Hybrid Analog–Digital Approach to Simulating the Abelian Higgs Model: (i) Theoretical Framework

Quantum computing is a promising platform for simulating lattice field theories in regimes where sampling-based, non-perturbative Monte Carlo methods fail due to the sign problem. However, simulating field theories on current quantum computers poses several challenges, and this necessitates the development of novel protocols which can improve the near-term utility of quantum devices. We develop a three-level hybrid analog–digital simulation protocol and compare it with a digital, gate-based simulation of the (1+1) D Abelian Higgs model. In this first part of our two-part talk, we discuss the mapping of the gauge theory to an approximate spin-1 model and show how different quantum operations can be represented as gates in both qubit and qutrit settings. We compute observables relevant to identifying key dynamics such as string breaking and demonstrate the application of error mitigation techniques in digital quantum simulators. These results serve as a reference for comparison with the hybrid protocol, which will be presented in the second part of our talk.