Could quantum computing improve chess engines?

Could and how quantum computing improve chess engines? Will it be able to think much faster and better than a classical chess computer?
Will a quantum computing chess engine be drastically better than current chess engines?

I believe my question is different than Will quantum computers be able to solve the game of chess?
From what I managed to understand, that question is talking about if a quantum computer will be able to tell who has 100% to win a game from a given position, and what are the moves to do that(?).

I might be wrong, but I think that quantum computer can search much faster than classical computer, $O(sqrt{n})$, and quantum copmuter has advatanges against classical computer.

Also, from the little I know, some chess engines have kind of tree of many games and a big database they use while playing against other chess engines. When some chess engines use kind of networking which has many computers running games and “learning” to make their Elo better to play against other chess engines.

I’m more interested about if it could be possible to use a quantum computer’s speed and its advantages against classical computer, to make a stronger chess engine with higher Elo than current chess engines. Could a quantum computer think better than a classical computer to win it in chess?
I am not interested about the question with a given chess position, who can force a checkmate.

I tried to make as clarified as I could, since I don’t have knowledge with quantum computing and how to apply it in different ways.