You will have to use a dual-link DVI-D cable or DisplayPort cable to support 1080p at 144Hz. Or you will have to use HDMI 1.3 or higher cable.
If you have HDMI2.0 support then it is the best. Here are the Specifications of HDMI 2.0
4K@50/60, (2160p), which is four times the clarity of 1080p/60 video resolution
Up to 32 audio channels for a multi-dimensional immersive audio experience
Up to 1536kHz audio sample frequency for the highest audio fidelity
Simultaneous delivery of dual video streams to multiple users on the same screen
Simultaneous delivery of multi-stream audio to multiple users (up to four)
Support for the wide-angle theatrical 21:9 video aspect ratio
Dynamic synchronization of video and audio streams
CEC extensions provide expanded command and control of consumer electronics devices through a single control point
As Fast As Possible. To output 1080p content at 144Hz, you will need either a Dual-Link DVI, a DisplayPort, or an HDMI 1.4 or higher (though some monitors with HDMI 1.4 are limited to 60Hz or 120Hz) cable.