This is a tricky one, hopefully some others will give their input to but there are a fair number of variables.
If you go for a solar heating system then there are evacuated tubes which are really efficient, they use these for hot water in Antarctica https://www.bas.ac.uk/about/antarctica/environmental-protection/ene...
With evacuated tubes you can heat your pool and when not in use, say mid winter use the system for under floor heating. The only real downsides are in summer when the pool is up to temperature you have to find something to do with the available hot water so you obviously can heat your hot water tank but then what.
You need a fair amount of space for the tube arrays as well.
Forget rubber mats they just leak after a while.
There are various other polypropylene solar collectors which pump the pool water through them all quite simple but again you need quite an area to put them in (roughly 50% of the pools surface area) and they will cause some restriction in the water flow possibly increasing your electricity consumption as well. This depends on what height the panels are at. A friend of mine has his on the roof which is quite high so he increases the variable speed pump when the heating is required and that uses an additional 1275 watts per hour, another has them at ground level so no real issues there.
Then there is the air to water heat pump, these will work at the turn of the key whereas the above solar is only really effective when it warm outside and the sun is shining . Different for Evacuated tubes, they can work when it's cold but bright outside.
The heat pumps are like a fridge working in reverse, for a smaller amount of electricity say 2.5Kw you get a heat output of 10-12.5Kw as they use a fridge type setup to grab the warm air through a compressor into a heat exchanger to heat the water. Depending on the model some can work down to a temperature of -5 c although the performance will drop off drastically to maybe 5Kw as it gets colder. These pumps also have a smaller area required to site them but they are noisier than solar. It should be possible when not heating your pool to utilise the heat pump for underfloor heating as well but careful attention needs to be placed in the flow rate as pools generally use a high flow rate. The flow through the heat pump has only a minimal restriction on the pump so these can also be used on an ultra efficient Eco pool filtration/pump setup.
Not forgetting of course the need for a good cover to retain the heat you have in the pool. Insulating floor and walls of the pool structure is often overlooked and treated with a Gallic shrug but it works and can save 50% of the heating requirements of an insulated pool.