This is a bit tricky at the moment (also Can't load_from_checkpoint with QuantizationAwareTraining callback during training · Issue #6457 · PyTorchLightning/pytorch-lightning · GitHub 15) and the problem is that the the model isn’t quantized yet.
If you model permits it, the easiest can be to save the scripted model (torch.jit.save(module.to_torchscript(), 'my_model.pt')), but there, too, there is the slight caveat that you need to call the quantization / dequantization yourself ( model.to_torchscript "forgets" input quantization that is automatically called for the model · Issue #7552 · PyTorchLightning/pytorch-lightning · GitHub 7 ).
Edit: to call quantization/dequantization: model.dequant(model(model.quant(inp))). This might break when PL gets fixed, but should do the trick until then.
I hope this helps.
Best regards
Thomas