IPA: //ˈkwɔːrtərˌfaɪnəlɪst//
KK: /ˈkwɔrtərˌfaɪnəlɪst/
A person or team that competes in the quarterfinal round of a competition.
The team became quarterfinalists after winning their last match.
Quarterfinalist → It is formed from "quarter" (from Old French *quart*, meaning one-fourth) and "finalist" (from "final" which comes from Latin *finalis*, meaning pertaining to the end, and the suffix "-ist" meaning a person who). A quarterfinalist is a person who has reached the stage of competition that is one-fourth of the way to the final round.
Think of someone who has made it to the 'one-fourth' stage ('quarter') of a competition, and is now a 'person' ('-ist') competing for the final round.
No commonly confused words.