Skip to 2:08:27 in this video https://youtu.be/nK4SNEbMn7s. What exactly is GMHikaru doing that?How can I be able to do that?Does it comes naturally with practice or their are exercises?
As was pointed out before me, that level of calculation is extremely impressive. You are at the end of the day looking at one of the top chess players in the world and, arguably, in history to this day.
Apart from that note, you should know that visualization is a matter of practice, and the acquisition of such skill is not different to that of arithmetic calculation. If you calculate a complicated sum today just in your head, a more complicated one tomorrow, a more complicated one the next day, etc., eventually you'll be able to quickly calculate sums and substractions. People may look at you add 1304592 + 2948535 in relatively small time and say "what a genius", but it's not being a genius it's just practicing a lot (the genius part just makes the learning curve faster).
So practice a lot. Get a book on positional chess and another one on tactics and go through the problems on your head. Try to visualize the resulting positions and not only visualize them but also judge them (best for white, equal, winning for black?). Do it A LOT. And do it when you play too. Don't just make moves (unless they are obvious or superficial ones), but say "I play x move, he plays z, then y, then v...", until you reach a conclusion (the position is best for me so I should go for this, the position is equal, etc.).
There will be MANY times when you miss a move on your calculations, maybe a crucial one that makes you lose. That's okay, it's normal. Just do it again on the next game and try to do better. But, bottom line, just do it a lot.
Once you acquire the habit of doing it, you'll do it without realizing it and you'll be practicing without realizing it during all your games.
Okay, this sequence is very impressive and Nakamura is a "beast". So I don't want to be too pessimistic but I'm afraid that this kind of performance, which consists in calculating at the speed of light a sequence of movements without error, is only possible for the highest rated players.
There is, however, a (little) hope. In the excellent perpetual chess podcast talk, GM Rustam Kasimdzhanov talks about Nakamura. He notices about his play and the play of some of the top teenagers in the chess world, including GMs Nodirbek Abdussatorov and Alireza Firouzja that they never blunder, even under stress, and their tactical perception of the position is extremely clear. The reason could be the thousands of games, especially blitz games, they have played. So go practice!
Not trying to belittle this achievement, but I think the hardest part is to speak as quickly as Hikaru does.
I do think that it is impressive but not to the extent that the other answers suggest. Reasons:
- black's position is clearly won by a variety of ways, in fact the cleanest and fastest way would be 1. Ne7 instead of Bf1
- the sequence that Hikaru calculates consists basically of only moves with check each move. It is a lot harder to calculate positions where there are many options including quiet moves.
- white's options are extremely limited because black is threatening mate in one
- it is a show without any consequences. I am sure that when playing a real match, Hikaru would slow down just to be sure not to make a mistake.
- judging from a single instance is meaningless, I am sure Hikaru is right most of the time but there might be the occasional blunders when calculating at that speed
To answer the OP's question. Yes, with practice (tactics puzzles, games) you will improve. Perhaps not to the level of Hikaru but half that speed is realistic IMO.