Simulating 2D Effects in Lattice Gauge Theories on a Quantum Computer

Towards quantum simulations in particle physics and beyond on noisy intermediate-scale quantum devices

“…Still, first quantum simulations of gauge theories in lower dimensions showing some of the relevant features of the SM have already been successfully performed [18][19][20][21][22][23][24][25][26][27]. In addition, resource efficient formulations of gauge theories for quantum computations have been developed [28][29][30][31][32][33], and the Hamiltonian formulation of the CP-violating topological θ-terms in three spatial dimensions has been derived [34]. In general, the path towards quantum simulations of 3 + 1D particle physics requires many incremental steps, including algorithmic development, hardware improvement, methods for circuit design, as well as error mitigation and correction techniques.…”

Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d

“…A central motivation for the present study is related to the rapid advances in the quantum simulation of U(1) lattice gauge theories in one spatial dimension, with several pioneering experiments 62,63,80,81 having opened the way also towards observing many-body effects such as quantum phase transitions and quantum thermalization. In parallel, there has been a strong effort towards developing feasible quantum-simulation proposals for U(1) lattice gauge theories in two spatial dimensions 68,[82][83][84][85][86][87][88][89][90] , with some first proof-of-principle experimental realizations 91 . In view of this rapid development, it becomes an urgent matter to understand the higher-dimensional phase diagrams of feasible gauge theory models that are likely the first targets of larger-scale experiments.…”

Two-dimensional $\mathbb{Z}_2$ lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order

“…We emphasize that the QAOA technique we propose can be easily combined to extend several proposals for the study of 2D LGTs through digital quantum simulations [49,54,[75][76][77][78][79][80][81]. Digital quantum simulations of LGTs on small systems have already been implemented in trapped ion experiments [82,83] and superconducting qubit platforms [84][85][86][87].…”