What is the current state of the art in hearts AI?
Update based on your comment: I gather that you are more interested in research than making a game. In that case I'll point you to a couple of papers that might be helpful. This paper talks about what makes Go a unique challenge, and the introduction has a quote (and some references) you might find useful:


  Minimax search variants are particu-
  larly effective in Chess, Checkers, Othello and Backgammon, whereas Monte-Carlo simulation has proven most successful in Scrabble and Hearts.


Regarding hearts, the reference is to this paper which is unfortunately not free but maybe you have access through an employer or university.

I hope that helps. I still recommend the programmers.SE question I linked below; there's some good discussion there about Monte-Carlo methods as they relate to card games.



State of the art? Maybe Deep Mind. It's a general purpose AI that seems to excel at a great many games. Not sure if it's been applied to hearts, but I don't see why it couldn't be.

Realistically? Maybe Monte Carlo. You can read some discussion of it here: https://softwareengineering.stackexchange.com/questions/213870/best-techniques-for-an-ai-of-a-card-game

If you want to make a Hearts game, as opposed to an AI research topic, remember this: Games are supposed to be fun. An AI that could beat practically any human player wouldn't be fun for practically any human players. Fun AI is what Søren Johnson focused on for Civilization IV, and he has some good thoughts on it in this video. Furthermore, it's usually easier to develop an AI that's kinda smart that one that's really really smart.