  The modern understanding of the Josephson effect in mesosopic devices derives
from the physics of Andreev bound states, fermionic modes that are localized in
a superconducting weak link. Recently, Josephson junctions constructed using
semiconducting nanowires have led to the realization of superconducting qubits
with gate-tunable Josephson energies. We have used a microwave circuit QED
architecture to detect Andreev bound states in such a gate-tunable junction
based on an aluminum-proximitized InAs nanowire. We demonstrate coherent
manipulation of these bound states, and track the bound-state fermion parity in
real time. Individual parity-switching events due to non-equilibrium
quasiparticles are observed with a characteristic timescale $T_\mathrm{parity}
= 160\pm 10~\mathrm{\mu s}$. The $T_\mathrm{parity}$ of a topological nanowire
junction sets a lower bound on the bandwidth required for control of Majorana
bound states.
