  We propose a quantum model of the Schwarzschild black hole as a quantum
mechanics of a system of fermionic degrees of freedom. The system has a
constant density of states and a Fermi energy that is inversely proportional to
the size of the system. Assuming equivalence principle, we show that the
degeneracy pressure of the Fermi degrees of freedom is able to withstand the
collapse of gravity if the radius of the system is given precisely by the
horizon radius of the Schwarzschild black hole. In our model, the fermionic
degrees of freedom at each energy level can be entangled in certain different
ways, giving rise to a multitude of degenerate ground states of the system. The
counting of these microstates reproduces precisely the Bekenstein-Hawking
entropy. This simple Fermi model is universal and works also for the
Reissner-Nordstr\"om charged black hole as well as black hole with a
cosmological constant. From the properties of the Fermi variables, we propose
that quantum gravity is characterized by a principle of {\it maximal capacity
of states} where there can be no more than $V /l_P^3$ quantum states in any
volume $V$. It implies a loss of spatial locality below the Planck length and
suggests that any singularity predicted by general relativity is resolved and
replaced by a quantum space in quantum gravity. In our model, a black hole
spacetime is equipped with an uniform distribution of energy levels. This is
another reason why black hole can be considered a simple harmonic oscillator of
quantum gravity.
