  Simulations of supersymmetric field theories on the lattice with
(spontaneously) broken supersymmetry suffer from a fermion sign problem related
to the vanishing of the Witten index. We propose a novel approach which solves
this problem in low dimensions by formulating the path integral on the lattice
in terms of fermion loops. For N = 2 supersymmetric quantum mechanics the loop
formulation becomes particularly simple and in this paper - the first in a
series of three - we discuss in detail the reformulation of this model in terms
of fermionic and bosonic bonds for various lattice discretisations including
one which is Q-exact.
