Absolute advantage refers to the ability of the producer of a good to be able to produce the good using lesser amount of resources than its competitor. The resources involved can include labor, fuel, raw material, financial resources, etc.
An innovative country is always striving to find means to be able to produce more using a lesser amount of resources per item. This would give it an absolute advantage compared to its competitors. The total resources spent on producing the same good would reduce with more innovative methods and most likely the cost of the goods will also fall. Some examples of this could be a nation that reduces the labor required for production by automating systems and the cost of the machinery that replaces human labor leads to a monetary saving; ways to produce the same using less fuel; a decrease in the raw material required by eliminating components in the product being made that are redundant, etc.
It is not possible to say that for a particular product, being innovative would provide comparative advantage because the process of innovation could be uniformly spread out over all products and there is a reduction in the cost of production of everything. The fact that a country is innovative does not change the opportunity cost of producing anything directly; though that could be case.