At the 2000 Summer Olympics in Sydney, Kvassov competed only in two swimming events. He eclipsed a FINA B-cut of 1:53.76 (200 m freestyle) from the Kazakhstan Open Championships in Almaty. On the first day of the Games, Kvassov placed twenty-first for the Kazakhstan team in the 4×100 m freestyle relay. Teaming with Sergey Borisenko, Pavel Sidorov, and Igor Sitnikov in heat three, Kvassov swam a second leg and recorded a split of 52.25, but the Kazakhs settled only for last place in a final time of 3:28.90. The following day, in the 200 m freestyle, Kvassov placed forty-eighth on the morning prelims. Swimming in heat two, he touched out Cyprus' Alexandros Aresti for a seventh seed by almost a full body length in 1:55.72.