  Motivated by the revitalized interest in the digital simulation of medium-
and high-energy physics phenomena, we investigate the dynamics following a
Yukawa-interaction quench on IBM Q. Adopting the zero-dimensional version of
the scalar Yukawa-coupling model as our point of departure, we design low-depth
quantum circuits emulating its dynamics with up to three bosons. In the
one-boson case we demonstrate circuit compression, i.e., a constant-depth
circuit containing only two controlled-NOT (CNOT) gates. In the more complex
three-boson case, we design a circuit in which one Trotter step entails $8$
CNOTs. Using an analogy with the traveling-salesman problem, we also provide a
CNOT-cost estimate for higher boson-number truncations. Based on these
circuits, we quantify the system dynamics by evaluating the expected boson
number at an arbitrary time after the quench and the survival probability of
the initial vacuum state (the Loschmidt echo). We also utilize these circuits
to drive adiabatic transitions and compute the energies of the ground- and
first-excited states of the considered model. Finally, through error mitigation
-- i.e, zero-noise extrapolation -- we demonstrate a good agreement of our
results with a numerically-exact classical benchmark.
