  The global supersymmetry is spontaneously broken if and only if the
ground-state energy is strictly positive. We propose to use this fact to
observe the spontaneous supersymmetry breaking in euclidean lattice
simulations. For lattice formulations that possess a manifest fermionic
symmetry, there exists a natural choice of a hamiltonian operator that is
consistent with a topological property of the Witten index. We confirm validity
of our idea in models of the supersymmetric quantum mechanics. We then examine
a possibility of a dynamical supersymmetry breaking in the two-dimensional
$\mathcal{N}=(2,2)$ super Yang-Mills theory with the gauge group $\SU(2)$, for
which the Witten index is unknown. Differently from a recent conjectural claim,
our numerical result tempts us to conclude that supersymmetry is not
spontaneously broken in this system.
