Quantum Computing 2+1-dimensional Quantum Electrodynamics

This thesis investigates advances in quantum simulation methods for lattice gauge theories, with a focus on (2+1)-dimensional quantum electrodynamics (QED), which shares important features with (3+1)-dimensional quantum chromodynamics (QCD), such as confinement and asymptotic freedom. Two main projects are developed. The first project investigates the ongoing coupling in a compact pure U(1) gauge theory using a step-scaling function approach. A quantum variational method allows calculations over a wide range of couplings. Plaquette expectation value results are compared with classical Monte Carlo simulations to obtain, in principle, the physical value of the lattice spacing. This method can potentially be extended to the study of QED, which also includes fermionic matter. The second project investigates the static potential between two charges, analyzing the Coulomb, confining, and string-breaking regimes. It involves the development of a tailored variational approach that incorporates system symmetries and mutual information to represent fermionic degrees of freedom. Results from a trapped-ion quantum device agree well with classical simulations, validating the method. Furthermore, this work evaluates superconducting quantum devices, noting issues with noise but also demonstrating improvements in hardware and potential through error limitation. Overall, this work underscores the feasibility of variational quantum algorithms for lattice gauge theory simulations and demonstrates their promise for advancing theoretical physics with quantum computers. This thesis explores advancements in quantum simulation methods for lattice gauge theories, focusing on (2+1)-dimensional Quantum Electrodynamics (QED), which shares key features with (3+1)-dimensional Quantum Chromodynamics (QCD), such as confinement and asymptotic freedom. Two main projects are developed. The first investigates the running coupling in a compact U(1) pure gauge theory using a step scaling function approach. A quantum variational method enables computation across a wide range of couplings. The plaquette expectation value is matched with classical Monte Carlo simulations to obtain, in principle, the physical value of the lattice spacing. This method can be eventually extended to study QED, where fermionic matter is included. The second project examines the static potential between two charges, analyzing Coulomb, confining, and string-breaking regimes. It involves developing a custom variational Ansatz that incorporates system symmetries and mutual information to represent fermionic degrees of freedom. Results from a trapped-ion quantum device align well with exact classical simulations, validating the method. Additionally, the thesis evaluates superconducting devices, identifying noise challenges but noting improvements in hardware and the potential of error mitigation. Overall, this work highlights the viability of variational quantum algorithms for lattice gauge theory simulations and demonstrates their promise for advancing theoretical physics with quantum computing.