There's a three-way battle developing between AlphaZero (as described in the article, courtesy of DeepMind), LCZero[5] (derived from LeelaZero[1] -- an open source interpretation of the same principles as AZ), and Stockfish[2] (a long-standing open source chess engine that has recently begun including neural network support).
The 'Top Chess Engine Championship'[3] seems to be a good way to follow the latest news; they also stream matches live on their website[4] (it is quite an information-dense site).
You can play against an up-to-date implementation of Stockfish in your browser -- no registration or signup required -- at https://lichess.org
[1] - https://zero.sjeng.org/
[2] - https://stockfishchess.org/
[3] - https://en.wikipedia.org/wiki/Top_Chess_Engine_Championship
[4] - https://tcec-chess.com/
[5] - https://www.lczero.org/
Edit: correct LeelaZero -> LCZero