  A transmon qubit embedded in a high-impedance environment acts in a way dual
to a conventional Josephson junction. In analogy to the AC Josephson effect,
biasing of the transmon by a direct current leads to the oscillations of
voltage across it. These oscillations are known as the Bloch oscillations. We
find the Bloch oscillations spectrum, and show that the zero-point fluctuations
of charge make it broad-band. Despite having a broad-band spectrum, Bloch
oscillations can be brought in resonance with an external microwave radiation.
The resonances lead to steps in the voltage-current relation, which are dual to
the conventional Shapiro steps. We find how the shape of the steps depends on
the environment impedance $R$, parameters of the transmon, and the microwave
amplitude. The Bloch oscillations rely on the insulating state of the transmon
which is realized at impedances exceeding the Schmid transition point, $R > R_Q
= h / (2e)^2$.
