Who does the roman god quirinius correspond to in greek mythology?

No one. There are a number of Roman deities that didn't come from Greek influence, but rather from the indigenous people you populated the Italian Peninsula before the Greeks arrived.

Quirinus was probably the Sabine God of War (one etymology suggests that Quirinus comes from the Word quiris, which means "spear". An alter to his honor was built on the Quirinal Hill (one of the seven hills of rome), which bears his name. After the Greek influence. Mars was made the god of war and combined with the Greek Ares. Quirinus was combined with Janus, and they represented two sides of the same person, though his flame was still part of the procession that proceeded the Pontifex Maximus (head priest).