To run H1Z1 on your PC you will not need a powerful computer. Today Sony has released the minimum and recommended official system requirements for H1Z1. If your computer does not have them, you can always buy it on PS4.
Minimum requirements:
OS: Windows 7 64-bit
Processor: Intel i3 Dual-Core with Hyper-Threading (required)
Memory: 4 GB RAM
Graphics: nVidia GeForce GTX 275 series or higher
DirectX: Version 10
Network: Broadband Internet connection
Hard Drive: 20 GB available space
Sound Card: DirectX Compatible Sound Card
Recommended requirements:
OS: Windows 7 64-bit
Processor: Intel i5 Quad Core or higher / AMD Phenom II X6 or higher
Memory: 8 GB RAM
Graphics: nVidia GeForce GTX 560 series or higher / AMD HD 6870 or higher
DirectX: Version 10
Network: Broadband Internet connection
Hard Drive: 20 GB available space
Sound Card: DirectX compatible Sound Card