"I think this one, it feels a bit better, honestly," he said.
"There was a lot of expectation coming into this tournament.
"I was obviously out for a couple weeks before Sydney. I wasn't expecting, you know, anything, especially not quarter-finals.
"It's just massive, especially to do it in front of your home crowd.
"Hisense is an unbelievable court. I'd never played on it before. It's definitely my favourite court now."
Kyrgios' reward is a meeting with Andy Murray, who won through in four tight sets against Grigor Dimitrov.
Murray won the pair's only previous meeting 6-2 6-2 in August last year; Kyrgios' heaviest loss as a professional.
The Scot has already knocked one Australian out of the Open - Marinko Matosevic in round two - but said the role of bad guy didn't enter his mind.
"I'm not planning on trying to break anybody's hearts," he said.
"This is tennis. This is sport.
"I plan on trying to beat Nick.
"Obviously the crowd will be right behind him. Understandably so.
"I've played in French Open against French players where the crowd can be very difficult.
"I've experienced it before, so hopefully I'll deal with it well."
The tournament's top seeds return to action on Monday, with Serena Williams playing 24th seed Garbine Muguruza and Novak Djokovic facing in-form Giles Muller.
Reigning men's champion Stan Wawrinka will attempt to return to the last eight at Melbourne Park against Spaniard Guillermo Garcia-Lopez.
Victoria Azarenka will attempt to knock out her third seed of the tournament against Dominika Cibulkova in the opening match on Rod Laver Arena.
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-AAP
