Quinn, a defenseman who says he models his game after Duncan Keith of the Chicago Blackhawks and Kris Letang of the Pittsburgh Penguins, played Bantam and Midget hockey in Toronto while his father worked for the Maple Leafs before joining the U.S. National Team Development Program in 2015. He excelled with the USNTDP's Under-17 and Under-18 teams, then followed through on a commitment to play at the University of Michigan, where he had 29 points (five goals, 24 assists) as a freshman. After helping the U.S. win bronze at the IIHF World Championship, Hughes was selected by the Vancouver Canucks in the first round (No. 7) of the 2018 NHL Draft.
Hughes played one more season at Michigan, finishing with 33 points (five goals, 28 assists) in 31 games before signing with the Canucks on March 10, 2019. After recovering from an ankle injury sustained during the Big Ten playoffs, Hughes made his NHL debut with the Canucks 18 days later, had an assist and was named Third Star of the Game in a 3-2 shootout win against the Los Angeles Kings.