Real-time dynamics of Plaquette Models using NISQ Hardware

Practical quantum computing holds clear promise in addressing problems not generally tractable with classical simulation techniques, and some key physically interesting applications are those of real-time dynamics in strongly coupled lattice gauge theories. In this article, we benchmark real-time dynamics of $\mathbb{Z}_2$ and $U(1)$ gauge invariant plaquette models using superconducting-qubit based quantum IBM Q computers. We design quantum circuits for models of increasing complexity and measure physical observables such as the return probability to the initial state, and locally conserved charges. Even though the quantum hardware suffers from decoherence, we demonstrate the use of error mitigation techniques, such as circuit folding methods implemented via the Mitiq package, and show what they can achieve within the quantum volume restrictions for the IBM Q quantum computers. Our study provides insight into the choice of quantum hardware topologies, construction of circuits, and the utility of error mitigation methods to devise large-scale quantum computation strategies for lattice gauge theories.