  BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the
most general sigma model target space geometry allowing for (2,2) world sheet
supersymmetry. In this paper, we work out supersymmetric quantum mechanics for
a biHermitian target space. We display the full supersymmetry of the model and
illustrate in detail its quantization procedure. Finally, we show that the
quantized model reproduces the Hodge theory for compact twisted generalized
Kaehler manifolds recently developed by Gualtieri. This allows us to recover
and put in a broader context the results on the biHermitian topological sigma
models obtained by Kapustin and Li.
