According to the system requirements, it seems that the minimum requirements needed to run the beta of the game will involve Windows 7 64-bit or later, an Intel Core i5 2500k or AMD equivalent, 8GB of RAM, 256GB of HD space, and an NVIDIA GeForce GTX 660, GTX 1050, or an AMD Radeon HD 7850 with 2GB of VRAM or better.
Note that those are the minimum hardware specs you’ll need to run the game, but if you’re hoping to squeeze more out of the game, then the recommended specs are calling for a Windows 10 64-bit OS, an Intel Core i7 4770k or AMD equivalent CPU, 12GB of RAM, and a GeForce GTX 970, GTX 1060 6GB, AMD Radeon R9 390, or an AMD RX 580 GPU.
As it has been pointed out, these are just the specs to run the beta version of the game. Treyarch notes that this could change when the game is released, so don’t go building a rig around those specs just yet.