  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 the real-time
dynamics of $\mathbb{Z}_2$ and $U(1)$ gauge invariant plaquette models using
noisy intermediate scale quantum (NISQ) hardware, specifically the
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.
NISQ hardware suffers from significant decoherence and corresponding difficulty
to interpret the results. We demonstrate the use of hardware-agnostic 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 hardware. Our study provides insight into the choice of
Hamiltonians, construction of circuits, and the utility of error mitigation
methods to devise large-scale quantum computation strategies for lattice gauge
theories.
