Kei Nishikori will next play against Novak Djokovic.
The 12-time grand slam champion, who has endured a hard 12 months due to an elbow injury, said he was nearing his best form once more.
"He's always like a big war for me".
"But I felt like in the last month and a half, the level of tennis has been very close to where I would like it to be, where I'm used to having it, so to say, and playing on". It's always a big challenge.
The Japanese player has already lost twice to the former world number one this year - on clay in Madrid and Rome. The world number 28 from Japan played a stunningly fast game, winning 6-1 7-6 6-4 to edge out Kyrgios, ranked 18th, as the light faded on Court One.
Alexander Zverev suffered a third-round exit at Wimbledon, losing to the Latvian Ernests Gulbis.
"My elbow was bothering me".
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Or being by turns self-reflective and sarcastic during the news conference afterward, including when a reporter noted that Kyrgios' tennis career has featured some complicated moments - a euphemism if ever there was one - and he shot a sideways glance toward his agent, smiled wryly and replied, "Have I?"
Seeded 12, Wednesday will Djokovic's 41st appearance in a Grand Slam quarterfinal. On those occasions it took Roger Federer and last year's Wimbledon finalist Marin Cilic to stop him.
"I'm happy to have gotten past that wall", said Nishikori. I just didn't want to pull out so I could even take the third set."The Latvian saved two set points with some strong returns but both players made unforced errors, Gulbis missing a volley and Nishikori serving two double faults before the Japanese finally clinched it 12-10 after nearly three and a half hours". I knew that he was much better than the first set. I was feeling physically really, really good.
Djokovic's run to the Queen's final on the eve of Wimbledon was his first appearance in a championship match since Eastbourne nearly 12 months earlier.
The Alicante-based 19-year-old played his part in an entertaining duel as he chased after everything Nadal could throw at him - and in turn kept the Spaniard on Centre Court longer than he would have liked.
"I just had to go back to basics and hit as many balls as I can on the practice courts, just get that feel". Also psychologically obviously, I was so fortunate to have so much success on the tour over the course of 10-plus years.
"I was a top 3 player for so many years in a row - it was quite a odd feeling for me not to be able to deliver my game".