  The study of real-time evolution of lattice quantum field theories using
classical computers is known to scale exponentially with the number of lattice
sites. Due to a fundamentally different computational strategy, quantum
computers hold the promise of allowing for detailed studies of these dynamics
from first principles. However, much like with classical computations, it is
important that quantum algorithms do not have a cost that scales exponentially
with the volume. Recently, it was shown how to break the exponential scaling of
a naive implementation of a U(1) gauge theory in two spatial dimensions through
an operator redefinition. In this work, we describe modifications to how
operators must be sampled in the new operator basis to keep digitization errors
small. We compare the precision of the energies and plaquette expectation value
between the two operator bases and find they are comparable. Additionally, we
provide an explicit circuit construction for the Suzuki-Trotter implementation
of the theory using the Walsh function formalism. The gate count scaling is
studied as a function of the lattice volume, for both exact circuits and
approximate circuits where rotation gates with small arguments have been
dropped. We study the errors from finite Suzuki-Trotter time-step, circuit
approximation, and quantum noise in a calculation of an explicit observable
using IBMQ superconducting qubit hardware. We find the gate count scaling for
the approximate circuits can be further reduced by up to a power of the volume
without introducing larger errors.
