The Scot saw off Jo-Wilfried Tsonga 7-5, 7-5, 6-4 to reach the last eight and a meeting with world No 1 Novak Djokovic.
Having notched his first win over a top-1o player since he beat Djokovic to win Wimbledon last summer, Murray believes he is moving into top form at the right time.
"I don't feel like I'm that far away from playing my best tennis," said Murray, who wrapped up victory in two hours, 35 minutes in hot, humid conditions.
"I know I'm still a long way from winning the tournament but it's only nine sets, three matches, five or six days away from winning another grand slam [tournament]. I'll leave everything out there on the court and hopefully I can play well."
Having almost gone out in round one when he suffered all-over body cramps before squeezing past Dutchman Robin Haase, Murray moved well and was ultimately just too good for ninth seed Tsonga.
"Today was a good match for the most part but you never know what will happen," he said.
"I feel like I'm playing well. I'm going to have to play extremely well to win the event or even win the next match. A week ago I didn't feel great at all and a week later I'm in the quarters so a lot can happen.
"Winning matches does build confidence. I've played against some very good players this year and lost a few close matches. How big today's win is, I don't know.
"I'll just try to take the confidence I gain from a win like this and take it into the next round and hopefully I'll have success."