In this talk I will propose a general correspondence which associates a non-perturbative quantum mechanical operator to a toric Calabi-Yau manifold, and I will propose a conjectural expression for its spectral determinant. As a consequence of these results, I will derive an exact quantization condition for the operator spectrum. I will give a concrete illustration of this conjecture by focusing on the example of local $P^2$ and local $P^1 \times P^1$. This approach also provides a non-perturbative Fermi gas picture of topological strings on toric Calabi-Yau manifolds and suggests the existence of an underlying theory of M2 branes behind this formulation.