In this talk, we will report some recent results in the direction of describing the Batalin-Vilkovisky formalism in the framework of spectral triples. If on one side spectral triples can be thought as noncommutative manifold, from a physical perspective they could be seen as quantum of spacetime. But can we relate them to other quantization procedure such as, for example, the BV construction? We will try to answer this question considering gauge theories induced by finite spectral triple. In this context we will see how our previous results concerning the classical BV formalism can be extended to the quantum case, that is, to the case where the action functional is asked to solve the quantum master equation. In the presentation, we will analyse the case of U(2)-gauge theories.