Yes, the quantization has a far better performance compared to simple and deprecated MKLDNN.
MKLDNN is not a quantization library. you cant use both mkldnn with quantized operators together, if I’m not mistaken.
either switch to quantization, or mkldnn. You may also have a look at TVM which supports Intel_graphics card and cpus as well. Unfortunetly, the Pytorch team, seems not to be active on  that project, while others such as TF, and specially MXNet, are investing in it heavily. (Pytorch had a pytorch-tvm, branch, which is not maintained and is not up to date unfortunetly) .
Your other option is to go OpenVino. While other frameworks are supported pretty well. Pytorch is missing and is only usable through the ONNX conversion (convert you pytorch to onnx models)
and the problem with that is that, not all operators are supported on ONNX (and OpenVino doesnt support all of it either) and the conversion is not ideal and error prune.
So your best bet is to wait for the Intel-Pytorch team to transition to DNNL which has support for Inetl-gpus (meaning you’ll get gpu acceleration). Currently one PR is awaiting to be merged and this would be the foundation, after that would hopefully come the support for OpenCL and thus supporting gpus other than nvidia or AMD rocm.