Toward scalable simulations of Lattice Gauge Theories on quantum computers

The simulation of real-time dynamics in lattice gauge theories is particularly hard for classical computing due to the exponential scaling of the required resources. On the other hand, quantum algorithms can potentially perform the same calculation with a polynomial dependence on the number of degrees of freedom. A precise estimation is however particularly challenging for the simulation of lattice gauge theories in arbitrary dimensions, where, gauge fields are dynamical variables, in addition to the particle fields. Moreover, there exist several choices for discretizing particles and gauge fields on a lattice, each of them coming at different prices in terms of qubit register size and circuit depth. Here we provide a resource counting for real-time evolution of $U(1)$ gauge theories, such as Quantum Electrodynamics, on arbitrary dimension using the Wilson fermion representation for the particles, and the Quantum Link Model approach for the gauge fields. We study the phenomena of flux-string breaking up to a genuine bi-dimensional model using classical simulations of the quantum circuits, and discuss the advantages of our discretization choice in simulation of more challenging $SU(N)$ gauge theories such as Quantum Chromodynamics.