Quantum Cohomology of Affine Toric Varieties

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I would like to know whether quantum cohomology rings of affine toric varieties have been calculated, if this is possible. Does anyone have a relevant paper they could refer me to?

I have seen it done for projective varieties in most places, but not affine. I realize this is probably because the projective varieties have some nicer compactness properties.

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After searching MathOverflow I found this, which seems relevant:

https://mathoverflow.net/questions/60742/quantum-cohomology-for-open-varieties/60759#60759