Tensor network and quantum simulations of 1+1-dimensional quantum electrodynamics

We consider the Schwinger model with a single fermion flavor in the presence of a topologicalθ-term as a benchmark model to develop quantum computing (QC) and tensor network (TN)techniques, as well as to probe its physics, which shares many similarities with quantumchromodynamics (QCD). The techniques developed aim to eventually enhance our capabilitiesin simulating strongly coupled non-perturbative regimes of the Standard Model, particularlyin unexplored regions of its phase diagram where the conventionally used techniques are notapplicable.Discretizing fermions on a lattice is a crucial step in simulating lattice gauge theory (LGT)models such as the Schwinger model. Using the two common discretization schemes of Wilsonand staggered fermions, we first explore the additive mass renormalization induced by theseschemes within the Hamiltonian formalism relevant for QC and TNs. By formulating a methodto measure this mass renormalization, we demonstrate its dependence on various systemparameters. This, in turn, allows for more reliable and precise continuum extrapolations ofrelevant observables, for which we achieve excellent agreement with results from continuummass perturbation theory. This work introduces, for the first time, a method to measure themass renormalization in the Hamiltonian formalism, enabling QC and TNs to require fewerresources to achieve higher precision in continuum extrapolations. These extrapolations areessential for LGTs computations in higher dimensions to match experimental results, such asthose from the large hadron collider (LHC) experiment.Secondly, we demonstrate the capabilities of quantum hardware in simulating the first-orderphase transition of the model, utilizing a composite set of state-of-the-art error mitigationtechniques. While we classically simulate the variational quantum eigensolver (VQE) algorithmto acquire the ground states at the relevant points of the phase diagram as parameterizedquantum circuits (PQCs), we perform inference runs by preparing these states on IBM’snoisy intermediate-scale quantum (NISQ) devices and measure observables that signal thephase transition. Our results show that these quantum devices are able to reproduce thetransition with reasonable accuracy, showcasing the potential of NISQ devices in probing thephase diagram of LGTs. Additionally, we perform continuum extrapolations of the electricfield observable using TNs, providing an estimate of the resources required for continuumextrapolations in QC.Finally, the Schwinger model is studied in the context of open quantum system (OQS) in the presence of a hot environment. We prepare mesonic states of the model, such as the Schwingerboson or the electric field flux state, and evolve them under the influence of this environment,following the dynamics governed by a Lindblad master equation in the Markovian quantumBrownian motion (QBM) limit. The evolution is carried out using TNs and the adaptivetime-dependent density matrix renormalization group (DMRG) (ATD-DMRG) algorithm.Specifically, we probe the thermalization time of these mesonic states as a function of variousrelevant parameters. Additionally, we explore the connection between the thermalization timeand mutual information within the states. Finally, we demonstrate how our method can scaleto larger system sizes, achieving excellent preservation of the expected parity symmetry ofthe electric field observable. The relevance of this work to quarkonia within the quark gluonplasma (QGP) produced at the LHC and relativistic heavy ion collider (RHIC) is discussedthroughout.