  A fundamental open issue in physics is whether and how the fermion sign
problem in quantum Monte Carlo (QMC) simulations can be solved generically.
Here, we show that Majorana-time-reversal (MTR) symmetries can provide a
unifying principle to solve the fermion sign problem in interacting fermionic
models. By systematically classifying Majorana-bilinear operators according to
the anti-commuting MTR symmetries they respect, we rigorously proved that there
are two and only two fundamental symmetry classes which are sign-problem-free
and which we call the "Majorana class" and "Kramers class", respectively. Novel
sign-problem-free models in the Majorana class include interacting topological
superconductors and interacting models of charge-4e superconductors. We believe
that our MTR unifying principle could shed new light on sign-problem-free QMC
simulation on strongly correlated systems and interacting topological matters.
