Abstract:

Gauge theories represent the most successful description of elementary particles and their fundamental interactions. In computing the real-time dynamics in lattice gauge theories however, standard classical numerical methods suffer from an exponential scaling of the required resources with growing system size and thus, display severe limitations for the simulation of real-time phenomena. Quantum computers might provide a potential framework to tackle this problem as lattice gauge theories can be efficiently represented using resources which are polynomial in the system size. Here, we review different encoding schemes for non-abelian Yang-Mills lattice gauge theories with dynamical fermionic matter such as quantum chromodynamics in arbitrary dimensions on digital circuit-based quantum computers. On the other hand, we apply promising variational quantum algorithms for near-term quantum computation to study the groundstate properties of small abelian lattice gauge theory systems like quantum electrodynamics in (1+1)- and (2+1)-spacetime dimensions. Specifically, we investigate the performance of physically motivated variational forms that preserve the gauge symmetry of the theory, thereby allowing for an efficient sampling in the physical Hilbert space of states. Therewith, we demonstrate the phenomenon of flux-string breaking in form of a phase diagram and further present the results of simulations on real superconducting quantum hardware as a proof-of-principle. By generalizing this scheme to non-abelian Yang-Mills theories, such gauge invariant variational forms might be included in variational real-time evolution algorithms, providing a potential path towards simulating real-time dynamics of lattice gauge theories on near-term quantum devices.