  Recently, transmission spectroscopy in the atmospheres of the TRAPPIST-1
planets revealed flat and featureless absorption spectra, which rule out
cloud-free hydrogen-dominated atmospheres. Earth-sized planets orbiting
TRAPPIST-1 likely have either a clear or a cloudy/hazy hydrogen-poor
atmosphere. In this paper, we investigate whether a proposed formation scenario
is consistent with expected atmospheric compositions of the TRAPPIST-1 planets.
We examine the amount of a hydrogen-rich gas that TRAPPIST-1-like planets
accreted from the ambient disk until disk dispersal. Since TRAPPIST-1 planets
are trapped into a resonant chain, we simulate disk gas accretion onto a
migrating TRAPPIST-1-like planet. We find that the amount of an accreted
hydrogen-rich gas is as small as 10$^{-2}$ wt% and 0.1 wt% for TRAPPIST-1b and
1c, 10$^{-2}$ wt% for 1d, 1 wt% for 1e, a few wt% for 1f and 1g and 1 wt% for
1h, respectively. We also calculate a long-term thermal evolution of
TRAPPIST-1-like planets after disk dissipation and estimate the mass loss of
their hydrogen-rich atmospheres driven by a stellar X-ray and UV irradiation.
We find that all the accreted hydrogen-rich atmospheres can be lost via
hydrodynamic escape. Therefore, we conclude that TRAPPIST-1 planets should have
no primordial hydrogen-rich gases but secondary atmospheres such as a
Venus-like one and water vapor, if they currently retain atmospheres.
