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World No.1 Ash Barty has the utmost respect for her Australian Open quarter-final opponent Karolina Muchova.

She was inspired by some heartfelt encouragement from Ash Barty three years ago but now Karolina Muchova threatens to break the world No.1's heart at the Australian Open on Wednesday.

Muchova has cut a swathe through the top half of the draw, taking out former French Open champion Jelena Ostapenko, ex-world No.1 Karolina Pliskova and fellow seed Elise Mertens, all in straight sets, to emerge as Barty's surprise quarter-final opponent.

A surprise to many, that is, but not to Barty.

Australia's top seed vividly recalls playing Muchova - and being super impressed - after ending the Czech's bold run from qualifying in the third round of the 2018 US Open.

Barty saw a piece of herself in Muchova that night, the silky backhand slice and court craft pushing the then-world No.17 in a tight 6-3 6-4 loss at Flushing Meadows.

"I remember coming off the court and saying to 'Tyz' (coach Craig Tyzzer) 'Karolina, she can play, she's a hell of a player.' At that time she was I think outside, maybe even 200 in the world," Barty said.

"It was a great match, a brilliant match. We moved courts, we were playing at all hours of the night. One of those funny experiences where you look back on it now and just realise how special it was."

And how special Muchova was, as since proven by the now-world No.27's charge to the Wimbledon quarter-finals 10 months later.

"She's got the ability to manoeuvre the ball all around the court, play with variety, play with shape," Barty said.

"Now we get another opportunity to do it in a quarter-final of a grand slam."

Muchova also has fond memories of that midnight meeting with Barty in New York.

"It was a nice game. We play a bit similar, I would say. I remember that after match she actually told me to keep working, that I can make it to the top. So that was nice," the 24-year-old said.

Like Muchova, Barty is yet to drop a set at this year's Open.

That's some feat given she hadn't played in almost a year until this month.

Unbeaten in eight matches since her return, Barty is the first home hope in 37 years to make the quarter-finals three years running.

Considering former world No.1s Lleyton Hewitt and Pat Rafter and long-time Aussie flagbearer Samantha Stosur could only manage two quarter-final showings between them from 48 attempts only enhances Barty's efforts in carrying the expectations of a nation following her lengthy layoff.

"The break itself is not a problem for me. It's not a concern," the 24-year-old said.

"I know if I do all the right things in preparation before starting again, that's what I aim to get right.

"That's what I do with my team. We try and dot all of our Is and cross our Ts, do all the right things to get to a point where we know that we're comfortable going out on the court and try and execute."

If she executes on Wednesday, Barty will return on Thursday to face the winner of the all-American quarter-final between her Open doubles partner Jennifer Brady and unseeded Jessica Pegula.