we propose a scheme for the digital formulation of lattice gauge theories with dynamical fermions in 3 + 1 dimensions. All interactions are obtained as a stroboscopic sequence of two-body interactions with an auxiliary system. This enables quantum simulations of lattice gauge theories where the magnetic four-body interactions arising in two and more spatial dimensions are obtained without the use of perturbation theory, thus resulting in stronger interactions compared with analogue approaches. The simulation scheme is applicable to lattice gauge theories with either compact or finite gauge groups. The required bounds on the digitization errors in lattice gauge theories, due to the sequential nature of the stroboscopic time evolution, are provided. Furthermore, an implementation of a lattice gauge theory with a non-abelian gauge group, the dihedral group D 3, is proposed employing the aforementioned simulation scheme using ultracold atoms in optical lattices.
Bibliographical noteFunding Information:
JIC is supported by the ERC QENOCOBA under the EU Horizon 2020 program (grant agreement 742102).
© 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft.
- lattice gauge theory
- quantum simulation
- ultracold atoms