  In quantum logic operations, information is carried by the wavefunction
rather than the energy distribution. Therefore, the relative phase is
essential. Abelian and non-Abelian phases can be emulated in classical waves
using passive coupled waveguides with geometric modulation. However, the
dynamic phases interference induced by waveguide structure variation is
inevitable.To overcome the challenges, we introduce an electroacoustic coupled
system that enables the precise control of phase distribution through dynamic
modulation of hopping. Such effective hopping is electronically controlled and
is utilized to construct various paths in parameter space. These paths lead to
state evolution with matrix-valued geometric phases, which correspond to logic
operations. We report experimental realizations of several logic operations,
including $Y$ gate, $Z$ gate, Hadamard gate and non-Abelian braiding. Our work
introduces a temporal process to manipulate transient modes in a compact
structure, providing a versatile experimental testbed for exploring other logic
gates and exotic topological phenomena.
